Mathematical research summaries. Volume 1 9781536120455, 1536120456

Table of contents :
Contents
Preface
Part I
Researcher Biographical Sketches
Chapter 1
Dr. Imre Ferenc Barna
Chapter 2
Rosamonde R. Cook
Chapter 3
Rudolf Eggers
Chapter 4
Snezhana Georgieva Gocheva-Ilieva
Chapter 5
James M. Honeycutt
Chapter 6
Iliycho Petkov Iliev
Chapter 7
Atanas Valev Ivanov
Chapter 8
Noelia Jiménez-Fanjul
Chapter 9
Carmen León-Mantero
Chapter 10
María José Madrid
Chapter 11
Alexander Maz-Machado
Chapter 12
Florian Meyer
Chapter 13
Ali Asghar Rastegari
Chapter 14
Marko Stamenic
Chapter 15
Yuriy S. Volkov
Chapter 16
Desislava Stoyanova Voynikova
Chapter 17
Irena Zizovic
Part II
Research Summaries
Chapter 18
Justification of the Courant-Friedrichs Conjecture for the Problem About Flow Around Wedge#
Research Summary
Chapter 19
Particle Swarm Optimization with Re-Initialization Strategies for Continuous Global Optimization#
Research Summary
Chapter 20
Particle Swarm Global Optimization of Orbital Maneuvers#
Research Summary
Chapter 21
Float-Encoded Genetic Algorithm Used for the Inversion Processing of Well-Logging Data#
Research Summary
Chapter 22
The Particle Collision Algorithm: A Metropolis Optimization Method#
Research Summary
Chapter 23
Classifier-Assisted Frameworks for Computationally Expensive Optimization Problems#
Research Summary
Chapter 24
Cutting Box Strategy: An Algorithmic Framework for Improving Metaheuristics for Continuous Global Optimization#
Research Summary
Chapter 25
RLS Wiener Smoother from Randomly Delayed Observations in Linear Discrete-Time Systems#
Research Summary
Chapter 26
A Non-Standard Practical Variational Approach via Fractional Calculus to the Optimal Control of Fractional Stochastic Systems Driven by White Noises#
Research Summary
Chapter 27
Representation of the Shoe-Last Bottom Based on Computer Algorithms and Laser Metrology#
Research Summary
Chapter 28
Role of Metrology on Current Food Safety Issues in China#
Research Summary
Chapter 29
Symmetric Random Vectors for which the Joint Quantum Operators Span a Lie Algebra#
Research Summary
Chapter 30
Pseudo Regularity in Commutative Banach Algebras#
Research Summary
Chapter 31
Dynamics of Viscous Barotropic Fluid on a Rotating Sphere#
Research Summary
Chapter 32
An Efficient Numerical Method for the Solution of Nonlinear Diffusion Equations on a Sphere #
Research Summary
Chapter 33
A Mathematical Modeling Approach to the Slug Flow Problem in Oil Production#
Research Summary
Chapter 34
Native Statistics for Natural Sciences#
Research Summary
Chapter 35
Deterministic and Random Evolution#
Research Summary
Chapter 36
Foundations of Iso-Differential Calculus. Volume 1#
Research Summary
Chapter 37
Introduction to Geometry and Relativity#
Research Summary
Chapter 38
An Overview on Theories and Methods of Self-organization#
Research Summary
Chapter 39
An Ant Colony Optimization-Based Approach of Feature Selection for Efficient Classification of Very Small Datasets by Mining Patterns#
Research Summary
Chapter 40
Self-organization and Task Allocation: An Application to Ant Algorithms#
Research Summary
Chapter 41
The Generalized Particle Swarm Optimization Algorithm with Application Examples#
Research Summary
Chapter 42
Weights And Structure Determination of Artificial Neuronets#
Research Summary
Chapter 43
Low-Dimensional Structures Embedded in Human Locomotion: Data Analysis and Modeling#
Research Summary
Chapter 44
Self-organization in Motion of a Set of Living Individuals#
Research Summary
Chapter 45
A Cellular Automata Method for Species Migration Process in a Heterogeneous Environment#
Research Summary
Chapter 46
Robust Self-Adaptive Kalman Filter with the R and Q Adaptations against Sensor/Actuator Failures#
Research Summary
Chapter 47
Regular Approximation of the Stochastic Pushdown Calculus#
Research Summary
Chapter 48
Lyapunov Stability of Non-Autonomous Dynamical Systems#
Research Summary
Chapter 49
Applications of Graph Theory in Architectural Analysis: Past, Present and Future Research#
Research Summary
Chapter 50
Miesian Intersections: Comparing and Evaluating Graph Theory Approaches to Architectural Spatial Analysis#
Research Summary
Chapter 51
The Algebraic Structure of Graphs#
Research Summary
Chapter 52
The Combination of Graph Theory and Unsupervised Learning Applied to Social Data Mining#
Research Summary
Chapter 53
About Organizing and Structuring the Contents of Mathematical Subjects Using Graph Theory#
Research Summary
Chapter 54
A Modularity Based Filtering Approach for Network Immunization#
Research Summary
Chapter 55
Particle of Life: Mathematical Abstraction or Reality?#
Research Summary
Chapter 56
Local Fractional Derivatives#
Research Summary
Chapter 57
Fractional Variational Embedding and Lagrangian Formulations of Dissipative Partial Differential Equations#
Research Summary
Chapter 58
A Class of Fractional Optimal Control Problems and Fractional Pontryagin's Systems. Variational Integrator and Existence of Continuous/Discrete Noether's Theorems#
Research Summary
Chapter 59
Fractal Traps and Fractional Dynamics#
Research Summary
Chapter 60
Numerical Approximations to Fractional Problems of the Calculus of Variations and Optimal Control#
Research Summary
Chapter 61
Selected Topics of Invariant Measures in Polish Groups#
Research Summary
Chapter 62
Foundations of Iso-Differential Calculus. Volume 2#
Research Summary
Chapter 63
Hypergraphs and Designs#
Research Summary
Chapter 64
Analysis of the Caputo Derivative and Pseudo State Representation with the Infinite State Approach#
Research Summary
Chapter 65
Stability of a Class of Fractional Cauchy Problem#
Research Summary
Chapter 66
Numerical Solution of Fractional Order Differential Equations Via Matrix-Based Methods#
Research Summary
Chapter 67
On Analytical Methods for Differential Equations with Local Fractional Derivative Operators#
Research Summary
Chapter 68
Extended Borel Transform and Fractional Calculus#
Research Summary
Chapter 69
Introduction to Stability Theory of Linear Fractional Difference Equations#
Research Summary
Chapter 70
Using The Hankel Operator to Initialize Fractional-Order Systems#
Research Summary
Chapter 71
Fractional Reaction-Transport Equations Arising From Evanescent Continuous Time Random Walks#
Research Summary
Chapter 72
Exponential Integrators For Fractional Differential Equations#
Research Summary
Chapter 73
Non-Fragile Tuning of Fractional-Order PD Controllers for Integrating and Double Integrating Time-Delay Systems#
Research Summary
Chapter 74
On Discrete, Finite-Dimensional Approximation of Linear, Infinite Dimensional Systems#
Research Summary
Chapter 75
Advanced Fractional Differential and Integral Equations#
Research Summary
Chapter 76
The Heuristic Power of the Non Integer Differential Operator in Physics: From Chaos to Emergence, Auto-Organisations and Holistic Rules#
Research Summary
Chapter 77
Dynamics of Fractional Order Chaotic System#
Research Summary
Chapter 78
Pressure Control of CNG Engines by Non-Integer Order Controllers: A New Trend in Application of Fractional Calculus to Automotive Systems#
Research Summary
Chapter 79
Linear Integer Order System Control by Fractional PI-State Feedback#
Research Summary
Chapter 80
From the Formal Concept Analysis to the Numerical Simulation of the Thermal Diffusion Phenomena in a Finite Medium#
Research Summary
Chapter 81
Temperature Control of a Diffusive Medium Using the CRONE Approach#
Research Summary
Chapter 82
Adaptive Second-Order Fractional Sliding Mode Control with Application to Water Tanks Level Control#
Research Summary
Chapter 83
Features of Fractional Operators Involving Fractional Derivatives and Their Applications to the Problems of Mechanics of Solids#
Research Summary
Chapter 84
Theory of Diffusive Stresses Based on the Fractional Advection-Diffusion Equation#
Research Summary
Chapter 85
Modelling Drug Effect Using Fractional Calculus#
Research Summary
Chapter 86
Fuzzy Fractional PID Controllers: Analysis, Synthesis and Implementation#
Research Summary
Chapter 87
Foundations of Iso-Differential Calculus. Volume 3: Ordinary Iso-Differential Equations#
Research Summary
Chapter 88
The Atomic Structure and Law#
Research Summary
Chapter 89
Computing Algorithms For Solutions of Problems in Applied Mathematics and their Standard Program Realization. Part 1: Deterministic Mathematics and Part 2: Stochastic Mathematics#
Research Summary
Chapter 90
Foundations of Iso-Differential Calculus. Volume 4: Iso-Dynamic Equations#
Research Summary
Chapter 91
A Proposed Cloud Computing Business Framework#
Research Summary
Chapter 92
The Complexities of Math Skills Development#
Research Summary
Chapter 93
Construction of an NP Problem with an Exponential Lower Bound#
Research Summary
Chapter 94
Misconceptions and Misunderstandings (M&M) of Exploratory Factor Analysis: Some Clarifications#
Research Summary
Chapter 95
Exploratory Structural Equation Modeling: A New Trend of Factor Analysis#
Research Summary
Chapter 96
Quantum Information Measures and Molecular Phase Equilibria#
Research Summary
Chapter 97
A Mathematical Model and Optimization of Rectangular Mufflers Hybridized with One-channel Splitters by SA Method#
Research Summary
Chapter 98
Worst-case Analysis versus Average-case Analysis for Combinatorial Optimization Problems#
Research Summary
Chapter 99
Mathematical and Statistical Applied Methods: Studying the Relationship between Climatic Variables and Cotton Production#
Research Summary
Chapter 100
Quantum Cryptography within Several Sequential Attacks in BB84 Protocol#
Research Summary
Chapter 101
Foundations of Iso-Differential Calculus. Volume 5: Iso-Stochastic Differential Equations#
Research Summary
Chapter 102
Computational Recipes of Linear and Non-Linear Singular Integral Equations and Relativistic Mechanics in Engineering and Applied Science. Volume I#
Research Summary
Chapter 103
Computational Recipes of Linear and Non-Linear Singular Integral Equations and Relativistic Mechanics in Engineering and Applied Science. Volume II#
Research Summary
Chapter 104
The Lax-Milgram Theorem and Some Applications to Partial Differential Equations#
Research Summary
Chapter 105
Coupled PDEs and Control Systems Arising in Climate Dynamics: Ocean-Atmosphere Interactions and Tropical Instability Waves#
Research Summary
Chapter 106
Integration of PDE with the Help of Analysis over Octonions and Cayley-Dickson Algebras#
Research Summary
Chapter 107
Mixed Boundary-Value Problem for Divergent Hyperbolic PDE: Existence and Properties of Solutions, Applications in Sequential Optimal Control with Pointwise in Time State Constraints*,#
Research Summary
Chapter 108
Using Mathematical Tessellation to Model Spherical Particle Packing Structures#
Research Summary
Chapter 109
Further Results on Fractional Calculus for Non-differentiable Functions Applications to Z-Transform and Generalized Functions#
Research Summary
Chapter 110
Low Earth Orbit Satellite Constellations for Local Telecommunication and Monitoring Services#
Research Summary
Chapter 111
Algorithm for Autonomously Calibrating Reference Flat of Interferometer and Residual Influence of Linear Shift with Two-Flat Method#
Research Summary
Chapter 112
Dealing with Non-Significant Interactions Statuses between Treatments by a Suggested Statistical Approach#
Research Summary
Chapter 113
Stochastic Simultaneous Perturbation As Powerful Method For State And Parameter Estimation In High Dimensional Systems#
Research Summary
Chapter 114
Bounded Trajectories of Unstable Piecewise Linear Systems And Its Applications#
Research Summary
Chapter 115
Mathematical Modeling For Predicting Battery Lifetime Through Electrical Models#
Research Summary
Chapter 116
Mathematical Modeling of the Lithium-Ion Battery Lifetime Using System Identification Theory#
Research Summary
Chapter 117
Nonlinear Evolution Equations and Soliton Solutions#
Research Summary
Chapter 118
The Determinants of Capital Structure Choice for Chinese Listed Companies Based on Structural Equation Modeling Approach#
Research Summary
Chapter 119
An Examination of Predictors and Outcomes Related to School Climate Using Latent Class Analysis#
Research Summary
Chapter 120
Assessing Mediation in Simple and Complex Models#
Research Summary
Chapter 121
Symmetric Boolean Functions#
Research Summary
Chapter 122
Boolean Functions: All-Optical Implementation Using Quantum-Dot Semiconductor Optical Amplifiers in Mach-Zehnder Interferometer#
Research Summary
Chapter 123
Selective Harvesting and Time Delay in a Predator-Prey Model with Infectious Preys#
Research Summary
Chapter 124
Analysis of an Age-Structured SEIL Model with Demographics Process and Lost of Sight Individuals#
Research Summary
Chapter 125
Realizations of sl(3, ) In Terms Of Chebyshev Polynomials and Orthogonal Systems of Functions. Symmetry Breaking and Variational Symmetries#
Research Summary
Chapter 126
Solitary Waves in the Nonlinear Dirac Equation at the Continuum Limit: Stability and Dynamics#
Research Summary
Chapter 127
Modeling of Corruption in Hierarchical Organizations#
Research Summary
Chapter 128
Binary Periodic Signals and Flows#
Research Summary
Chapter 129
Pseudo-Matroids and Cuts of Matroids#
Research Summary
Chapter 130
Foundations of Iso-Differential Calculus. Volume 6: Theory of Iso-Functions of a Real Iso-Variable#
Research Summary
Chapter 131
Calculating Characterization of Monopsonic Degree in the Recycled Solid Waste Market in Metropolitan Regions of Brazil#
Research Summary
Chapter 132
Estimation of Derivatives, from Economy to Environment: A Study of the Management of Eutrophication of a Fresh Water Basin’s Data#
Research Summary
Chapter 133
Modeling Environmental Phenomena and Medical Classification of Patients: Case Studies#
Research Summary
Chapter 134
Analysis of Effect of Environmental Discharge and Awareness Programs on Japanese Encephalitis Spread Using Mathematical Modeling and Simulation#
Research Summary
Chapter 135
Estimation and Comparison of the Likelihood Ratios of Binary Diagnostic Tests#
Research Summary
Chapter 136
Health Planning Information Acquired from Unstructured Data about Diabetes Mellitus#
Research Summary
Chapter 137
Applying Fuzzy Model to Map Vulnerability Areas of Trypanosoma Cruzi Transmission#
Research Summary
Chapter 138
Usage of Automatic Theorem Proving in the Recognition of Brain Emotions Activations#
Research Summary
Chapter 139
Radiology Information System with Knowledge Reasoning#
Research Summary
Chapter 140
Design of Routes for Waste Collection: Centro Habana’s Case Study#
Research Summary
Chapter 141
Comparison Methods of Digital Elevation Model Correction, in the Subwatershed V Aniversario, Cuyaguateje Basin Cuba#
Research Summary
Chapter 142
An Integer Optimization Model for Waste Collection Frequency Problem#
Research Summary
Chapter 143
Evolving an Intelligent Framework for Decision-Making Process in E-Health Systems#
Research Summary
Chapter 144
Heart Diseases Prediction Using Data from Health Assurance Systems#
Research Summary
Chapter 145
Iterative Algorithms I#
Research Summary
Chapter 146
Iterative Algorithms II#
Research Summary
Chapter 147
Chaos Theory and Financial Statements#
Research Summary
Chapter 148
Applying Chaos Theory to Work: The Chaos Theory of Careers#
Research Summary
Chapter 149
Application of Chaos Theory to Ventricular Wall Biomechanics#
Research Summary
Chapter 150
Complexity and Synchronization in the Process of Biochemical Substance Exchange in a Diffusively Coupled Ring of Cells#
Research Summary
Chapter 151
Unveiling the Escape Mechanism of Orbits in Hamiltonian Systems with Multiple EXIT Channels#
Research Summary
Chapter 152
Mathematical Modeling of Intracellular Processes#
Research Summary
Chapter 153
Improving the Efficiency of Bezier Basis Function in Object Surface Modeling#
Research Summary
Chapter 154
Performance Evaluation of Two-Dimensional Linear Discriminant Analysis for Images#
Research Summary
Chapter 155
From Pseudoholomorphic Functions to the Associated Real Manifold#
Research Summary
Chapter 156
Numerical and Analytical Methods for Bond Pricing in Short Rate Convergence Models of Interest Rates*,#
Research Summary
Chapter 157
Structural Transformations in the Relationships between Mathematics and Music up to the Renaissance and the Emergence of the Idea of Number as a Continuous Quantity#
Research Summary
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MATHEMATICAL RESEARCH SUMMARIES

MATHEMATICAL RESEARCH SUMMARIES (WITH BIOGRAPHICAL SKETCHES) VOLUME 1

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MATHEMATICAL RESEARCH SUMMARIES Additional books in this series can be found on Nova’s website under the Series tab.

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MATHEMATICAL RESEARCH SUMMARIES

MATHEMATICAL RESEARCH SUMMARIES (WITH BIOGRAPHICAL SKETCHES) VOLUME 1

MATTHEW A. ROWE EDITOR

Copyright © 2017 by Nova Science Publishers, Inc. All rights reserved. No part of this book may be reproduced, stored in a retrieval system or transmitted in any form or by any means: electronic, electrostatic, magnetic, tape, mechanical photocopying, recording or otherwise without the written permission of the Publisher. We have partnered with Copyright Clearance Center to make it easy for you to obtain permissions to reuse content from this publication. Simply navigate to this publication’s page on Nova’s website and locate the “Get Permission” button below the title description. This button is linked directly to the title’s permission page on copyright.com. Alternatively, you can visit copyright.com and search by title, ISBN, or ISSN. For further questions about using the service on copyright.com, please contact: Copyright Clearance Center Phone: +1-(978) 750-8400 Fax: +1-(978) 750-4470 E-mail: [email protected]. NOTICE TO THE READER The Publisher has taken reasonable care in the preparation of this book, but makes no expressed or implied warranty of any kind and assumes no responsibility for any errors or omissions. No liability is assumed for incidental or consequential damages in connection with or arising out of information contained in this book. The Publisher shall not be liable for any special, consequential, or exemplary damages resulting, in whole or in part, from the readers’ use of, or reliance upon, this material. Any parts of this book based on government reports are so indicated and copyright is claimed for those parts to the extent applicable to compilations of such works. Independent verification should be sought for any data, advice or recommendations contained in this book. In addition, no responsibility is assumed by the publisher for any injury and/or damage to persons or property arising from any methods, products, instructions, ideas or otherwise contained in this publication. This publication is designed to provide accurate and authoritative information with regard to the subject matter covered herein. It is sold with the clear understanding that the Publisher is not engaged in rendering legal or any other professional services. If legal or any other expert assistance is required, the services of a competent person should be sought. FROM A DECLARATION OF PARTICIPANTS JOINTLY ADOPTED BY A COMMITTEE OF THE AMERICAN BAR ASSOCIATION AND A COMMITTEE OF PUBLISHERS. Additional color graphics may be available in the e-book version of this book.

Library of Congress Cataloging-in-Publication Data ISBN: H%RRN

Published by Nova Science Publishers, Inc. † New York

CONTENTS Preface

xvii

Part I

Researcher Biographical Sketches

1

Chapter 1

Imre Ferenc Barna

3

Chapter 2

Rosamonde R. Cook

5

Chapter 3

Rudolf Eggers

9

Chapter 4

Snezhana Georgieva Gocheva-Ilieva

11

Chapter 5

James M. Honeycutt

15

Chapter 6

Iliycho Petkov Iliev

17

Chapter 7

Atanas Valev Ivanov

21

Chapter 8

Noelia Jiménez-Fanjul

23

Chapter 9

Carmen León-Mantero

25

Chapter 10

María José Madrid

27

Chapter 11

Alexander Maz-Machado

29

Chapter 12

Florian Meyer

31

Chapter 13

Ali Asghar Rastegari

33

Chapter 14

Marko Stamenic

35

Chapter 15

Yuriy S. Volkov

37

Chapter 16

Desislava Stoyanova Voynikova

39

Chapter 17

Irena Zizovic

41

vi

Contents

Part II

Research Summaries

Chapter 18

Justification of the Courant-Friedrichs Conjecture for the Problem About Flow Around Wedge Alexander M. Blokhin and Dimitry L. Tkachev and Evgenia V. Mishchenko

Chapter 19

Particle Swarm Optimization with Re-Initialization Strategies for Continuous Global Optimization D. D. Kennedy, H. Zhang, G. P. Rangaiah and A. Bonilla-Petriciolet

Chapter 20

Particle Swarm Global Optimization of Orbital Maneuvers Mauro Pontani

Chapter 21

Float-Encoded Genetic Algorithm Used for the Inversion Processing of Well-Logging Data Norbert P. Szabó and Mihály Dobróka

Chapter 22

Chapter 23

Chapter 24

Chapter 25

Chapter 26

Chapter 27

The Particle Collision Algorithm: A Metropolis Optimization Method Wagner F. Sacco, Anderson Alvarenga de Moura Meneses, Ana Carolina Rios-Coelho and Nélio Henderson

45

47 49

51

53

Classifier-Assisted Frameworks for Computationally Expensive Optimization Problems Yoel Tenne

55

Cutting Box Strategy: An Algorithmic Framework for Improving Metaheuristics for Continuous Global Optimization Wendel Melo, Marcia Fampa and Fernanda Raupp

57

RLS Wiener Smoother from Randomly Delayed Observations in Linear Discrete-Time Systems Seiichi Nakamori

59

A Non-Standard Practical Variational Approach via Fractional Calculus to the Optimal Control of Fractional Stochastic Systems Driven by White Noises Guy Jumarie Representation of the Shoe-Last Bottom Based on Computer Algorithms and Laser Metrology J. Apolinar Muñoz-Rodríguez

Chapter 28

Role of Metrology on Current Food Safety Issues in China Can Quan, Ting Huang and Hongmei Li

Chapter 29

Symmetric Random Vectors for which the Joint Quantum Operators Span a Lie Algebra Aurel I. Stan

Chapter 30

43

Pseudo Regularity in Commutative Banach Algebras J. C. Prajapati

61

63 65

67 69

Contents

vii

Chapter 31

Dynamics of Viscous Barotropic Fluid on a Rotating Sphere Yuri N. Skiba

71

Chapter 32

An Efficient Numerical Method for the Solution of Nonlinear Diffusion Equations on a Sphere Yuri N. Skiba and Denis M. Filatov

Chapter 33

A Mathematical Modeling Approach to the Slug Flow Problem in Oil Production Airam Sausen, Paulo Sérgio Sausen, Maurício de Campos and Leandro Kreuzberger

73

75

Chapter 34

Native Statistics for Natural Sciences Nabil Semmar

77

Chapter 35

Deterministic and Random Evolution Jens Lorenz

79

Chapter 36

Foundations of Iso-Differential Calculus. Volume 1 Svetlin Georgiev

81

Chapter 37

Introduction to Geometry and Relativity David C. Mello

83

Chapter 38

An Overview on Theories and Methods of Self-organization WenJun Zhang

85

Chapter 39

An Ant Colony Optimization-Based Approach of Feature Selection for Efficient Classification of Very Small Datasets by Mining Patterns N. K. Sreeja and A. Sankar

Chapter 40

Chapter 41

Self-organization and Task Allocation: An Application to Ant Algorithms Jose B. Escario, Juan F. Jimenez, and Jose M. Giron-Sierra The Generalized Particle Swarm Optimization Algorithm with Application Examples Željko S. Kanović, Milan R. Rapaić, Zoran D. Jeličić, Milan J. Rackov, Mirna N. Kapetina and Jelena T. Atanacković-Jeličić

Chapter 42

Weights And Structure Determination of Artificial Neuronets Yunong Zhang, Xiaotian Yu, Lin Xiao, Weibing Li and Zhengping Fan

Chapter 43

Low-Dimensional Structures Embedded in Human Locomotion: Data Analysis and Modeling Shinya Aoi

Chapter 44

Self-organization in Motion of a Set of Living Individuals Milovan Živanović and Ivan Stojković

87

89

91

93

95 97

viii Chapter 45

Chapter 46

Contents A Cellular Automata Method for Species Migration Process in a Heterogeneous Environment WenJun Zhang, YanHong Qi and ZhiGuo Zhang Robust Self-Adaptive Kalman Filter with the R and Q Adaptations against Sensor/Actuator Failures Chingiz Hajiyev and Halil Ersin Soken

99

101

Chapter 47

Regular Approximation of the Stochastic Pushdown Calculus Marco Carpentieri

103

Chapter 48

Lyapunov Stability of Non-Autonomous Dynamical Systems David N. Cheban

105

Chapter 49

Applications of Graph Theory in Architectural Analysis: Past, Present and Future Research Michael J. Dawes and Michael J. Ostwald

107

Miesian Intersections: Comparing and Evaluating Graph Theory Approaches to Architectural Spatial Analysis Michael J. Ostwald and Michael J. Dawes

109

Chapter 50

Chapter 51

The Algebraic Structure of Graphs Antonios Kalampakas and Vassilios Tsiantos

Chapter 52

The Combination of Graph Theory and Unsupervised Learning Applied to Social Data Mining Héctor D. Menéndez and José Luis Llorente

Chapter 53

About Organizing and Structuring the Contents of Mathematical Subjects Using Graph Theory Angélica Martínez-Zarzuelo, Eugenio Roanes-Lozano and María José Fernández-Díaz

111

113

115

Chapter 54

A Modularity Based Filtering Approach for Network Immunization Tetsuya Yoshida and Yuu Yamada

117

Chapter 55

Particle of Life: Mathematical Abstraction or Reality? Michail Zak

119

Chapter 56

Local Fractional Derivatives N. C. Dias and J. N. Prata

121

Chapter 57

Fractional Variational Embedding and Lagrangian Formulations of Dissipative Partial Differential Equations Jacky Cresson

Chapter 58

A Class of Fractional Optimal Control Problems and Fractional Pontryagin's Systems. Variational Integrator and Existence of Continuous/Discrete Noether's Theorems Loïc Bourdin

125

127

Contents Chapter 59

Fractal Traps and Fractional Dynamics Pierre Inizan

Chapter 60

Numerical Approximations to Fractional Problems of the Calculus of Variations and Optimal Control Shakoor Pooseh, Ricardo Almeida and Delfim F. M. Torres

ix 129

131

Chapter 61

Selected Topics of Invariant Measures in Polish Groups Gogi Pantsulaia

133

Chapter 62

Foundations of Iso-Differential Calculus. Volume 2 Svetlin Georgiev

135

Chapter 63

Hypergraphs and Designs Mario Gionfriddo, Lorenzo Milazzo and Vitaly Voloshin

137

Chapter 64

Analysis of the Caputo Derivative and Pseudo State Representation with the Infinite State Approach Jean-Claude Trigeassou, Nezha Maamri and Alain Oustaloup

139

Chapter 65

Stability of a Class of Fractional Cauchy Problem Rabha W. Ibrahim

Chapter 66

Numerical Solution of Fractional Order Differential Equations Via Matrix-Based Methods Matthew Harker and Paul O’Leary

143

On Analytical Methods for Differential Equations with Local Fractional Derivative Operators Xiao-Jun Yang, Dumitru Baleanu and J. A. Tenreiro Machado

145

Chapter 67

Chapter 68

Extended Borel Transform and Fractional Calculus Akira Asada

Chapter 69

Introduction to Stability Theory of Linear Fractional Difference Equations Jan Čermák and Tomáš Kisela

Chapter 70

Using The Hankel Operator to Initialize Fractional-Order Systems Jay L. Adams, Robert J. Veillette and Tom T. Hartley

Chapter 71

Fractional Reaction-Transport Equations Arising From Evanescent Continuous Time Random Walks E. Abad, S. B. Yuste, and K. Lindenberg

Chapter 72

Exponential Integrators For Fractional Differential Equations Roberto Garrappa and Marina Popolizio

Chapter 73

Non-Fragile Tuning of Fractional-Order PD Controllers for Integrating and Double Integrating Time-Delay Systems MirSaleh Bahavarnia and Mohammad Saleh Tavazoei

141

147

149 151

153 155

157

x Chapter 74

Contents On Discrete, Finite-Dimensional Approximation of Linear, Infinite Dimensional Systems Milan R. Rapaić, Tomislav B. Šekara and Mihailo P. Lazarević

Chapter 75

Advanced Fractional Differential and Integral Equations Said Abbas, Mouffak Benchohra and Gaston Mandata N'Guerekata

Chapter 76

The Heuristic Power of the Non Integer Differential Operator in Physics: From Chaos to Emergence, Auto-Organisations and Holistic Rules Alain Le Méhauté

Chapter 77

Dynamics of Fractional Order Chaotic System Sachin Bhalekar

Chapter 78

Pressure Control of CNG Engines by Non-Integer Order Controllers: A New Trend in Application of Fractional Calculus to Automotive Systems Paolo Lino and Guido Maione

Chapter 79

Chapter 80

Chapter 81

Chapter 82

Chapter 83

Chapter 84

Chapter 85

Linear Integer Order System Control by Fractional PI-State Feedback Rachid Mansouri, Maamar Bettayeb, Chahira Boussalem and Ubaid M. Al-Saggaf From the Formal Concept Analysis to the Numerical Simulation of the Thermal Diffusion Phenomena in a Finite Medium Riad Assaf, Roy Abi Zeid Daou, Xavier Moreau and Fady Christophy Temperature Control of a Diffusive Medium Using the CRONE Approach Fady Christophy, Xavier Moreau, Roy Abi Zeid Daou and Riad Assaf

159 161

163 165

167

169

171

173

Adaptive Second-Order Fractional Sliding Mode Control with Application to Water Tanks Level Control Danial Senejohnny, Mohammadreza Faieghi and Hadi Delavari

175

Features of Fractional Operators Involving Fractional Derivatives and Their Applications to the Problems of Mechanics of Solids Yury A. Rossikhin and Marina V. Shitikova

177

Theory of Diffusive Stresses Based on the Fractional AdvectionDiffusion Equation Yuriy Povstenko

179

Modelling Drug Effect Using Fractional Calculus Clara M. Ionescu

181

Contents Chapter 86

Chapter 87

Fuzzy Fractional PID Controllers: Analysis, Synthesis and Implementation Ramiro S. Barbosa and Isabel S. Jesus

183

Foundations of Iso-Differential Calculus. Volume 3: Ordinary Iso-Differential Equations Svetlin Georgiev

185

Chapter 88

The Atomic Structure and Law Kunming Xu

Chapter 89

Computing Algorithms For Solutions of Problems in Applied Mathematics and their Standard Program Realization. Part 1: Deterministic Mathematics and Part 2: Stochastic Mathematics K. J. Kachiashvili, D. YU. Melikdzhanian and A. I. Prangishvili

Chapter 90

xi

Foundations of Iso-Differential Calculus. Volume 4: Iso-Dynamic Equations Svetlin Georgiev

187

189

191

Chapter 91

A Proposed Cloud Computing Business Framework Victor Chang

193

Chapter 92

The Complexities of Math Skills Development Robert Perna and Ashlee R. Loughan

195

Chapter 93

Construction of an NP Problem with an Exponential Lower Bound Roman V. Yampolskiy

197

Chapter 94

Misconceptions and Misunderstandings (M&M) of Exploratory Factor Analysis: Some Clarifications Eddie T. C. Lam and Anita N. Lee

199

Exploratory Structural Equation Modeling: A New Trend of Factor Analysis Anita N. Lee and Eddie T. C. Lam

201

Chapter 95

Chapter 96

Quantum Information Measures and Molecular Phase Equilibria Roman F. Nalewajski

Chapter 97

A Mathematical Model and Optimization of Rectangular Mufflers Hybridized with One-channel Splitters by SA Method Min-Chie Chiu

205

Worst-case Analysis versus Average-case Analysis for Combinatorial Optimization Problems Nodari Vakhania

207

Mathematical and Statistical Applied Methods: Studying the Relationship between Climatic Variables and Cotton Production Zakaria M. Sawan

209

Chapter 98

Chapter 99

203

xii Chapter 100

Chapter 101

Chapter 102

Chapter 103

Chapter 104

Chapter 105

Chapter 106

Chapter 107

Chapter 108

Chapter 109

Chapter 110

Chapter 111

Contents Quantum Cryptography within Several Sequential Attacks in BB84 Protocol Mustapha Dehmani, Hamid Ez-Zahraouy and Abdelilah Benyoussef

211

Foundations of Iso-Differential Calculus. Volume 5: Iso-Stochastic Differential Equations Svetlin Georgiev

213

Computational Recipes of Linear and Non-Linear Singular Integral Equations and Relativistic Mechanics in Engineering and Applied Science. Volume I Evangelos G. Ladopoulos Computational Recipes of Linear and Non-Linear Singular Integral Equations and Relativistic Mechanics in Engineering and Applied Science. Volume II Evangelos G. Ladopoulos

215

217

The Lax-Milgram Theorem and Some Applications to Partial Differential Equations Paul Bracken

219

Coupled PDEs and Control Systems Arising in Climate Dynamics: Ocean-Atmosphere Interactions and Tropical Instability Waves Aziz Belmiloudi

221

Integration of PDE with the Help of Analysis over Octonions and Cayley-Dickson Algebras Sergey V. Ludkovsky

223

Mixed Boundary-Value Problem for Divergent Hyperbolic PDE: Existence and Properties of Solutions, Applications in Sequential Optimal Control with Pointwise in Time State Constraints V. S. Gavrilov and M. I. Sumin

225

Using Mathematical Tessellation to Model Spherical Particle Packing Structures Larysa Burtseva and Frank Werner

227

Further Results on Fractional Calculus for Non-differentiable Functions Applications to Z-Transform and Generalized Functions Jumarie Guy

229

Low Earth Orbit Satellite Constellations for Local Telecommunication and Monitoring Services Mauro Pontani

231

Algorithm for Autonomously Calibrating Reference Flat of Interferometer and Residual Influence of Linear Shift with Two-Flat Method Ikumatsu Fujimoto

233

Chapter 112

Chapter 113

Chapter 114

Chapter 115

Chapter 116

Contents

xiii

Dealing with Non-Significant Interactions Statuses between Treatments by a Suggested Statistical Approach Zakaria M. Sawan

235

Stochastic Simultaneous Perturbation As Powerful Method For State And Parameter Estimation In High Dimensional Systems Hong Son Hoang and Remy Baraille

237

Bounded Trajectories of Unstable Piecewise Linear Systems And Its Applications L. J. Ontañón–García and E. Campos–Cantón

239

Mathematical Modeling For Predicting Battery Lifetime Through Electrical Models Cleber M. D. Porciuncula, Airam Sausen and Paulo Sérgio Sausen

241

Mathematical Modeling of the Lithium-Ion Battery Lifetime Using System Identification Theory Leugim Corteze Romio, Airam Sausen, Paulo Sérgio Sausen and Manuel Reimbold

Chapter 117

Nonlinear Evolution Equations and Soliton Solutions Yucui Guo and Anjan Biswas

Chapter 118

The Determinants of Capital Structure Choice for Chinese Listed Companies Based on Structural Equation Modeling Approach Xin-Dan Li, Xiang-Nan Feng, Bin Lu and Xin-Yuan Song

Chapter 119

An Examination of Predictors and Outcomes Related to School Climate Using Latent Class Analysis Christine DiStefano, Elizabeth Leighton, Mihaela Ene and Diane M. Monrad

243

245

251

253

Chapter 120

Assessing Mediation in Simple and Complex Models Thomas Ledermann and Siegfried Macho

255

Chapter 121

Symmetric Boolean Functions Peter M. Maurer

257

Chapter 122

Boolean Functions: All-Optical Implementation Using Quantum-Dot Semiconductor Optical Amplifiers in Mach-Zehnder Interferometer K. E. Zoiros, E. Dimitriadou and T. Houbavlis

Chapter 123

Chapter 124

259

Selective Harvesting and Time Delay in a Predator-Prey Model with Infectious Preys A. Tchuinté Tamen, A. Laohombe, J. J. Tewa and S. Bowong

261

Analysis of an Age-Structured SEIL Model with Demographics Process and Lost of Sight Individuals Demasse Djidjou, A. Mendy, Lam Mountaga and J. J. Tewa

263

xiv Chapter 125

Chapter 126

Contents Realizations of sl(3, ) In Terms Of Chebyshev Polynomials and Orthogonal Systems of Functions. Symmetry Breaking and Variational Symmetries R. Campoamor-Stursberg and E. Fernández Saiz Solitary Waves in the Nonlinear Dirac Equation at the Continuum Limit: Stability and Dynamics Jesús Cuevas-Maraver, Panayotis G. Kevrekidis, Avadh Saxena, Fred Cooper and Franz Mertens

265

267

Chapter 127

Modeling of Corruption in Hierarchical Organizations Olga I. Gorbaneva, Guennady A. Ougolnitsky and Anatoly B. Usov

269

Chapter 128

Binary Periodic Signals and Flows Serban E. Vlad

271

Chapter 129

Pseudo-Matroids and Cuts of Matroids Sergey A. Gizunov and V. N. Lyamin

273

Chapter 130

Foundations of Iso-Differential Calculus. Volume 6: Theory of Iso-Functions of a Real Iso-Variable Svetlin Georgiev

275

Calculating Characterization of Monopsonic Degree in the Recycled Solid Waste Market in Metropolitan Regions of Brazil Rilton Gonçalo Bonfim Primo and José Félix García Rodríguez

277

Chapter 131

Chapter 132

Chapter 133

Chapter 134

Chapter 135

Chapter 136

Estimation of Derivatives, from Economy to Environment: A Study of the Management of Eutrophication of a Fresh Water Basin’s Data Sira M. Allende-Alonso, Dan C. Chen, Carlos N. Bouza, José M. Sautto-Vallejo and Agustín Santiago-Moreno Modeling Environmental Phenomena and Medical Classification of Patients: Case Studies Carlos N. Bouza Analysis of Effect of Environmental Discharge and Awareness Programs on Japanese Encephalitis Spread Using Mathematical Modeling and Simulation Nita H. Shah, Urmila Chaudhari, Jyoti Gupta and Bijal Yeolekar

279

281

283

Estimation and Comparison of the Likelihood Ratios of Binary Diagnostic Tests José Antonio Roldán-Nofuentes and Raid M. Amro

285

Health Planning Information Acquired from Unstructured Data about Diabetes Mellitus Rodrigo Santos Souza, Edilberto Strauss and Flávio Luis de Mello

287

Contents Chapter 137

Chapter 138

Applying Fuzzy Model to Map Vulnerability Areas of Trypanosoma Cruzi Transmission Samanta Cristina das Chagas Xavier, Marcello Goulart Teixeira, André Luiz Rodrigues Roque, Ana Maria Jansen and Luiz Felipe Coutinho Ferreira da Silva Usage of Automatic Theorem Proving in the Recognition of Brain Emotions Activations Flávio Luis de Mello and Edilberto Strauss

Chapter 139

Radiology Information System with Knowledge Reasoning Sérgio Ricardo Pereira Soares, Edilberto Strauss and Flávio Luis de Mello

Chapter 140

Design of Routes for Waste Collection: Centro Habana’s Case Study Joanna Campbell Amos and Sira Allende Alonso

Chapter 141

Chapter 142

Chapter 143

Chapter 144

Comparison Methods of Digital Elevation Model Correction, in the Subwatershed V Aniversario, Cuyaguateje Basin Cuba Yeleine Almoza Hernández, Abdiel Fernández Alvarez, Yasser Vázquez and Andrea Petroseli An Integer Optimization Model for Waste Collection Frequency Problem Joanna Campbell Amos, Sira Allende Alonso and Marcos José Negreiros Gomes Evolving an Intelligent Framework for Decision-Making Process in E-Health Systems Leonardo M. Gardini, Carina Oliveira, Reinaldo Braga, Ronaldo Ramos, Luiz O. M. Andrade and Mauro Oliveira Heart Diseases Prediction Using Data from Health Assurance Systems Ronaldo Ramos, César Mattos, Amauri Júnior, Ajalmar Neto, Guilherme Barreto, Helio Mazza and Márcio Mota

xv

289

291 293

295

297

299

301

303

Chapter 145

Iterative Algorithms I Ioannis K. Argyros and Á. Alberto Magreñán

305

Chapter 146

Iterative Algorithms II Ioannis K. Argyros and Á. Alberto Magreñán

307

Chapter 147

Chaos Theory and Financial Statements Fernando Juárez

309

Chapter 148

Applying Chaos Theory to Work: The Chaos Theory of Careers Robert Pryor

311

xvi

Contents

Chapter 149

Application of Chaos Theory to Ventricular Wall Biomechanics Walter E. Legnani, Leandro J. Cymberkno and Ricardo L. Armentano

Chapter 150

Complexity and Synchronization in the Process of Biochemical Substance Exchange in a Diffusively Coupled Ring of Cells D. T. Mihailović, G. Mimić and I. Arsenić

315

Unveiling the Escape Mechanism of Orbits in Hamiltonian Systems with Multiple EXIT Channels Euaggelos E. Zotos

317

Chapter 151

313

Chapter 152

Mathematical Modeling of Intracellular Processes P. M. Gotovtsev, Ya. E. Sergeeva, A. V. Komova, I. A. Konova, K. V. Gorin, G. U. Badranova, V. M. Pojidaev and R. G. Vasilov

Chapter 153

Improving the Efficiency of Bezier Basis Function in Object Surface Modeling J. A. Muñoz-Rodríguez

321

Performance Evaluation of Two-Dimensional Linear Discriminant Analysis for Images Tetsuya Yoshida and Yuu Yamada

323

From Pseudoholomorphic Functions to the Associated Real Manifold Giampiero Esposito and Raju Roychowdhury

325

Numerical and Analytical Methods for Bond Pricing in Short Rate Convergence Models of Interest Rates Zuzana Bučková, Beáta Stehlíková and Daniel Ševčovič

327

Chapter 154

Chapter 155

Chapter 156

Chapter 157

Structural Transformations in the Relationships between Mathematics and Music up to the Renaissance and the Emergence of the Idea of Number as a Continuous Quantity Oscar João Abdounur

319

329

PREFACE This new book compiles biographical sketches of top professionals in the field of mathematics as well as research summaries from a number of different focuses in this important field.

PART I RESEARCHER BIOGRAPHICAL SKETCHES

In: Mathematical Research Summaries. Volume 1 Editor: Matthew A. Rowe

ISBN: 978-1-53612-021-9 © 2017 Nova Science Publishers, Inc.

Chapter 1

DR. IMRE FERENC BARNA Affiliation: Wigner Research Center of the Hungarian Academy of Sciences, Konkoly-Thege Miklós út 29 – 33. Budapest, Hungary and ELI-ALPS Nonprofit Ltd, Dugonics tér 13, Szeged, Hungary Budapest, Hungary

Education: Master Thesis: 1997 Technical University of Budapest, Phd: 2002 Justus-Liebig-Universität Giessen, Germany

Research and Professional Experience: 2002-2004

2004- June 2005 July 2005 - June 2013

July 2013 – Present

June 2012 - Present

Post-Doc Max-Planck-Institute for the Physics of Complex Systems Dresden, Germany Post-Doc Institute for Theoretical Physics TU-Vienna, Austria Research Associate Atomic Energy Research Institute later Energy Research Center of the Hungarian Academy of Sciences, Budapest, Hungary Research Associate Wigner Research Center of the Hungarian Academy of Sciences, Budapest, Hungary Research Associate ELI-ALPS, Szeged, Hungary, half position

Publications Last 3 Years: 1. I.F. Barna and L Mátyás. "Analytic solutions for the one-dimensional compressible Euler equation with heat conduction closed with different kind of equation of states" Miskolc Mathematical Notes 14, (2013) 785 2. M. Aladi, J.S. Bakos, I.F. Barna et al. "Pre-Excitation Studies for Rubidium-Plasma Generation". Nucl. Instr. Meth. in Physics Res. A 740, (2014) 203

4

Imre Ferenc Barna 3. I.F. Barna, L. Mátyás. "Analytic solutions for the three dimensional compressible Navier-Stokes equation". Fluid. Dyn. Res. 46, (2014) 055508 4. I.F. Barna. "Self-similar shock wave solutions of the non-linear Maxwell equations". Laser Phys. 24, (2014) 086002 5. I.F. Barna and S. Varró. “Laser assisted proton collision on light nuclei at moderate energies". Laser and Particle Beams 33, (2015) 299. 6. M.A. Pocsai, S. Varró and I.F. Barna. "Electron acceleration in under dense plasmas described with a classical effective theory". Laser and Particle Beams 33, (2015) 307. 7. I.F. Barna and L. Mátyás. "Analytic self-similar solutions of the OberbeckBoussinesq equation". Chaos Solitons and Fractals 78, (2015) 249. 8. I.F. Barna, M. A. Pocsai, A. Guba and A. Imre. "Theoretical study of steam condensation induced water hammer phenomena in horizontal pipelines". Kerntechnik 80, (2015) 5. 9. I.F. Barna, G. Bognár and K. Hriczó. "Self-similar analytic solution of the two dimensional Navier-Stokes equation with a non-Newtonian type of viscosity". Mathematical Modelling and Analysis 21, (2016) 83. 10. I.F. Barna and S. Varró. "Proton scattering on carbon nuclei in bichromatic laser field at moderate energies". Nucl. Instr. Meth. in Phys. Res. B. 369, (2016) 77. 11. M.A Pocsai, S. Varró and I.F. Barna. "Electron acceleration by a bichromatic chirped laser pulse in underdense plasmas". Nucl. Instr. Meth. in Phys. Res. B. 369, (2016) 50. 12. T. Csörgő, I.F. Barna and M.I. Nagy. "Observables and initial conditions for rotating and expanding fireballs with spheroidal symmetry". Phys. Rev. C 93, (2016) 024916. 13. I.F. Barna and R. Kersner. "Heat conduction: hyperbolic self-similar shock-waves in solid medium" accepted in 2016 march. Journal of Generalized Lie Theory and Applications.

In: Mathematical Research Summaries. Volume 1 Editor: Matthew A. Rowe

ISBN: 978-1-53612-021-9 © 2017 Nova Science Publishers, Inc.

Chapter 2

ROSAMONDE R. COOK Affiliation: Biological Monitoring Program, Western Riverside Multi-Species Habitat Conservation Plan

Address: 4800 Glenwood Drive, Bldg C., Riverside, California, 92501

Date of Birth: 8/4/1959

Education: University of California, Davis Ph.D. Ecology with emphases in Conservation Biology, Community Ecology, and Population Ecology M.S. Ecology University of California, San Diego B.A. Ecology, Evolution, and Behavior

Research and Professional Experience: 2008-Present. Ecologist and Data Manager. Biological Monitoring Program, Western Riverside County Multi-Species Habitat Conservation Plan. Designing a scientifically valid long-term ecological monitoring program for multiple species and their habitats. Applying data management best practices and procedures for ensuring quality data in support of longterm monitoring objectives. 2004-2007 Ecologist/Data Manager. U.S. National Park Service, Vital Signs Monitoring Program, Sierra Nevada Network. Identifying critical indicators of environmental health and designing scientifically valid long term monitoring protocols for detection of change. Applying data management best practices and procedures for ensuring quality data in support of long-term monitoring objectives.

6

Rosamonde R. Cook

2001-2003 Postdoctoral Research Associate. University of Connecticut and the Northeast Underwater Research Technology & Education Center. Design of marine protected areas for multi-species assemblages of demeral fishes on the eastern continental shelf of the United States using simulated annealing and research trawl survey data. Developing a bioregional classification for the continental shelf of northeastern North America. Applying simulated annealing to the prioritization of protected areas in Stellwagen Bank National Marine Sanctuary. 1997-2000 Postdoctoral Fellow. Colorado State University. Development of an extensive spatial database for mapping and analysis of vertebrate and butterfly species diversity patterns on forest lands in the American Southwest. Unraveling mechanisms for nested subset patterns of community composition in Virginia stream fish assemblages. 1991-1996 Doctoral Student. University of California, Davis. Nested species subsets and what they tell us about extinction and colonization processes in communities of species over large spatial scales; Extinction risk as a function of body size in island bird populations – a metapopulation analysis; simulation null models in community ecology. 1991-1993 Post-graduate Researcher. University of California, Davis. Inventorying the terrestrial and aquatic mammals and herptiles of several State Parks in California’s Central Valley: The difference between predicted and assessed species occurrence. 1986 – 1990 Masters Student. University of California, Davis. Dispersal functions, isolation, and resultant patterns of community composition in model metacommunities.

Honors: 2002, 2003 - Research Grant Awards, Conservation Law Foundation, Boston, Massachusetts. Marine Ecosystem Conservation for New England and Eastern Canada: A Science-Based Approach to the Identification of Priority Areas for Conservation. $10,000. 2002 - Research Grant Award, Environmental Defense. Alternatives for Optimal Representation of Seafloor Habitats and Associated Communities in Stellwagen Bank National Marine Sanctuary. $5,000. 2001 - Postdoctoral Research Associate, University of Connecticut and the Northeast Underwater Research Technology & Education Center. 1999 - Potential grazing impacts on regional biodiversity in New Mexico and Arizona. USDA Forest Service. Rocky Mountain Research Station. $48,977. 1998 - Biological Diversity Assessment of New Mexico and Arizona. USDA Forest Service. Rocky Mountain Research Station. $114,000. 1996 - Postdoctoral Fellowship, Colorado State University, Department of Fish, Wildlife, and Conservation Biology

Biography of Rosamonde R. Cook

7

1992 - Mildred Methias Graduate Research Grant Award, University of California, Davis $1,200. 1992 - Jastro-Shield Graduate Research Award. $1,400. 1987 - University of California, Travel Grant for Research $400.

Publications Last 3 Years: 1. Cook R.R. and Auster P.J. 2013. The biodiversity value of marine protected areas for multi-species fishery management in the Gulf of Maine. Aquatic Conservation: Marine and Freshwater Ecosystems. 23(3) · June 2013. Published online in Wiley Online Library (wileyonlinelibrary.com). DOI: 10.1002/aqc.2312 2. Heard A.M., Starcevich L.A.H., Sickman J.O., Cook R, Schweizer D.W., Paolilli D., and Fong C. 2012. Sierra Nevada Network Lake Monitoring Protocol: Standard Operating Procedures. Natural Resource Report NPS/SIEN/NRR—2012/551.1. U.S. National Park Service, Fort Collins, Colorado. 3. Cook R.R. and Auster P.J. 2014. Simulated Annealing: Strategies, Potential Uses and Advantages, Chapter: 9, Nova Publishers, Editors: Marcos de Sales Guerra Tsuzuki, Thiago de Castro Martins, pp.221-242.

In: Mathematical Research Summaries. Volume 1 Editor: Matthew A. Rowe

ISBN: 978-1-53612-021-9 © 2017 Nova Science Publishers, Inc.

Chapter 3

RUDOLF EGGERS Affiliation: Hamburg University of Technology, Institute for Thermal Separation Processes, Heat and Mass Transfer

Address: Eißendorfer Str. 38, 21073 Hamburg, Germany

Date of Birth: 08/01/1947

Education: 1984 – present Professor at Hamburg University of Technology, Institute for Thermal Separation Processes, Heat and Mass Transfer 1977 – 1984 Head of Department of Process Technology, Thyssen Maschinenbau company, Witten, Germany and Krupp Industrietechnik company, Hamburg, Germany 1972 – 1977 Scientific Employee, Institute for Heat engineering, University of Technology, Clausthal, Germany, PhD degree: 1976 1966 – 1972 Mechanical engineering / process engineering studies, University of Hannover, Germany

Research and Professional Experience: -

Food Engineering High Pressure Technology Interfacial Process Engineering Energy Process Engineering

Publications Last 3 Years: 1. Jeschke, S. and Eggers, R. (2013), Experimentelle Ermittlung von Permeabilitäten für die Durchströmung von salinen Aquiferen mit CO2. (Experimental Investigation

10

Rudolf Eggers of Permeability in Case of Permeation of Saline Aquifers with CO2). Chemie Ingenieur Technik, 85: 1605–1611. doi:10.1002/cite.201200208 2. J. Ivanovic, F. Meyer, D. Misic, J. Asanin, P. Jaeger, I. Zizovic, R. Eggers (2013). Influence of different pre-treatment methods on isolation of extracts with strong antibacterial activity from lichen Usnea barbata using carbon dioxide as a solvent. Journal of Supercritical Fluids 76. 1-9.

In: Mathematical Research Summaries. Volume 1 Editor: Matthew A. Rowe

ISBN: 978-1-53612-021-9 © 2017 Nova Science Publishers, Inc.

Chapter 4

SNEZHANA GEORGIEVA GOCHEVA-ILIEVA Affiliation: Plovdiv University Paisii Hilendarski, Faculty of Mathematics and Informatics, Plovdiv, Bulgaria

Address: 24 Tzar Asen Street, 4000 Plovdiv, Bulgaria

Date of Birth: 03/07/1950

Education: Ph.D. in Physics and Mathematics (Computational Mathematics) (1981), Taras Shevchenko State University of Kiev, Ukraine B.Sc. and M.Sc. in Computational Mathematics (1973), St. Climent Ohridski University of Sofia, Bulgaria

Research and Professional Experience: She taught in bachelor and master programs disciplines of applied mathematics, statistics and computer science. She has published over 120 articles in international journals, 14 books and has presented many research papers at international conferences. Her research interests include various fields of mathematical modeling in physics and engineering, modeling in environmental science, applied computational statistics, predictive data mining techniques and software, and more.

Professional Appointments: Full professor of applied mathematics at the Department of Applied Mathematics and Modeling from Paisii Hilendarski University of Plovdiv, Bulgaria

Publications Last 3 Years: 1 . Iliev I.P., S.G. Gocheva-Ilieva. Modeling and simulation of output power of a highpower He–SrBr2 laser by using multivariate adaptive regression splines, Optics &

12

Snezhana Georgieva Gocheva-Ilieva Laser Technology, vol. 45, No1, pp. 461-468, 2013. ISSN: 0030-3992 http://dx.doi.org/10.1016/j.optlastec.2012.06.009 2 . Iliev I. P., D. S. Voynikova, and S. G. Gocheva-Ilieva, Application of the classification and regression trees for modeling the laser output power of a copper bromide vapor laser, Mathematical Problems in Engineering, vol. 2013, Article ID 654845, pp. 1-10. Accepted 20 April, 2013, ISSN 1024-123X , http://dx.doi.org/10.1155/2013/654845 3 . Gocheva S.G., I. H. Feschiev, New recursive representations for the Favard constants with application to multiple singular integrals and summation of series, Abstract and Applied Analysis, vol. 2013, Article ID: 523618, 12 pages, Accepted 22 April 2013. ISSN 1085-3375, 2013, http://dx.doi.org/10.1155/2013/523618 4 . Iliev I. P., S. G. Gocheva-Ilieva, Study of UV Cu + Ne – CuBr laser lifetime by statistical methods, Quantum Electronics, 43 (11), pp. 1014–1018, 2013, ISSN: 10637818, e-ISSN: 1468-4799 http://iopscience.iop.org/1063-7818/43/11/1014 5 . Denev N., I. Iliev, S. Gocheva-Ilieva, Second-Degree Polynomial Model of Laser Generation for a CuBr Laser, WSEAS Transactions on circuits and systems, Vol. 12, Issue 4, pp.129-139, April 2013, Print ISSN: 1109-2734, E-ISSN: 2224-266X. http://www.wseas.org/multimedia/journals/circuits/2013/035701-103.pdf 6 . Voynikova D. S., S. G. Gocheva-Ilieva and I. P. Iliev, MARS Models of Laser Efficiency of Copper Bromide Laser, Proc. of Fifth Conference of the Euro-American Consortium for Promoting the Application of Mathematics in Technical and Natural Sciences, (AMiTaNS'2013), Albena, Bulgaria, June 24-29, 2013. Ed. M. Todorov, AIP Conference Proceedings, Vol. 1561, pp. 240-247, 2013. ISBN: 978-0-7354-11890. http://dx.doi.org/10.1063/1.4827234 7 . Ivanov А. V., S. G. Gocheva-Ilieva, Short-Time Particulate Matter PM10 Forecasts Using Predictive Modeling Techniques, Proc. of Fifth Conference of the EuroAmerican Consortium for Promoting the Application of Mathematics in Technical and Natural Sciences (AMiTaNS'2013), Albena, Bulgaria, June 24-29, 2013. Ed. M. Todorov, AIP Conference Proceedings, Vol. 1561, pp. 209-218, 2013. ISBN: 978-07354-1189-0, http://dx.doi.org/10.1063/1.4827230 8 . Iliev I.P., Gocheva-Ilieva S.G., Modeling and Analysis of the Breakdown Curve of a High-Frequency Discharge in Hydrogen, Intern J Sci Technol Res, vol.3, No 3, pp. 85-88, March 2014. ISSN 2277-8616. http://www.ijstr.org/research-paperpublishing.php?month=mar2014 9 . Gocheva-Ilieva S.G., Application of the Generalized Pathseeker regularized regression, Mathematics and Education in Mathematics, Rusev P. (Ed.),vol. 2014, Proc. 43th Spring Conference of the Union of Bulgarian Mathematicians, 2-6 April 2014, Borovetz, pp. 34-43, 2014. ISSN1313-3330. http://www.math.bas.bg/smb /2014_PK/tom_2014/pdf/034-043.pdf 1 0 . Gocheva-Ilieva S. G., Ivanov A. V., Voynikova D. S., Boyadzhiev D. T., Time Series Analysis and Forecasting for Air Pollution in Small Urban Area: an SARIMA and Factor Analysis Approach, Stoch. Env. Res. Risk A., vol. 28 (4), pp. 1045-1060, 2014, Springer, DOI: 10.1007/s00477-013-0800-4, ISSN: 1436-3240 (Print) 14363259 (Online) http://link.springer.com/article/10.1007/s00477-013-0800-4 1 1 . Iliev I.P., Gocheva-Ilieva S.G., Analytic Model of the Breakdown of Argon at Low Pressure in Combined Electric Fields, Proc. 2nd Intl’ Conference on Advances in

Biography of Snezhana Georgieva Gocheva-Ilieva

13

Engineering Sciences and Applied Mathematics (ICAESAM2014), organized by International Institute of Engineers, May 4-5, 2014 Istanbul (Turkey), pp. 96-98, 2014. ISBN 978-93-82242-91-8. 1 2 . Iliev I.P., Gocheva-Ilieva S.G., A Non-linear Parametric Second-Degree Model for the Lifetime of Ultraviolet Cu+ Ne-CuBr Laser, Proc. 11th Intern. Conf. on Modeling, Simulation and Visualization Methods (MSV'14), WORLDCOMP’14 (World Congress in Computer Science, Computer Engineering and Applied Computing), Las Vegas, 21-24 July, 2014, pp. 52-56, Eds. Arabnia H.R., Deligiannidis L., You J., CSREA Press, USA. ISBN: 1-60132-281-X http://www.store.slicebooks.com/ ebooks/801034-session-simulation-numerical-methods-and-applications 1 3 . A.Yordanova, S. Gocheva-Ilieva, H. Kulina, L. Yordanova, I. Marinov, Classification and regression tree analysis in modeling the milk yield and conformation traits for Holstein cows in Bulgaria, AGRICULTURAL SCIENCE AND TECHNOLOGY, VOL. 7, No 2, pp. 208 - 213, 2015. ISSN 1313 – 8820. http://agriscitech.eu/wpcontent/uploads/2015/06/011.pdf 1 4 . A.Ivanov, D. Voynikova, S. Gocheva-Ilieva, H. Kulina and I. Iliev, Using principal component analysis and general path seeker regression for investigation of air pollution and CO modeling, 7th Conference of the Euro-American Consortium for Promoting the Application of Mathematics in Technical and Natural Sciences, Albena, Bulgaria, June 28-July 3, 2015, AIP Conf. Proc. 1684, ed. M. Todorov, 100004, pp. 111 (2015); http://dx.doi.org/10.1063/1.4934341 1 5 . D.S. Voynikova, S. G. Gocheva-Ilieva, A. V. Ivanov and I. P. Iliev, Studying the effect of meteorological factors on the SO2 and PM10 pollution levels with refined versions of the SARIMA model, 7th Conference of the Euro-American Consortium for Promoting the Application of Mathematics in Technical and Natural Sciences, Albena, Bulgaria, June 28-July 3, 2015, AIP Conf. Proc. 1684, ed. M. Todorov, 100005, pp. 1-12 (2015); http://dx.doi.org/10.1063/1.4934342 1 6 . Gocheva-Ilieva S. G., Ivanov A. V., Iliev I. P., Modeling of Air Pollutants and Ozone Concentration by Using Multivariate Analysis: Case Study of Dimitrovgrad, Bulgaria, British Journal of Applied Science & Technology, 14(3): 1-8, 2016, Article no.BJAST.23910. ISSN: 2231-0843, NLM ID: 101664541. DOI: 10.9734/BJAST/2016/23910 http://sciencedomain.org/issue/1567

In: Mathematical Research Summaries. Volume 1 Editor: Matthew A. Rowe

ISBN: 978-1-53612-021-9 © 2017 Nova Science Publishers, Inc.

Chapter 5

JAMES M. HONEYCUTT Affiliation: Louisiana State University

Address: Dept. of Communication Studies, Louisiana State University, Baton Rouge, LA 708033923

Date of Birth: 12/21/1956

Education: Ph.D. from the University of Illinois, 1987; MS from Purdue University, 1979; BS from the University of Texas at Austin, 1979

Honors: 

  





Special panel programmed by the Southern States Communication Association devoted to exclusively previewing the edited volume, “The Influence of Communication in Physiology and Health.” New Orleans, April, 2014 SEC Faculty Exchange Scholar Award, spring 2014 Southern States Communication Theory Outstanding Scholar Award, Louisville, KY, April 2013. Recognition for a Top 3 paper in the Communication and Social Cognition Division of the National Communication Association with Graham Bodie & Andrea Vickery, November 2012. Recipient of the 2012 LSU Distinguished Faculty Award in the Humanities and Social Sciences recognizing a sustained record of excellence in research, teaching, and/or service, May 2012. Recipient of the 2011 LSU Senior Scholar Rainmaker Award in the Humanities and Social Sciences for scholarly research, April 2012.

16

James M. Honeycutt

Publications Last 3 Years: 1. Honeycutt, J. M., Sawyer, C. R., & Keaton, S. A. (2014). The Influence of Communication in Physiology and Health. New York: Peter Lang. ISBN 978-14331-2219-4 2. Honeycutt, J. M. (2013). Diversity in family communication. San Diego, CA: Cognella. ISBN:978-1-62131-155-1 3. Honeycutt, J. M., Sheldon, P., Pence, M. E., & Hatcher, L. C. (2014, in press). Predicting aggression, conciliation, and concurrent rumination in escalating conflict. Journal of Interpersonal Violence. 29,doi: 10.1177/0886260514532717

In: Mathematical Research Summaries. Volume 1 Editor: Matthew A. Rowe

ISBN: 978-1-53612-021-9 © 2017 Nova Science Publishers, Inc.

Chapter 6

ILIYCHO PETKOV ILIEV Affiliation: Technical University – Sofia, branch Plovdiv, Bulgaria

Address: 25 Tsanko Djustabanov, 4000 Plovdiv, Bulgaria

Date of Birth: 10/19/1955

Education: D.Sc. in Physics, Bulgarian Academy of Sciences (2015); Ph.D. in Physics (2003), Sofia University; Master in Condensed Matter Physics, Plovdiv University Paisii Hilendarski (2010); Bachelor and Master in Light Sources Engineering, Moscow Power Engineering Institute, Russia in 1982.

Research and Professional Experience: He taught in bachelor programs courses of general physics. He has published over 100 articles in international journals, 6 books and has presented many research papers at international conferences. His research interests include laser physics, mathematical and statistical modeling in physics and engineering, and environmental sciences.

Professional Appointments: Associate Professor in Physics, Technical university - Sofia, branch Plovdiv, Bulgaria

Publications Last 3 Years: 1 . Iliev I.P., S.G. Gocheva-Ilieva. Modeling and simulation of output power of a highpower He–SrBr2 laser by using multivariate adaptive regression splines, Optics & Laser Technology, vol. 45, No1, pp. 461-468, 2013. ISSN: 0030-3992 http://dx.doi.org/10.1016/j.optlastec.2012.06.009 2 . Iliev I. P., D. S. Voynikova, and S. G. Gocheva-Ilieva, Application of the classification and regression trees for modeling the laser output power of a copper

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Iliycho Petkov Iliev bromide vapor laser, Mathematical Problems in Engineering, vol. 2013, Article ID 654845, pp. 1-10. Accepted 20 April, 2013, ISSN 1024-123X, http://dx.doi.org /10.1155/2013/654845 3 . Iliev I. P., S. G. Gocheva-Ilieva, Study of UV Cu + Ne – CuBr laser lifetime by statistical methods, Quantum Electronics, 43 (11), pp. 1014–1018, 2013, ISSN: 1063-7818, e-ISSN: 1468-4799 http://iopscience.iop.org/1063-7818/43/11/1014 4 . Denev N., I. Iliev, S. Gocheva-Ilieva, Second-Degree Polynomial Model of Laser Generation for a CuBr Laser, WSEAS Transactions on circuits and systems, Vol. 12, Issue 4, pp.129-139, April 2013, Print ISSN: 1109-2734, E-ISSN: 2224-266X. http://www.wseas.org/multimedia/journals/circuits/2013/035701-103.pdf 5 . Voynikova D. S., S. G. Gocheva-Ilieva and I. P. Iliev, MARS Models of Laser Efficiency of Copper Bromide Laser, Proc. of Fifth Conference of the EuroAmerican Consortium for Promoting the Application of Mathematics in Technical and Natural Sciences, (AMiTaNS'2013), Albena, Bulgaria, June 24-29, 2013. Ed. M. Todorov, AIP Conference Proceedings, Vol. 1561, pp. 240-247, 2013. ISBN: 978-07354-1189-0. http://dx.doi.org/10.1063/1.4827234 6 . Iliev I.P., Gocheva-Ilieva S.G., Modeling and Analysis of the Breakdown Curve of a High-Frequency Discharge in Hydrogen, Intern J Sci Technol Res, vol.3, No 3, pp. 85-88, March 2014. ISSN 2277-8616. http://www.ijstr.org/research-paperpublishing.php?month=mar2014 7 . Iliev I.P., Gocheva-Ilieva S.G., Analytic Model of the Breakdown of Argon at Low Pressure in Combined Electric Fields, Proc. 2nd Intl’ Conference on Advances in Engineering Sciences and Applied Mathematics (ICAESAM2014), organized by International Institute of Engineers, May 4-5, 2014 Istanbul (Turkey), pp. 96-98, 2014. ISBN 978-93-82242-91-8. 8 . Iliev I.P., Gocheva-Ilieva S.G., A Non-linear Parametric Second-Degree Model for the Lifetime of Ultraviolet Cu+ Ne-CuBr Laser, Proc. 11th Intern. Conf. on Modeling, Simulation and Visualization Methods (MSV'14), WORLDCOMP’14 (World Congress in Computer Science, Computer Engineering and Applied Computing), Las Vegas, 21-24 July, 2014, pp. 52-56, Eds. Arabnia H.R., Deligiannidis L., You J., CSREA Press, USA. ISBN: 1-60132-281-X http://www.store.slicebooks.com/ebooks/801034-session-simulation-numericalmethods-and-applications 9 . A.Ivanov, D. Voynikova, S. Gocheva-Ilieva, H. Kulina and I. Iliev, Using principal component analysis and general path seeker regression for investigation of air pollution and CO modeling, 7th Conference of the Euro-American Consortium for Promoting the Application of Mathematics in Technical and Natural Sciences, Albena, Bulgaria, June 28-July 3, 2015, AIP Conf. Proc. 1684, ed. M. Todorov, 100004, pp. 1-11 (2015); http://dx.doi.org/10.1063/1.4934341 1 0 . D.S. Voynikova, S. G. Gocheva-Ilieva, A. V. Ivanov and I. P. Iliev, Studying the effect of meteorological factors on the SO2 and PM10 pollution levels with refined versions of the SARIMA model, 7th Conference of the Euro-American Consortium for Promoting the Application of Mathematics in Technical and Natural Sciences, Albena, Bulgaria, June 28-July 3, 2015, AIP Conf. Proc. 1684, ed. M. Todorov, 100005, pp. 1-12 (2015); http://dx.doi.org/10.1063/1.4934342

Biography of Iliycho Petkov Iliev

19

1 1 . Gocheva-Ilieva S. G., Ivanov A. V., Iliev I. P., Modeling of Air Pollutants and Ozone Concentration by Using Multivariate Analysis: Case Study of Dimitrovgrad, Bulgaria, British Journal of Applied Science & Technology, 14(3): 1-8, 2016, Article no.BJAST.23910. ISSN: 2231-0843, NLM ID: 101664541. DOI: 10.9734/ BJAST/2016/23910 http://sciencedomain.org/issue/1567

In: Mathematical Research Summaries. Volume 1 Editor: Matthew A. Rowe

ISBN: 978-1-53612-021-9 © 2017 Nova Science Publishers, Inc.

Chapter 7

ATANAS VALEV IVANOV Affiliation: Plovdiv University Paisii Hilendarski, Plovdiv, Bulgaria

Address: 24 Tsar Asen Street, 4000 Plovdiv, Bulgaria

Date of Birth: 06/29/1986

Education: Ph.D. in Applied Mathematics and Modeling (2015), Plovdiv University Paisii Hilendarski; Bachelor and Master in Applied Mathematics (2010), Plovdiv University Paisii Hilendarski

Research and Professional Experience: He taught in bachelor programs disciplines of applied mathematics and statistics. He has published 7 articles in international journals, and has presented some research papers at international conferences. His research interests include mathematical modeling in environmental science, applied statistics, predictive data mining techniques and software.

Professional Appointments: Assistant professor at the Department of Applied Mathematics and Modeling, Plovdiv University Paisii Hilendarski

Publications Last 3 Years: 1 . Gocheva-Ilieva S. G., Ivanov A. V., Voynikova D. S., Boyadzhiev D. T., Time Series Analysis and Forecasting for Air Pollution in Small Urban Area: an SARIMA and Factor Analysis Approach, Stoch. Env. Res. Risk A., vol. 28 (4), pp. 1045-1060, 2014, Springer, DOI: 10.1007/s00477-013-0800-4, ISSN: 1436-3240 (Print) 14363259 (Online) http://link.springer.com/article/10.1007/s00477-013-0800-4

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Atanas Valev Ivanov 2 . A.Ivanov, D. Voynikova, S. Gocheva-Ilieva, H. Kulina and I. Iliev, Using principal component analysis and general path seeker regression for investigation of air pollution and CO modeling, 7th Conference of the Euro-American Consortium for Promoting the Application of Mathematics in Technical and Natural Sciences, Albena, Bulgaria, June 28-July 3, 2015, AIP Conf. Proc. 1684, ed. M. Todorov, 100004, pp. 1-11 (2015); http://dx.doi.org/10.1063/1.4934341 3 . D.S. Voynikova, S. G. Gocheva-Ilieva, A. V. Ivanov and I. P. Iliev, Studying the effect of meteorological factors on the SO2 and PM10 pollution levels with refined versions of the SARIMA model, 7th Conference of the Euro-American Consortium for Promoting the Application of Mathematics in Technical and Natural Sciences, Albena, Bulgaria, June 28-July 3, 2015, AIP Conf. Proc. 1684, ed. M. Todorov, 100005, pp. 1-12 (2015); http://dx.doi.org/10.1063/1.4934342 4 . Gocheva-Ilieva S. G., Ivanov A. V., Iliev I. P., Modeling of Air Pollutants and Ozone Concentration by Using Multivariate Analysis: Case Study of Dimitrovgrad, Bulgaria, British Journal of Applied Science & Technology, 14(3): 1-8, 2016, Article no.BJAST.23910. ISSN: 2231-0843, NLM ID: 101664541. DOI: 10.9734/BJAST/2016/23910 http://sciencedomain.org/issue/1567

In: Mathematical Research Summaries. Volume 1 Editor: Matthew A. Rowe

ISBN: 978-1-53612-021-9 © 2017 Nova Science Publishers, Inc.

Chapter 8

NOELIA JIMÉNEZ-FANJUL Affiliation: Mathematics Education, Department of Mathematics, University of Cordoba

Address: Faculty of Education. San Alberto Magno, s/n. E-14071 Córdoba (SPAIN)

Education: PhD Education

Research and Professional Experience: I got a Ph.D. in Education at University of Cordoba focus on mathematics education. I have been working as an adjunct professor in the department of mathematics of the University of Cordoba since 2010, lecturing in early childhood and primary teacher training degrees as well as secondary teacher training at master level. My research lines are related to impact and diffusion of science, mathematics education, history of mathematics, attitudes towards mathematics and teacher training. I have participated in several research projects at school and university levels.

Publications Last 3 Years: 1. Maz-Machado, A., Jiménez-Fanjul, N. N., & Villarraga, E. (2016). La producción científica colombiana en SciELO: un análisis bibliométrico. Revista Interamericana de Bibliotecología, 39(2), 15-26. doi: 10.17533/udea.rib.v39n2a03 2. Maz-Machado, A., Jiménez-Fanjul, N., Adamuz-Povedano, N., & Bracho-López, R. (2015). Análisis bibliométrico de la revista RELIME (1997-2011). Investigación Bibliotecológica, 29(66), 91-104. 3. Maz-Machado, A., Jiménez-Fanjul, N., & Madrid, M. J. (2015). Collaboration in the Iberoamerican Journals in the category Information Science & Library Science in WOS. Library Philosophy and Practice (e-journal), Paper 1270. Retrieved from http:\\digitalcommons.unl.edu\libphilprac\1270 4. Bracho-López, R., Jiménez-Fanjul, N., Maz-Machado, A., Torralbo-Rodríguez, M., & Fernández-Cano, A. (2014). Producción científica sobre narrativa en Educación

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Noelia Jiménez-Fanjul Matemática en la Web of Science. BOLEMA-Boletim de Educação Matemática, 28(49), 744-761. doi: 10.1590/1980-4415v28n49a14 5. Maz-Machado, A., Jiménez-Fanjul, N., & Adamuz-Povedano, N. (2014). Spanish journals of education & Educational research in the JCR: A bibliometric analysis of the citations. Library Philosophy and Practice (e-journal), Paper 1121. Retrieved from http://digitalcommons.unl.edu/libphilprac/1121

In: Mathematical Research Summaries. Volume 1 Editor: Matthew A. Rowe

ISBN: 978-1-53612-021-9 © 2017 Nova Science Publishers, Inc.

Chapter 9

CARMEN LEÓN-MANTERO Affiliation: Mathematics Education, Department of Mathematics, University of Cordoba

Address: Faculty of Education. San Alberto Magno, s/n. E-14071 Córdoba (SPAIN)

Education: Master’s Degree (M) in mathematics education

Research and Professional Experience: I am a PhD student in Education at University of Cordoba focus on mathematics education. I have been working as an adjunct professor in the department of mathematics of the University of Cordoba since 2012, lecturing in primary teacher training degree as well as secondary teacher training at master level. My research lines are related to impact and diffusion of science, mathematics education, history of mathematics, attitudes towards mathematics and teacher training. I have participated in several research projects at school and university levels.

Publications Last 3 Years: 1. León-Mantero, C., Madrid, M. J. y Maz-Machado, A. (2016). Efemérides de Agustín de Pedrayes y Foyo: un destacado matemático español del siglo XVIII. Números, 92, 49-56. 2. Maz-Machado, A., León-Mantero, C. M., Casas, J. C. and Renaudo, J. (2015). Attitude towards mathematics of computer engineering students. British Journal of Education, Society & Behavioural Science, 8(2), 127-133. 3. Maz-Machado, A., León-Mantero, C. M. and Renaudo, J. (2015). Student teachers valued the practices with materials in the subjects of mathematics. Journal of Modern Education Review, 5(1),1-7. 4. León-Mantero, C. and Casas, J. C. (2014). Estudiando probabilidad con el juego Chinesespiel. Epsilon, Revista de Educación Matemática, 88,67-70.

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Carmen León-Mantero 5. Madrid, M.J., Maz-Machado, A. and León-Mantero, C. (2015). Representations in the Sixteenth-Century Arithmetic Books. Universal Journal of Educational Research, 6(3), 402-406. 6. León-Mantero, C. and Maz-Machado, A. (2015). Juan Cortázar y sus aportaciones a la Educación Matemática española del siglo XIX. ENSAYOS, Revista de la Facultad de Educación de Albacete, 30(1), 55-62.

In: Mathematical Research Summaries. Volume 1 Editor: Matthew A. Rowe

ISBN: 978-1-53612-021-9 © 2017 Nova Science Publishers, Inc.

Chapter 10

MARÍA JOSÉ MADRID Affiliation: Universidad Pontifica de Salamanca

Address: C/ Henry Collet, 52-70 37007 Salamanca España

Education: PhD in Mathematics Education

Research and Professional Experience: Adjunct Professor at Universidad Pontificia de Salamanca. Researcher about History of Mathematics Education

Publications Last 3 Years: 1. Madrid, M. J., Maz-Machado, A. and López C. (2015). Fenomenología y representaciones en el dorado contador de Miguel Gerónimo de Santa Cruz, Ensayos, Revista de la Facultad de Educación de Albacete, 30(1), 63-72. 2. Madrid, M. J., Maz-Machado, A. y López, C. (2016). 500 años de historia de las matemáticas: la obra de Juan Andres. Suma, 82, 51-58. 3. Madrid. M. J. and Maz-Machado, A. (2015). Analysis of two Spanish arithmetic books written in the XVI-century. Journal of Education, Psychology an Social Sciences, 3(2), 117-121. 4. Madrid, M. J., León-Mantero, C. and Maz-Machado, A. (2015). Assessment of the Attitudes towards Mathematics of the Students for Teacher of Primary Education. Open Access Library Journal, 2: e1936. 5. Maz-Machado, A., Madrid, M. J. and León-Mantero, C. (2015). Research on the productivity of the journal Review of Educational Research: A scientometric study. Journal of Advances in Library and Information Science, IV(4), 288-293.

In: Mathematical Research Summaries. Volume 1 Editor: Matthew A. Rowe

ISBN: 978-1-53612-021-9 © 2017 Nova Science Publishers, Inc.

Chapter 11

ALEXANDER MAZ-MACHADO Affiliation: Department of Mathematics, University of Cordoba

Address: Avda. San Alberto Magno s/n, 14071 Córdoba España

Education: PhD in Mathematics Education

Research and Professional Experience: Professor at Universidad de Córdoba. Researcher about History of Mathematics Education and Bibliometrics

Publications Last 3 Years: 1. Maz-Machado, A., Jiménez-Fanjul, N. y Villarraga, M. (2016). La producción colombiana SciELO: un análisis bibliométrico. Revista Interamericana de Bibliotecología, 39(2), 15-26. (ISSN: 0120-0976). 2. Almaraz, F. y Maz, A. (2016). La figura del Chief Digital Officer (CDO) en las Instituciones de Educación Superior. Revista Telos. Cuadernos de comunicación e innovación, 103, 1-7. 3. Maz-Machado, A., Jiménez-Fanjul, N., Madrid, M. J. (2015). Collaboration in the Iberoamerican Journals in the category Information Science & Library Science in WOS. Library Philosophy and Practice (e-journal). Paper 1270. 4. Maz-Machado, A., Jiménez-Fanjul, N., Adamuz-Povedano, N. y Bracho-López, R. (2015). Análisis bibliométrico de la revista RELIME (1997-2011). Investigación Bibliotecológica, 29(86), 90-102. 5. Maz-Machado, A. y Rico, L. (2015). Principios didácticos en textos españoles de matemáticas en los siglos XVIII y XIX. RELIME, Revista latinoamericana de Investigación Educativa, 18(1), 49-76. (ISBN:1665-2436) 6. Madrid, M. J., Maz-Machado, A. y López C. (2015). Fenomenología y representaciones en el dorado contador de Miguel Gerónimo de Santa

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Alexander Maz-Machado Cruz, Ensayos, Revista de la Facultad de Educación de Albacete, 30(1), 63-72. (ISBN: 2171-9098).. 7. Bracho-López, R., Torralbo-Rodríguez, M., Maz-Machado, A. y Adamuz-Povedano, N. (2014). Tendencias temáticas de la investigación en educación matemática en España. BOLEMA-Boletín de Educaçao Matemática, 28(50). 8. Bracho-López, R., Jiménez-Fanjul, N., Maz-Machado, A., Torralbo-Rodríguez, M. y Fernández-Cano, A . (2014). Producción scientífica sobre narrativa en Educación Matemática en la Web of Science. BOLEMA-Boletín de Educaçao Matemática, 28(49), 744-761.

In: Mathematical Research Summaries. Volume 1 Editor: Matthew A. Rowe

ISBN: 978-1-53612-021-9 © 2017 Nova Science Publishers, Inc.

Chapter 12

FLORIAN MEYER Affiliation: Hamburg University of Technology, Institute for Thermal Separation Processes, Heat and Mass Transfer

Address: Eißendorfer Str. 38, 21073 Hamburg, Germany

Date of Birth: 02/19/1982

Education: 2002 – 2008: Biochemical engineering studies, Faculty of Chemical and Biochemical Engineering, TU Dortmund University Diploma Degree 2008 2008 – present: PhD student, Hamburg University of Technology, Institute for Thermal Separation Processes, Heat and Mass Transfer, Prof. Dr.-Ing. R. Eggers

Research and Professional Experience: High Pressure Extraction Natural Materials Pre-treatment methods

Publications Last 3 Years: 1. J. Ivanovic, F. Meyer, D. Misic, J. Asanin, P. Jaeger, I. Zizovic, R. Eggers (2013). Influence of different pre-treatment methods on isolation of extracts with strong antibacterial activity from lichen Usnea barbata using carbon dioxide as a solvent. Journal of Supercritical Fluids 76 (2013) 1-9.

In: Mathematical Research Summaries. Volume 1 Editor: Matthew A. Rowe

ISBN: 978-1-53612-021-9 © 2017 Nova Science Publishers, Inc.

Chapter 13

ALI ASGHAR RASTEGARI Affiliation: Falavarjan Branch, Islamic Azad University

Address: Department of Molecular and Cell Biochemistry, Falavarjan Branch, Islamic Azad University, Isfahan, Iran

Date of Birth: 05/24/1962

Education: PhD in Molecular biophysics

Research and Professional Experience: Biophysical Chemistry, Nanobiotechnology

Computational

Biology,

Enzymes

Biotechnology,

Publications Last 3 Years: 1. Physico-chemical properties and network modeling: The behavior of cellulase with (DTAB) cationic surfactant Journal of Environmental Chemical Engineering 1 (2013) 805–812. 2. Thermal denaturation of pepsin at acidic media: Using DSC, MALDI-TOF MS and PAGE techniques. Thermochimica Acta 568 (2013) 165– 170. 3. The Unfolding Process of Apo-Human Serum Transferrin in the Presence of Cetylpyridinium Chloride: An Isothermal Titration Calorimetry Study. Acta Chim. Slov. 61(2014) 645–649. 4. Computational evaluation on the binding affinity of non-specific lipid-transfer protein-2 with fatty acids. Computers in Biology and Medicine 43(2013)1732–1738.

In: Mathematical Research Summaries. Volume 1 Editor: Matthew A. Rowe

ISBN: 978-1-53612-021-9 © 2017 Nova Science Publishers, Inc.

Chapter 14

MARKO STAMENIC Affiliation: University of Belgrade, Faculty of Technology and Metallurgy

Address: Karnegijeva 4, 11000 Belgrade, Serbia

Date of Birth: 09/06/1979

Education: 2004 BSc, University of Belgrade, Faculty of Technology and Metallurgy 2006 MSc, University of Belgrade, Faculty of Technology and Metallurgy 2010 PhD University of Belgrade, Faculty of Technology and Metallurgy

Research and Professional Experience: High Pressure Technologies Mathematical Modeling Food Engineering

Professional Appointments: 2005-2010, Research Assistant, University of Belgrade, Faculty of Technology and Metallurgy 2010-present Senior Research Assistant, University of Belgrade, Faculty of Technology and Metallurgy

Publications Last 3 Years: 1. Stamenic, M., Ivanovic, J., Grujic, S., Milovanovic, S., Zizovic, I., Petrovic, S., Comparative analysis of mathematical models for supercritical extraction simulation from industrially valuable Lamiaceae herbs, Canadian Journal of Chemical Engineering (2013) Article in Press

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Marko Stamenic 2. Stamenic, M., Zizovic, I., The mathematics of modelling the supercritical fluid extraction of essential oils from glandular trichomes, Computers and Chemical Engineering 48 (2013) 89-95

In: Mathematical Research Summaries. Volume 1 Editor: Matthew A. Rowe

ISBN: 978-1-53612-021-9 © 2017 Nova Science Publishers, Inc.

Chapter 15

YURIY S. VOLKOV Affiliation: Sobolev Institute of Mathematics, Novosibirsk, Russia

Address: Sobolev Institute of Mathematics, 4 Koptyug Ave., Novosibirsk, 630090, Russia

Date of Birth: 5/22/1959

Education: Novosibirsk State University, Novosibirsk, Russia

Research and Professional Experience: Degree of Doctor of Science in Computational Mathematics

Professional Appointments: Deputy Director of Sobolev Institute of Mathematics; Professor at Novosibirsk State University

Publications Last 3 Years: 1. Yuriy S. Volkov. The interpolation by splines of even degree in the senses of Subbotin and Marsden. Ukrainskyj Matematyczny Zhurnal, 2014. V.66, n.7, 891-908 (in Russian). 2. Yuriy S. Volkov, Yu.N.Subbotin. 50 years to Schoenberg’s problem on the convergence of spline interpolation. Trudy Instituta Matematiki i Mekhaniki, 2014. V.20, n.1, 52-67 (in Russian). 3. Yuriy S. Volkov, I.E. Svetov, E.Yu. Derevtsov and T. Schuster. A numerical solver based on B-splines for 2D vector field tomography in a refracting medium. Mathematics and Computers in Simulation, 2014. V.97, 207-223.

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Yuriy S. Volkov 4. Yuriy S. Volkov, E.G.Pytkeev and V.T. Shevaldin. Orders of approximation by local exponential splines. Proceedings of the Steklov Institute of Mathematics, 2014. V.284, n.1 Supplement, S175-S184. 5. Yuriy S. Volkov, V.V.Bogdanov, W.V.Karsten and V.L.Miroshnichenko. Application of splines for determining the velocity characteristic of a medium from a vertical seismic survey. Central European Journal of Mathematics, 2013. V.11, n.4, 779-786. 6. Yuriy S. Volkov, Yu. E. Anikonov, S.B. Gorshkalev, E. Yu. Derevtsov and S.V.Mal’tseva. A criterion for the horizontal homogeneity of a medium in the inverse kinematic problem of seismics. Journal of Mathematical Sciences, 2013. V.195, n.6, 741-753 7. Yuriy S. Volkov, V.T.Shevaldin and E.V.Strelkova. Local approximation by splines with displacement of nodes. Siberian Advances in Mathematics, 2013. V.23, n.1, 6975.

In: Mathematical Research Summaries. Volume 1 Editor: Matthew A. Rowe

ISBN: 978-1-53612-021-9 © 2017 Nova Science Publishers, Inc.

Chapter 16

DESISLAVA STOYANOVA VOYNIKOVA Affiliation: Plovdiv University Paisii Hilendarski, Faculty of Mathematics and Informatics, Plovdiv, Bulgaria

Address: 24 Tsar Asen street, 4000 Plovdiv, Bulgaria

Date of Birth: 5/25/1985

Education: PhD in Applied Mathematics and Modeling (2013), Plovdiv University Paisii Hilendarski; Bachelor and Master in Applied Mathematics (2009), Plovdiv University Paisii Hilendarski

Research and Professional Experience: She taught in bachelor degree level disciplines of applied mathematics, and statistics. She has published over 15 scientific papers in the field of applied mathematics, modeling and simulation in physics, environmental sciences, applied statistics and predictive data mining techniques.

Professional Appointments: Head assistant professor at the Department of Applied Mathematics and Modeling, Plovdiv University Paisii Hilendarski

Publications Last 3 Years: 1 . Iliev I. P., D. S. Voynikova, and S. G. Gocheva-Ilieva, Application of the classification and regression trees for modeling the laser output power of a copper bromide vapor laser, Mathematical Problems in Engineering, vol. 2013, Article ID 654845, pp. 1-10. Accepted 20 April, 2013, ISSN 1024-123X , http://dx.doi.org/10.1155/2013/654845

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Desislava Stoyanova Voynikova 2 . Voynikova D. S., S. G. Gocheva-Ilieva and I. P. Iliev, MARS Models of Laser Efficiency of Copper Bromide Laser, Proc. of Fifth Conference of the EuroAmerican Consortium for Promoting the Application of Mathematics in Technical and Natural Sciences, (AMiTaNS'2013), Albena, Bulgaria, June 24-29, 2013. Ed. M. Todorov, AIP Conference Proceedings, Vol. 1561, pp. 240-247, 2013. ISBN: 978-07354-1189-0. http://dx.doi.org/10.1063/1.4827234 3 . Gocheva-Ilieva S. G., Ivanov A. V., Voynikova D. S., Boyadzhiev D. T., Time Series Analysis and Forecasting for Air Pollution in Small Urban Area: an SARIMA and Factor Analysis Approach, Stoch. Env. Res. Risk A., vol. 28 (4), pp. 1045-1060, 2014, Springer, DOI: 10.1007/s00477-013-0800-4, ISSN: 1436-3240 (Print) 14363259 (Online) http://link.springer.com/article/10.1007/s00477-013-0800-4 4 . A.Ivanov, D. Voynikova, S. Gocheva-Ilieva, H. Kulina and I. Iliev, Using principal component analysis and general path seeker regression for investigation of air pollution and CO modeling, 7th Conference of the Euro-American Consortium for Promoting the Application of Mathematics in Technical and Natural Sciences, Albena, Bulgaria, June 28-July 3, 2015, AIP Conf. Proc. 1684, ed. M. Todorov, 100004, pp. 1-11 (2015); http://dx.doi.org/10.1063/1.4934341 5 . D.S. Voynikova, S. G. Gocheva-Ilieva, A. V. Ivanov and I. P. Iliev, Studying the effect of meteorological factors on the SO2 and PM10 pollution levels with refined versions of the SARIMA model, 7th Conference of the Euro-American Consortium for Promoting the Application of Mathematics in Technical and Natural Sciences, Albena, Bulgaria, June 28-July 3, 2015, AIP Conf. Proc. 1684, ed. M. Todorov, 100005, pp. 1-12 (2015); http://dx.doi.org/10.1063/1.4934342

In: Mathematical Research Summaries. Volume 1 Editor: Matthew A. Rowe

ISBN: 978-1-53612-021-9 © 2017 Nova Science Publishers, Inc.

Chapter 17

IRENA ZIZOVIC Affiliation: University of Belgrade, Faculty of Technology and Metallurgy

Address: Faculty of Technology and Metallurgy, Karnegijeva 4, 11000 Belgrade, Serbia

Date of Birth: 04/02/1969

Education: PhD degree: 2003-2006 at University of Belgrade, Faculty of Technology and Metallurgy MSc degree: 1992-1996 at University of Belgrade, Faculty of Technology and Metallurgy BSc degree: 1986-1992 in Chemical Engineering at University of Belgrade, Faculty of Technology and Metallurgy

Research and Professional Experience: -

High Pressure Technology Mathematical Modeling Food Engineering

Professional Appointments: 1992 – 2003

Teaching assistant at University of Belgrade, Faculty of Technology and Metallurgy 2006 – present Professor at University of Belgrade, Faculty of Technology and Metallurgy

Publications Last 3 Years: 1. M. Stamenic, I. Zizovic, The mathematics of modelling the supercritical fluid extraction of essential oils from glandular trichomes, Computers and Chemical Engineering 48 (2013) 89-95.

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Irena Zizovic 2. F. Meyer, M. Stamenic, I. Zizovic, R. Eggers, Fixed bed property changes during scCO2 extraction of natural materials – Experiments and modeling, Journal of Supercritical Fluids 72 (2012) 140-149. 3. J. Ivanovic, S. Dimitrijevic-Brankovic, D. Misic, M. Ristic, I. Zizovic, Evaluation and improvement of antioxidant and antibacterial activities of supercritical extracts from clove buds, Journal of Functional Foods 5 (2013) 416-423. 4. J. Ivanovic, F. Meyer, D. Misic, J. Asanin, P. Jaeger, I. Zizovic, R. Eggers, Influence of different pre-treatment methods on isolation of extracts with strong antibacterial activity from lichen Usnea barbata using carbon dioxide as a solvent, Journal of Supercritical Fluids, 76 (2013) 1-9. 5. M.A. Fanovich, J. Ivanovic, D. Misic, M.V. Alvarez, P. Jaeger, I. Zizovic, R. Eggers, Development of polycaprolactone scaffold with antibacterial activity by an integrated supercritical extraction and impregnation process, Journal of Supercritical Fluids, 78 (2013) 42-53.

PART II RESEARCH SUMMARIES

In: Mathematical Research Summaries. Volume 1 Editor: Matthew A. Rowe

ISBN: 978-1-53612-021-9 © 2017 Nova Science Publishers, Inc.

Chapter 18

JUSTIFICATION OF THE COURANT-FRIEDRICHS CONJECTURE FOR THE PROBLEM ABOUT FLOW AROUND WEDGE #

Alexander M. Blokhin and Dimitry L. Tkachev and Evgenia V. Mishchenko, PhD* Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences, Novosibirsk, Russia

RESEARCH SUMMARY In this book, the authors study the classical problem of a steady-state supersonic flow of an inviscid non-heat-conductive gas around an infinite plane wedge. As is known, if the vertex angle is sufficiently small, then from the theoretical point of view, the problem has two discontinuous solutions, one of which is associated with a strong shock wave (the gas velocity behind the shock wave is less than the sound speed) and the second one corresponds to the weak shock wave (the gas velocity behind the shock wave is, in general, larger than the sound speed). Justification of the Courant-Friedrichs conjecture at the linear level is discussed. The authors hope that this book will be useful for specialists in gas dynamics and in applied mathematics as well.

#

This chapter was previously published as a book: Justification of the Courant-Friedrichs Conjecture for the Problem About Flow Around Wedge, by Alexander M. Blokhin and Dimitry L. Tkachev. Edited by Evgenia V. Mishchenko, Ph.D., New York: Nova Publishers Inc., 2013. * Editor of volume; email: [email protected]

In: Mathematical Research Summaries. Volume 1 Editor: Matthew A. Rowe

ISBN: 978-1-53612-021-9 © 2017 Nova Science Publishers, Inc.

Chapter 19

PARTICLE SWARM OPTIMIZATION WITH RE-INITIALIZATION STRATEGIES FOR CONTINUOUS GLOBAL OPTIMIZATION

#

D. D. Kennedy1, H. Zhang1, G. P. Rangaiah1 and A. Bonilla-Petriciolet2 1

National University of Singapore, Department of Chemical and Biomolecular Engineering, Singapore 2 InstitutoTecnologico de Aguascalientes, Deparment of Chemical Engineering, Mexico

RESEARCH SUMMARY Particle Swarm Optimization (PSO) is a population-based algorithm inspired by social behavior of animals such as bird flocking and fish schooling. PSO algorithm can be easily implemented with few parameters involved, and several modifications have been introduced to the original PSO algorithm to discourage premature convergence in global optimization. In this study, we propose re-initialization strategies for improving the performance of PSO for continuous global optimization. The first re-initialization strategy focuses on individual particle level, where a particle whose pbest fails to improve after certain number of iterations will be reinitialized. The second re-initialization strategy focuses on the population level, where the entire population will be reinitialized. In this case, re-initialization is conducted when the number of pbests having objective function value similar to that of gbest exceeds a certain threshold number. The combination of these two re-initialization strategies has also been studied. The proposed PSO algorithms have been tested using 15 benchmark functions, each with both 10 and 30 variables. The results are compared with the efficient population utilization strategy PSO (EPUS-PSO), comprehensive learning PSO (CLPSO), cooperative PSO (CPSO), unified PSO (UPSO) and unified bare-bones PSO (UBBPSO). #

This chapter was previously published in Global Optimization: Theory, Developments and Applications, edited by Angelika Michalski, New York: Nova Publishers Inc., 2013.  Corresponding Author: Department of Chemical and Biomolecular Engineering, National University of Singapore, Singapore, 117576, e-mail: [email protected].

In: Mathematical Research Summaries. Volume 1 Editor: Matthew A. Rowe

ISBN: 978-1-53612-021-9 © 2017 Nova Science Publishers, Inc.

Chapter 20

PARTICLE SWARM GLOBAL OPTIMIZATION OF ORBITAL MANEUVERS #

Mauro Pontani Scuola di Ingegneria Aerospaziale, University “La Sapienza”, Rome, Italy

RESEARCH SUMMARY The particle swarm optimization algorithm is a population-based stochastic method developed in recent years and successfully applied in several fields of research, ranging from chemical engineering to computer science. It represents a very intuitive methodology for global optimization, inspired by the behavior of bird flocks while searching for food. The particle swarm optimization technique takes advantage of the mechanism of information sharing that affects the overall behavior of a swarm, with the intent of determining the optimal values of the unknown parameters of the problem under consideration. This work describes the application of the method to a variety of space trajectory optimization problems that exhibit multiple local optimal solutions. Specifically, the swarming algorithm is applied to: (i) transfer trajectories between two coplanar circular orbits; (ii) two-impulse transfer between two non-coplanar elliptic orbits; (iii) four-impulse rendezvous trajectory between a pursuer spacecraft and a target space vehicle; (iv) two impulse transfer from a low Earth orbit to a low Moon orbit. Despite its simplicity and intuitiveness, the particle swarm algorithm proves to be quite effective in finding the globally optimal solution to all of the applications considered in the chapter, with great numerical accuracy.

#

This chapter was previously published in Global Optimization: Theory, Developments and Applications, edited by Angelika Michalski, New York: Nova Publishers Inc., 2013.  Email: [email protected]

In: Mathematical Research Summaries. Volume 1 Editor: Matthew A. Rowe

ISBN: 978-1-53612-021-9 © 2017 Nova Science Publishers, Inc.

Chapter 21

FLOAT-ENCODED GENETIC ALGORITHM USED FOR THE INVERSION PROCESSING OF WELL-LOGGING DATA #

Norbert P. Szabó1 and Mihály Dobróka1,2 1

University of Miskolc, Department of Geophysics, Hungary MTA-ME Research Group for Earth Science and Engineering, Hungary

2

RESEARCH SUMMARY A Float-Encoded Genetic Algorithm is presented in this chapter for solving the welllogging inverse problem. The aim of the global inversion of well-logging data is to provide a robust and reliable estimate of petrophysical properties, such as porosity, water saturation, shale volume and mineral content, associated with geological structures. There are two possible ways to solve the interpretation problem. The first is a conventional inversion scheme, separately estimating the unknowns to different depths. In the forward modeling phase of the local inversion procedure the theoretical well-logging data set is calculated by using locally defined probe response functions, which are then fit to real data in order to estimate model parameters to one depth only. This procedure leads to a marginally overdetermined inverse problem, which results in relatively poor parameter estimates. A further disadvantage of the latter technique is that some crucial quantities, such as the thickness of layered geological formations, cannot be extracted by inversion because they do not appear explicitly in local response equations. A new inversion methodology introduced by the authors gives much more freedom in choosing the inversion parameters. The so-called interval inversion method inverts all data measured from a greater depth interval in a joint inversion process. By a series expansion-based discretization of the petrophysical model, a highly over-determined inverse problem can be formulated, enabling an estimation of the petrophysical parameters including new unknowns, such as zone parameters and layer #

This chapter was previously published in Global Optimization: Theory, Developments and Applications, edited by Angelika Michalski, New York: Nova Publishers Inc., 2013.  Corresponding author’s e-mail address: [email protected]

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Norbert P. Szabó and Mihály Dobróka

thicknesses, more accurately compared to local inversion methods. The authors give further references for several applications of the global inversion method. In this chapter, one synthetic and two field examples are presented to demonstrate the application of the Genetic Algorithm-based inversion method. It is shown that the combination of the new inversion strategy and global optimization tools forms a highly effective and adaptive algorithm for earth scientists who are interested in a more reliable calculation of the reserves of hydrocarbons and other mineral resources.

In: Mathematical Research Summaries. Volume 1 Editor: Matthew A. Rowe

ISBN: 978-1-53612-021-9 © 2017 Nova Science Publishers, Inc.

Chapter 22

THE PARTICLE COLLISION ALGORITHM: A METROPOLIS OPTIMIZATION METHOD

#

Wagner F. Sacco1*, Anderson Alvarenga de Moura Meneses1, Ana Carolina Rios-Coelho1 and Nélio Henderson2 1

2

Universidade Federal do Oeste do Pará, Brazil Instituto Politécnico da Universidade do Estado do Rio de Janeiro, Brazil

RESEARCH SUMMARY Stochastic optimization methods based on the simulated annealing paradigm have been actively developed in the last thirty years and successfully applied to many complex optimization problems. These methods though very powerful are not free from practical drawbacks, the main one being that performance is too sensitive to the choice of free parameters. Ideally, an optimization algorithm should not rely on user-defined or problemdependent parameters, except a stopping criterion. One such algorithm, that was recently introduced and applied to real-world problems, is reviewed here. Denoted the “Particle Collision Algorithm” (PCA), the algorithm is loosely inspired by the physics of nuclear particle collision reactions, particularly scattering and absorption. These events promote the exploration of the search space and the exploitation of its most promising areas. The PCA resembles in its structure that of simulated annealing and can also be considered a Metropolis algorithm, as a worse trial solution can be accepted with a certain probability. This acceptance may avoid the convergence to local optima. Since its introduction, some variants of the original algorithm have been created, and it has also been hybridized with other techniques. The PCA and its derivations have been successfully applied to real-world optimization problems, such as a nuclear reactor design optimization problem, radiative transference and pollutant localization inverse problems, chemical equilibrium nonlinear systems, and coursetimetabling problems.

#

This chapter was previously published in Global Optimization: Theory, Developments and Applications, edited by Angelika Michalski, New York: Nova Publishers Inc., 2013.

In: Mathematical Research Summaries. Volume 1 Editor: Matthew A. Rowe

ISBN: 978-1-53612-021-9 © 2017 Nova Science Publishers, Inc.

Chapter 23

CLASSIFIER-ASSISTED FRAMEWORKS FOR COMPUTATIONALLY EXPENSIVE OPTIMIZATION PROBLEMS #

Yoel Tenne Ariel University Centre, Ariel, Israel

RESEARCH SUMMARY The modern engineering design optimization process often replaces laboratory experiments with computer simulations. This setup formulates an optimization problem of a black-box function, namely, which has no analytic expression and which is computationally expensive to evaluate. However, computer simulations introduce an additional challenge into the design optimization process: often there will exist candidate designs which cause the simulation to fail, which implies that a large portion of the optimization resources may be wasted, and this can lead to a poor final result. To effectively handle such problems, this chapter describes two optimization frameworks which incorporate a classifier into the search. The classifier’s role is to predict which solutions are expected to crash the simulation, and this prediction is then used to bias the search towards solutions for which the simulation is expected to succeed. A baseline framework is described which incorporates a single classifier, followed by a more elaborate framework which selects an optimal type of classifier out of a family candidates. Performance analysis using a representative simulation-driven engineering problem of airfoil shape optimization shows the effectiveness of the proposed frameworks and highlights the merit of incorporating a classifier into the search.

#

This chapter was previously published in Global Optimization: Theory, Developments and Applications, edited by Angelika Michalski, New York: Nova Publishers Inc., 2013.  E-mail address: [email protected]

In: Mathematical Research Summaries. Volume 1 Editor: Matthew A. Rowe

ISBN: 978-1-53612-021-9 © 2017 Nova Science Publishers, Inc.

Chapter 24

CUTTING BOX STRATEGY: AN ALGORITHMIC FRAMEWORK FOR IMPROVING METAHEURISTICS FOR CONTINUOUS GLOBAL OPTIMIZATION# Wendel Melo1,2, Marcia Fampa1,2 and Fernanda Raupp3 1

Institute of Mathematics, Federal University of Rio de Janeiro, Brazil 2 Alberto Luiz Coimbra Institute - Graduate School and Research in Engineering (COPPE), Federal University of Rio de Janeiro, Brazil 3 Department of Industrial Engineering, Pontifical Catholic University of Rio de Janeiro, Brazil

RESEARCH SUMMARY In this work, the authors present a new framework to increase effectiveness of metaheuristics in seeking good solutions for the general nonlinear optimization problem, called Cutting Box Strategy (CBS). CBS is based on progressive reduction of the search space through the use of intelligent multi-starts, where solutions already obtained cannot be revisited by the adopted metaheuristic. Computational experiments with the CBS strategy are conducted with a variant of the population-based metaheuristic Differential Evolution to solve 36 test instances. The numerical results show that CBS can substantially increase the quality of the results of a metaheuristic applied for a nonlinear optimization problems.

#

This chapter was previously published in Global Optimization: Theory, Developments and Applications, edited by Angelika Michalski, New York: Nova Publishers Inc., 2013.  E-mail address: [email protected]

In: Mathematical Research Summaries. Volume 1 Editor: Matthew A. Rowe

ISBN: 978-1-53612-021-9 © 2017 Nova Science Publishers, Inc.

Chapter 25

RLS WIENER SMOOTHER FROM RANDOMLY DELAYED OBSERVATIONS IN LINEAR DISCRETE-TIME SYSTEMS #

Seiichi Nakamori* Department of Technology, Faculty of Education, Kagoshima University, Kagoshima, Japan

RESEARCH SUMMARY In this book, the new recursive least-squares (RLS) Wiener filter and fixed-point smoother are designed from randomly delayed observed values by one sampling time in linear discrete-time stochastic systems. The probability is given as a function of time. If the conditional probability is not a function of time, the length of the derivation for the RLS Wiener estimators becomes shorter than the current RLS Wiener algorithms for the fixedpoint smoothing and filtering estimates. The proof for deriving the RLS Wiener fixed-point smoother and filter is shown in the case of the conditional probability as a function of time k. A numerical simulation example in Chapter 4 shows that the fixed-point smoothing and filtering algorithms, proposed in this book, are feasible. The RLS Wiener estimators do not use the information of the variance of the input noise and the input matrix in the state equation, in comparison with the estimation technique by the Kalman filter. Hence, the RLS Wiener estimation technique has an advantage that the estimation accuracy of the RLS Wiener estimators is not influenced by the estimation errors for the input noise variance and the input matrix.

#

This chapter was previously published as a book: RLS Wiener Smoother from Randomly Delayed Observations in Linear Discrete-Time Systems, by Seiichi Nakamori, New York: Nova Publishers Inc., 2013. * email: [email protected]

In: Mathematical Research Summaries. Volume 1 Editor: Matthew A. Rowe

ISBN: 978-1-53612-021-9 © 2017 Nova Science Publishers, Inc.

Chapter 26

A NON-STANDARD PRACTICAL VARIATIONAL APPROACH VIA FRACTIONAL CALCULUS TO THE OPTIMAL CONTROL OF FRACTIONAL STOCHASTIC SYSTEMS DRIVEN BY WHITE NOISES

#

Guy Jumarie Department of Mathematics, University of Quebec at Montreal, Montreal, QC, Canada

RESEARCH SUMMARY The present chapter proposes a practical approach to the optimal control of some stochastic differential systems of fractional order, by combining fractional calculus, white noise calculus and Lagrangian variational calculus. The basic argument is that, if one comes back to the engineering mathematics framework which has been in fashion a few decades ago, it is possible to expand an approach, irrespective of Brownian motion, but instead involving the well known Gaussian white noise. Shortly, the basic elemental process is not the Brownian motion but the Gaussian white noise. Loosely speaking, the present contribution comprises three main parts. The first one is related to the essential of fractional calculus via fractional difference, the second one deals with variational fractional calculus for non-random variables, and then we shall so have at hand all the material which we need to tackle the stochastic optimal control of fractional systems by using the state moments as new dynamical states. Then, as a “beware of the dog” warning, we shall comments on some care which must be exercised when one describes dynamical systems by using fractional calculus on the one hand, and on the chains rules for fractional derivatives on the other hand. Incidentally, we shall come across a new approach to modelling fractional Brownian motion. There are many tricks not yet completely clarified and which, at first glance, could provide not quite accurate models. #

This chapter was previously published in Advances in Mathematics Research. Volume 18, edited by Albert R. Baswell, New York: Nova Publishers Inc., 2013.  E-mail address: jumarie.guy @ uqam.ca. Phone office: 1(415) 987 30 00, Ext 7792, Phone home: 1(450) 670 99 81, Facsimile: 1(514) 89 35.

In: Mathematical Research Summaries. Volume 1 Editor: Matthew A. Rowe

ISBN: 978-1-53612-021-9 © 2017 Nova Science Publishers, Inc.

Chapter 27

REPRESENTATION OF THE SHOE-LAST BOTTOM BASED ON COMPUTER ALGORITHMS AND LASER METROLOGY #

J. Apolinar Muñoz-Rodríguez Centro de Investigaciones en Optica, A. C., León, Guanajuato, Mexico

RESEARCH SUMMARY We present a review of our computer algorithms to represent the topography of the shoelast bottom. The study of this chapter involves: laser metrology, shape representation, Bezier networks, and vision parameters. The proposed technique retrieves the topography of the shoe-last bottom by a Bezier network via laser scanning. This network performs the contouring based on the behavior of the laser line when it is projected on the surface. Additionally, the vision parameters are determined based on the network and image processing of the laser line. From the retrieved surface, the Bezier network constructs a mathematical model to represent the shoe-last bottom. This method provides a better fitting than the methods that perform the modeling of the shoe-last bottom. It is because the network is forced to produce the known surface data. Thus, the proposed model improves the accuracy of the representation of the shoe last bottom. Also, the model reduces the number of the terms to determine the shape representation. Therefore, the computational process consumes less time to achieve the representation than the traditional models. The viability of the proposed method is proven by an evaluation based on the model of the shoe-last bottom performed via NURBS.

#

This chapter was previously published in Advances in Mathematics Research. Volume 18, edited by Albert R. Baswell, New York: Nova Publishers Inc., 2013.  E-mail address: [email protected]; Tel: (477) 441 42 00; Leon, Gto, 37150 Mexico.

In: Mathematical Research Summaries. Volume 1 Editor: Matthew A. Rowe

ISBN: 978-1-53612-021-9 © 2017 Nova Science Publishers, Inc.

Chapter 28

ROLE OF METROLOGY ON CURRENT FOOD SAFETY ISSUES IN CHINA #

Can Quan, Ting Huang and Hongmei Li Division of Chemistry, National Institute of Metrology, Chaoyang District, Beijing, China

RESEARCH SUMMARY The rapid expansion of food industry and the highly decentralized nature of the production, processing and marketing sectors of this new industry have created important food safety problems. The increased concern about China food safety such as milk powder, beef has coincided with increased consciousness of the safety of all foods in originally from China. The objective of this review is to introduce current food safety status of China including the official agencies, standards, assurance systems, testing laboratories, certified reference materials and other challenging facing China, and then some recommendations were made to improve food safety in China.

#

This chapter was previously published in Advances in Mathematics Research. Volume 18, edited by Albert R. Baswell, New York: Nova Publishers Inc., 2013.  E-mail address: [email protected]

In: Mathematical Research Summaries. Volume 1 Editor: Matthew A. Rowe

ISBN: 978-1-53612-021-9 © 2017 Nova Science Publishers, Inc.

Chapter 29

SYMMETRIC RANDOM VECTORS FOR WHICH THE JOINT QUANTUM OPERATORS SPAN A LIE ALGEBRA

#

Aurel I. Stan* Department of Mathematics, Ohio State University at Marion, Marion, Ohio, US

RESEARCH SUMMARY The joint quantum (annihilation, creation, and preservation) operators of a finite family of classic (commuting) random variables, having finite moments of all orders, are introduced first. The authors make the observation that, in the one–dimensional case, the random variables whose vector space spanned by the quantum and identity operators, equipped with the commutator bracket, forms a Lie algebra, are exactly the Meixner random variables, except the symmetric two parameter hyperbolic secondly distributed ones and the symmetric binomial random variables. The authors call these random variables Meixner random variables of class L, and use the Lie Algebra property to define the Meixner random vectors of class L. The two–dimensional non–degenerate Meixner random vectors (X, Y) of class L have already been studied and described completely before. The only Meixner random variables, that were not of class L, are exactly those symmetric random variables, whose vector space spanned by the annihilation, creation, and the commutator between the annihilation and creation operators, equipped with the commutator bracket, forms a Lie algebra. The authors call them Meixner random variables of class S. We use the Lie Algebra property to define the Meixner random vectors of class S and describe all two– dimensional random vectors (X, Y ) of this type. Many computations have been carried out in the one–dimensional case and not so much is known in the multi–dimensional case. This chapter shows that the computations in the multi–dimensional case are much more laborious #

This chapter was previously published in Advances in Mathematics Research. Volume 18, edited by Albert R. Baswell, New York: Nova Publishers Inc., 2013. * E-mail address: [email protected]

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Aurel I. Stan

than those in the one–dimensional case. Moreover, some consistency conditions, that do not appear in the one–dimensional case, show up in the multi–dimensional case. In order to characterize the two–dimensional non–degenerate Meixner random vectors of class S, the authors have employed a combination of techniques that include both heavy computations and simple invertible affine transformations that ease those computations.

In: Mathematical Research Summaries. Volume 1 Editor: Matthew A. Rowe

ISBN: 978-1-53612-021-9 © 2017 Nova Science Publishers, Inc.

Chapter 30

PSEUDO REGULARITY IN COMMUTATIVE BANACH ALGEBRAS #

J. C. Prajapati Department of Mathematical Sciences, Faculty of Applied Sciences, Charotar University of Science and Technology (CHARUSAT), Changa, Gujarat, India

RESEARCH SUMMARY Functional analysis is broadly the study of normed linear space, Banach space and functionals on them. The examples for this subject come mainly from classical function spaces. Now many of these spaces have the additional algebraic structure; they are algebras. Not only that, but the corresponding norm is also related with multiplication operation. In Chapter 5 the authors are going to study a special aspect of this class of objects known as Banach algebras. Banach algebras were formally defined and studied by Gelfand around 1941. Actually he and his Russian school gave a beautiful characterization of commutative Banach algebras, known as the Gelfand theory. This theory has many interesting applications in other branches of mathematics. In the theory of Banach algebras, the algebraic structure plays an important role and the algebraic and normed structure are nicely related, e.g. if the algebra has an identity, then the set of invertible(regular) elements is open. Well this leads one to think that it may be possible to generalize the concept of invertibility using the norm. Arens did that. He defined the idea of pseudo regularity. Johnson related the idea of pseudo regularity to introduce a new algebraic idea ’auxiliary multiplication’. Two more generalization of invertibility viz. subregularity and invertibility are also studied by Arens and Johnson.

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This chapter was previously published in Advances in Mathematics Research. Volume 18, edited by Albert R. Baswell, New York: Nova Publishers Inc., 2013.

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In this chapter, the authors mainly study this generalization, their inter-relation and some examples. The authors need some preliminaries of Banach algebras for that. They discuss this, in this chapter. In the second chapter the work of Arens and Johnson. The nonlinear barotropic vorticity equation (BVE) describing the vortex dynamics of viscous incompressible and forced fluid on a rotating two-dimensional unit sphere is considered. Orthogonal projectors and fractional derivatives on the sphere are introduced. Hilbert and Banach spaces of smooth functions on the sphere and some embedding assertions are given. The unique solvability of a nonstationary problem of vortex dynamics of viscous incompressible fluid on a rotating sphere is shown. The existence of a weak solution to stationary problem is proved too, and a condition guaranteeing the uniqueness of solution is also given.

In: Mathematical Research Summaries. Volume 1 Editor: Matthew A. Rowe

ISBN: 978-1-53612-021-9 © 2017 Nova Science Publishers, Inc.

Chapter 31

DYNAMICS OF VISCOUS BAROTROPIC FLUID ON A ROTATING SPHERE #

Yuri N. Skiba* Centro de Ciencias de la Atmósfera Universidad Nacional Autónoma de México, Mexico

RESEARCH SUMMARY The asymptotic behavior of solutions of nonstationary BVE as t → ∞ is studied. Particular forms of the external vorticity source have been found which guarantee the existence of such bounded set in a phase space that eventually attracts all the BVE solutions. It is shown that the asymptotic behavior of the BVE solutions depends on both the structure and the smoothness of external vorticity source. Sufficient conditions for the global asymptotic stability of both smooth and weak solutions are also given. Simple attractive sets of a viscous incompressible fluid on a sphere under quasiperiodic polynomial forcing are considered. Each set is the BVE quasi-periodic solution of the complex (2n + 1)-dimensional subspace Hn of homogeneous spherical polynomials of degree n. The Hausdorff dimension of its trajectory, being an open spiral densely wound around a 2n-dimensional torus in Hn, equals to 2n. As the generalized Grashof number G becomes small enough then the basin of attraction of such spiral solution is expanded from Hn to the entire BVE phase space. It is shown that for given G, there exists an integer nG such that each spiral solution generated by a forcing of Hn with n ≥ nG is globally asymptotically stable. Thus, whereas the dimension of the fluid attractor under a stationary forcing is limited above by G, the dimension of the spiral attractive solution (equal to 2n) may, for a fixed bounded G, become arbitrarily large as the degree n of the quasi-periodic polynomial forcing grows. Since the small scale quasi-periodic functions, unlike the stationary ones, more adequately depict #

This chapter was previously published in Advances in Mathematics Research. Volume 18, edited by Albert R. Baswell, New York: Nova Publishers Inc., 2013. * E-mail address: [email protected], Tel: (5255) 5622-4247, Fax: (5255) 5622-4090, Address: Centro de Ciencias de la Atmósfera, Universidad Nacional Autónoma de México, Av. Universidad # 3000, Ciudad Universitaria, C. P. 04510, México, D. F., Mexico

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Yuri N. Skiba

the BVE forcing in the atmosphere, this result is of meteorological interest and shows that the dimension of attractive sets depends not only on the forcing amplitude, but also on its spatial and temporal structure. This example also shows that the search of finite-dimensional global attractor in the barotropic atmosphere is not well justified.

In: Mathematical Research Summaries. Volume 1 Editor: Matthew A. Rowe

ISBN: 978-1-53612-021-9 © 2017 Nova Science Publishers, Inc.

Chapter 32

AN EFFICIENT NUMERICAL METHOD FOR THE SOLUTION OF NONLINEAR DIFFUSION EQUATIONS ON A SPHERE #

Yuri N. Skiba1,* and Denis M. Filatov2,± 1

Centro de Ciencas de la Atmosfera (CCA), Universidad Nacional Autonoma de Mexico (UNAM), Cd. Universitaria, Mexico D. F., Mexico 2 Centro de Investigacion en Computacion (CIC), Instituto Politecnico Nacional (IPN), Mexico D. F., Mexico

RESEARCH SUMMARY A new method for the numerical simulation of the nonlinear diffusion phenomena on a sphere is developed in in this chapter. The core of the method is operator splitting by coordinates that allows representing the sphere by two different coordinate maps. This results in 1D second- and fourth-order computationally cheap finite difference schemes with trivial periodic boundary conditions. The schemes possess the properties imposed by the original diffusion equation: they are balanced and dissipative. Numerical results demonstrate the skillfulness of the approach in simulating diverse nonlinear diffusion phenomena on a sphere.

#

This chapter was previously published in Advances in Mathematics Research. Volume 18, edited by Albert R. Baswell, New York: Nova Publishers Inc., 2013. * E-mail address: skiba@unam. ± E-mail address: denisfilatov@gmail.

In: Mathematical Research Summaries. Volume 1 Editor: Matthew A. Rowe

ISBN: 978-1-53612-021-9 © 2017 Nova Science Publishers, Inc.

Chapter 33

A MATHEMATICAL MODELING APPROACH TO THE SLUG FLOW PROBLEM IN OIL PRODUCTION #

Airam Sausen, Paulo Sérgio Sausen, Maurício de Campos and Leandro Kreuzberger* Master’s Program in Mathematical Modeling, Regional University of Northwestern Rio Grande do Sul State (UNIJUÍ), Ijuí – RS – Brazil

RESEARCH SUMMARY This chapter presents the development of a dynamic model based in the mass conservation equations for a pipeline-separator system under the slug flow. The model proposed has 5 (five) Ordinary Differential Equations (ODEs) coupled nonlinear, 6 (six) tuning parameters and more than 40 (forty) internal, geometric and transport equations that have been obtained by coupling both the simplified dynamic model of Storkaas for a pipeline system under the slug flow, and the model for a biphase horizontal cylindrical separator. This paper also presents the application of a methodology for sensitivity analysis of the dynamic model whose objective is to determine the effect of the variations of the tuning parameters on the results obtained by applying the dynamic model. Extensive simulation results have shown that the dynamic model represented in a satisfactory way the slug flow in pipeline system as well as within the separator and that the dynamic model is highly sensitive to changes in its tuning parameters.

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This chapter was previously published in Advances in Mathematics Research. Volume 18, edited by Albert R. Baswell, New York: Nova Publishers Inc., 2013. * E-mail addresses: {airam,sausen,campos}@unijui.edu.br,[email protected]

In: Mathematical Research Summaries. Volume 1 Editor: Matthew A. Rowe

ISBN: 978-1-53612-021-9 © 2017 Nova Science Publishers, Inc.

Chapter 34

NATIVE STATISTICS FOR NATURAL SCIENCES

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Nabil Semmar* University of Tunis El Manar, Tunis, Tunisia

RESEARCH SUMMARY "Native Statistics for Natural Sciences" is a book which presents step-by-step the interest of several complementary and chained tools helping to statistically analyze natural systems to gradually understand and control their complexity. These different tools are organized into a serial of chapters which are extensively illustrated by intuitive figures and simple numerical examples. Natural systems are characterized by a big complexity linked to high diversity and variability of their quantitative and qualitative states. Such variability is linked to functional events and evolutional trends manifesting at different scales of system and generating gradual or frank differences between its elements. Understanding structural and functional aspects of natural systems requires serials of statistical analyses implying system decomposition into elementary or homogeneous components (subsets, subspaces) a priori. At a later stage, computational, graphical and modeling tools are applied on different components to explore and control system complexity and variability. Statistics represent a large field of applied mathematics aiming to extract and analyze information from sampled data issued from studied systems or populations. Extraction of reliable information from systems requires a priori the application of strategic rules by which the intrinsic variability and extrinsic limits of such systems are considered. These strategic rules are given by sampling designs and experimental designs which are applied for open and close systems, respectively. These two types of statistical designs are also appropriate for a posteriori analysis of complex systems under respectively exploratory or predictive aspects:

#

This chapter was previously published as a book: Native Statistics for Natural Sciences, by Nabil Semmar, New York: Nova Publishers Inc., 2013. * email address: [email protected]

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Nabil Semmar 1. Random systems containing infinite number of diversified elements within wide heterogeneous spaces require appropriate decomposition and sampling rules for their studying. Such rules are associated to different sampling designs by which small sets of elements (samples) are reliably collected to proceed to an exploratory analysis of several variability dimensions in the studied random system. 2. Due to their targeted nature, controlled systems are studied by delimiting their studied spaces by well-defined variation ranges of influent factors and integrating multi-way variations of studied system response. Such constraints and control rules of systems are given by several designs of experiments from which system response(s) can be analyzed and modeled to be optimized and predicted.

Collected data from sampling or experimental designs (including descriptor parameters, influent factors and system response) will be subjected to several types of statistical calculations and graphical visualizations to carry out exploratory or predictive analyses of system states, behaviors and trends: 1. From a random sample of n points, state levels and variability aspects of population can be accessed by calculating location, dispersion, precision and shape parameters. These parameters are also used to carry out robust comparisons between sample data and some reference values leading to detection of (1a) trends (sub-populations) within the studied population and (1b) new populations. The different induction tools helping to identify general states and variation fields of population from a finite sizesample are known by the term of "statistical inference". Beyond estimation and comparison of population characteristics, scale and probability distribution analyses of sampled data are applied to highlight organization laws governing relative frequencies and space occupation of system elements. 2. Controlled systems, initially subjected to experimental designs, are constrained to variations within well-defined geometric space with cubic, spherical or triangular types. Such spatial geometries of experimental fields depend both on the types of controlled factors a priori and on precision level of system response a posteriori. Therefore, recorder system response is statistically analyzed to (2a) predict its variations or (2b) optimize its levels in relation to controlled factors. These two aims concerning systems control are reached by determining efficient linear combinations of factors on response prediction (2a), and by graphically analyzing variation trajectories of response within the whole experimental field leading to identify some interesting (desired) variation area(s) (2b).

In: Mathematical Research Summaries. Volume 1 Editor: Matthew A. Rowe

ISBN: 978-1-53612-021-9 © 2017 Nova Science Publishers, Inc.

Chapter 35

DETERMINISTIC AND RANDOM EVOLUTION

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Jens Lorenz* Dept. of Mathematics and Statistics, The University of New Mexico, Albuquerque, NM, USA

RESEARCH SUMMARY The first notes for this text were written during the summers of 2008–2010 when I taught a short course on mathematical modeling at the University of New Mexico. The audience consisted mostly of undergraduate mathematics students, and an aim of the course was to interest them in math at the graduate level. The students had some basic knowledge of ordinary differential equations and numerics. I tried to build on this foundation, but instead of increasing the technical skills of the students, I tried to lead them to more fundamental questions. What can one model with differential equations? What is determinism? If the universe evolves deterministically, what about free will and responsibility? Does it help if there are elements of randomness in the laws of evolution? Of course, these are deep questions, and in this text we can only scratch the surface in our discussion. Nevertheless, mathematics — even at a rather elementary level — may help to clarify what is at stake. Throughout, I try to put the discussion into historical context. For example, the text contains a rather detailed description of the derivation of Kepler’s laws of planetary motion using ordinary differential equations. After all, Newton’s great success in deriving these laws were an important starting point of the scientific revolution and a deterministic world view. It made classical mechanics a model for all sciences. Even if a deterministic description of an evolution is possible, there are often practical limitations of predictability because of the exponential growth in time of any uncertainty in the initial condition. Iteration with the logistic map gives an example. However, even if the accurate determination of future states is impractical, the average behavior of a system may #

This chapter was previously published as a book: Deterministic and Random Evolution, by Jens Lorenz, New York: Nova Publishers Inc., 2013. * email address: [email protected]

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still be very robustly determined. The logistic map again serves as an example. Do we have a similar situation for weather and climate? We cannot predict the weather two weeks in advance, but it may still be possible to determine the average weather 30 years from now. There are similarities to random evolution. When throwing a fair coin, we cannot predict the outcome of the n–th throw, but we can be rather certain to have between 450 and 550 heads in a thousand throws. If you do not want to compute the exact probability for this claim and also do not want to throw a coin many thousand times, you can test the claim using a Matlab code and Matlab’s random number generator. Some simple Matlab codes are provided in the text. They may encourage the readers to get their own experience students, with models for deterministic or random evolution. The mathematical level of the text corresponds to the ability and experience of undergraduate mathematics students making the critical transition to graduate work. The text is accessible if you had an undergraduate course on ordinary differential equations and numerical methods. For some parts, it is good to be familiar with elementary concepts of probability and statistics, though the concepts will be reviewed in the text. The course was part of an MCTP program, Mentoring through Critical Transition Points, supported by the NSF. This material is based upon work supported by the National Science Foundation under Grant No. 0739417.

In: Mathematical Research Summaries. Volume 1 Editor: Matthew A. Rowe

ISBN: 978-1-53612-021-9 © 2017 Nova Science Publishers, Inc.

Chapter 36

FOUNDATIONS OF ISO-DIFFERENTIAL CALCULUS. VOLUME 1 #

Svetlin Georgiev* Faculty of Mathematics and Informatics, Department of Differential Equations, Sofia University, Sofia, Bulgaria

RESEARCH SUMMARY The 'genious idea' is the Santilli's generalization of the basic unit of quantum mechanics into an integro-differential operator. This depends on local variables, and it is assumed to be the inverse of the isotopic element (the Santilli isounit). It was believed for centuries that the differential calculus is independent of the assumed basic unit, since the latter was traditionally given by the trivial number 1. Santilli has disproved this belief by showing that the differential calculus can be dependent on the assumed unit by formulating the isodifferential calculus with basic isodifferential. In this book, the authors introduce the main definitions and properties of isonumbers, isofunctions and isodifferentials. The book is provided with examples and exercises making it suitable for an introductory one- or two-semester undergraduate course on some of the major aspects of isodifferential calculus. Alternatively, it may be used for beginning graduate level course and as a reference work. With exercises at the end of each chapter and its straightforward writing style, the book addresses readers who have no prior knowledge on this subject but have a basic background in graduate mathematics courses, such as theory of functions and differential calculus.

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This chapter was previously published as a book: Foundations of Iso-Differential Calculus. Volume 1, by Svetlin Georgiev, New York: Nova Publishers Inc., 2014. * Email: [email protected] or [email protected]

In: Mathematical Research Summaries. Volume 1 Editor: Matthew A. Rowe

ISBN: 978-1-53612-021-9 © 2017 Nova Science Publishers, Inc.

Chapter 37

INTRODUCTION TO GEOMETRY AND RELATIVITY

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David C. Mello* Department of Mathematics, John Hazen White School of Arts & Sciences, Johnson & Wales University, Providence, Rhode Island, USA

RESEARCH SUMMARY This book provides a lucid introduction to both modern differential geometry and relativity for advanced undergraduates and first-year graduate students of applied mathematics and physical sciences. This book meets an overwhelming need for a book on modern differential geometry and relativity that is student-friendly, and which is also suitable for self-study. The book presumes a minimal level of mathematical maturity so that any student who has completed the standard Calculus sequence should be able to read and understand the book. The key features of the book are: • • • •

Detailed solutions are provided to the exercises in each chapter. Many of the ‘missing steps’ that are often omitted from standard mathematical derivations have been provided to make the book easier to read and understand. A detailed introduction to Electrodynamics is provided so that the book is accessible to students who have not had a formal course in this area. n its treatment of modern differential geometry, the book employs both a modern, coordinate-free approach, and the standard coordinate-based approach. This makes the book attractive to a large audience of readers.

Also, the book is particularly attractive to professional non-specialists who would like an easy to read introduction to the subject.

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This chapter was previously published as a book: Introduction to Geometry and Relativity, by David C. Mello, New York: Nova Publishers Inc., 2013. * email address: [email protected]

In: Mathematical Research Summaries. Volume 1 Editor: Matthew A. Rowe

ISBN: 978-1-53612-021-9 © 2017 Nova Science Publishers, Inc.

Chapter 38

AN OVERVIEW ON THEORIES AND METHODS OF SELF-ORGANIZATION

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WenJun Zhang Sun Yat-sen University, Guangzhou, China International Academy of Ecology and Environmental Sciences, Hong Kong

RESEARCH SUMMARY Self-organization is a universe mechanism in nature. Self-organizing systems are the systems which can evolve and improve the organizational behavior or structure by themselves. In a self-organizing system, the system evolves automatically to form an ordered structure based on some compatible rules. Without any external instruction and force, the self-organizing system emerges only from the interactions between the basic components of the system. In this chapter, theories and methods of self-organization are briefly overviewed.

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This chapter was previously published in Self-organization: Theories and Methods, edited by WenJun Zhang, New York: Nova Publishers Inc., 2013.  E-mail: [email protected], [email protected]

In: Mathematical Research Summaries. Volume 1 Editor: Matthew A. Rowe

ISBN: 978-1-53612-021-9 © 2017 Nova Science Publishers, Inc.

Chapter 39

AN ANT COLONY OPTIMIZATION-BASED APPROACH OF FEATURE SELECTION FOR EFFICIENT CLASSIFICATION OF VERY SMALL DATASETS BY MINING PATTERNS #

N. K. Sreeja*1 and A. Sankar2 1

Department of Computer Applications, Sri Krishna College of Technology, India 2 PSG College of Technology, India

RESEARCH SUMMARY Classification is a data mining functionality that assigns instances in a collection to target classes. The goal of classification is to accurately predict the target class for an unlabelled sample by learning from instances described by a set of attributes and a class label. Conventional classification methods specified in literature are less efficient in classifying very small datasets with repeated attribute values. To overcome this drawback, the study explores a classification method by mining similar patterns among the instances in very small datasets. Classification by Mining Patterns (CMP) algorithm is proposed to predict the class label of the unlabelled sample by mining similar patterns among the instances in the dataset. To mine similar patterns, the instances in the dataset belonging to the same class label are grouped. The instances in each group that differ by one attribute value are merged. Such merged instances form mined patterns. To predict the class label of the unlabelled samples, the attribute values in the mined patterns are compared with the corresponding attribute values of the unlabelled sample. The count of number of attribute values in the mined patterns matching with that of the unlabelled sample gives the attribute match count. The mined patterns having the maximum attribute match count are grouped and the majority class label #

This chapter was previously published in Self-organization: Theories and Methods, edited by WenJun Zhang, New York: Nova Publishers Inc., 2013. * E-mail: [email protected].

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of the mined patterns is predicted as the class label of the unlabelled sample. To choose the attributes in the mined patterns for comparison, an Ant Colony Optimization based Feature Selection Mined Patterns (ACOFSMP) is proposed. Simulation results are shown to prove that the CMP algorithm is efficient for classifying very small datasets with repeated attribute values.

In: Mathematical Research Summaries. Volume 1 Editor: Matthew A. Rowe

ISBN: 978-1-53612-021-9 © 2017 Nova Science Publishers, Inc.

Chapter 40

SELF-ORGANIZATION AND TASK ALLOCATION: AN APPLICATION TO ANT ALGORITHMS #

Jose B. Escario, Juan F. Jimenez, and Jose M. Giron-Sierra Department of Arquitectura de Computadores y Automatica Universidad Complutense, Spain, Madrid

RESEARCH SUMMARY The aim of this chapter is to present an auto-organization study in the context of Ant Colony Optimization (ACO). When using heuristic optimization algorithms, it is needed to decide how to share efforts between the exploration of the latest solutions, and the exploitation of those which were previously discovered. In classical ACO algorithms, this decision is taken beforehand by setting up various algorithm parameter values. Usually it is necessary to change them every time the latest or newest problem is tackled. Our purpose with ACO is to introduce a self-organization dynamic that allows for the balance between exploitation and the exploration. Inspired by biological studies on the organization of actual ant colonies, two kinds of ants are defined: one dedicated to the exploration, and the other assigned to the exploitation. This defined population dynamics shall establish the relationship between both populations. This allows to self-regulate the populations between each of them, according to the quality of the solutions found. The ultimate outcome developed is the Ant Colony Extended (ACE), a new algorithm with the capability to self-organize, which eliminates the necessity of using parameters. This chapter is focused on the population dynamics and its influence on the algorithm’s behavior. The results are promising and encourage further investigation of how to apply this approach to other heuristic optimization algorithms.

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This chapter was previously published in Self-organization: Theories and Methods, edited by WenJun Zhang, New York: Nova Publishers Inc., 2013.  E-mail address: [email protected]

In: Mathematical Research Summaries. Volume 1 Editor: Matthew A. Rowe

ISBN: 978-1-53612-021-9 © 2017 Nova Science Publishers, Inc.

Chapter 41

THE GENERALIZED PARTICLE SWARM OPTIMIZATION ALGORITHM WITH APPLICATION EXAMPLES #

Željko S. Kanović, Milan R. Rapaić, Zoran D. Jeličić, Milan J. Rackov, Mirna N. Kapetina and Jelena T. Atanacković-Jeličić Faculty of Technical Sciences, Novi Sad, Serbia

RESEARCH SUMMARY In this chapter, a generalization of the popular and widely used Particle Swarm Optimization (PSO) algorithm is presented. This novel optimization technique, named Generalized PSO (GPSO), is inspired by linear control theory. It overcomes some typical flaws of the classical PSO, enabling direct control over the key aspects of particle dynamics during the optimization process. The basic idea of this algorithm with its detailed theoretical and empirical analysis is presented, and parameter-tuning schemes are proposed. GPSO is also compared to the classical PSO and Genetic Algorithm (GA) on a set of benchmark problems. The presented results demonstrate the effectiveness of the proposed algorithm. Finally, two practical engineering applications of the GPSO algorithm are described, in the area of optimal gear design and architecture and urban design.

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This chapter was previously published in Self-organization: Theories and Methods, edited by WenJun Zhang, New York: Nova Publishers Inc., 2013.

In: Mathematical Research Summaries. Volume 1 Editor: Matthew A. Rowe

ISBN: 978-1-53612-021-9 © 2017 Nova Science Publishers, Inc.

Chapter 42

WEIGHTS AND STRUCTURE DETERMINATION OF ARTIFICIAL NEURONETS #

Yunong Zhang, Xiaotian Yu, Lin Xiao, Weibing Li and Zhengping Fan School of Information Science and Technology, Sun Yat-sen University, Guangzhou, Guangdong, China

RESEARCH SUMMARY Artificial neuronets (AN), especially with error back-propagation (BP) training algorithms, have been widely investigated and applied in various scientific and engineering fields. However, BP-type neuronets, which are self-adaptive systems, have shown some inherent weaknesses, such as, the possibility of being trapped into local minima, the difficulty in choosing appropriate learning rate, and most importantly, the inability to determine the optimal neuronet structure. To solve the inherent weaknesses of AN, lots of improvements for BP-type algorithms have been investigated. However, as researchers (including the authors) realize and experience quite frequently, the inherent weaknesses of BP-type neuronets still exist. In this chapter, differing from others’ algorithmic improvements on the training procedure, our way about the problem solving exploits some elegant structure-design, parameter-setting, pseudoinverse and numerical optimization techniques. In other words, a new kind of AN using linearly-independent or orthogonal polynomials as activation functions, is presented and analyzed by us (the authors). These finally lead us to propose a weights and structure determination (WASD) method, which is based on a weightsdirect determination (WDD) method, for our presented feedforward AN. Based on the authors’ previous work, single-input neuronets equipped with the WASD method have successfully overcome the above weaknesses. To investigate and verify two- or multiple-input neuronets equipped with this method, the authors firstly put forward various novel neuronets based on #

This chapter was previously published in Self-organization: Theories and Methods, edited by WenJun Zhang, New York: Nova Publishers Inc., 2013.  E-mail addresses: [email protected]; [email protected]

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different activation functions. Then, corresponding WASD algorithms are proposed for the presented neuronets. For better performance (e.g., more efficiency and conciseness in selforganizing systems), the authors further propose pruning techniques in the neuronet structure determination. Finally, based on various target functions, numerical results further substantiate the efficacy of the proposed neuronets equipped with the corresponding WASD algorithms, which shows the better performance in terms of training (or say, approximation or learning), generalization (or say, testing or validation) and prediction.

In: Mathematical Research Summaries. Volume 1 Editor: Matthew A. Rowe

ISBN: 978-1-53612-021-9 © 2017 Nova Science Publishers, Inc.

Chapter 43

LOW-DIMENSIONAL STRUCTURES EMBEDDED IN HUMAN LOCOMOTION: DATA ANALYSIS AND MODELING #

Shinya Aoi Dept. of Aeronautics and Astronautics, Graduate School of Engineering, Kyoto University, Yoshida-honmachi, Sakyo-ku, Kyoto, Japan JST, CREST, Chiyoda-ku, Tokyo, Japan

RESEARCH SUMMARY Humans produce adaptive locomotion through dynamic interactions among the nervous system, the musculoskeletal system, and the environment in a self-organized manner. A human musculoskeletal system has more degrees of freedom (DOFs) than necessary for locomotion and humans solve the redundancy problem in some way to establish locomotion. It has been suggested that individual DOFs are not manipulated independently, but some DOFs are functionally connected by object tasks to reduce the number of DOFs. These relationships among DOFs appear as low-dimensional structures in the DOFs. This chapter shows such low-dimensional structures in joint movements and muscle activities (kinematic and muscle synergies) during human locomotion based on the analysis of measured data. In addition, it shows a constructive approach using a computer simulation with a neuromusculoskeletal model based on anatomical and physiological findings to examine the functional roles of the low-dimensional structures that generate adaptive locomotor behaviors through dynamic interactions among the nervous system, the musculoskeletal system, and the environment.

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This chapter was previously published in Self-organization: Theories and Methods, edited by WenJun Zhang, New York: Nova Publishers Inc., 2013.  Correspondence: shinya [email protected]

In: Mathematical Research Summaries. Volume 1 Editor: Matthew A. Rowe

ISBN: 978-1-53612-021-9 © 2017 Nova Science Publishers, Inc.

Chapter 44

SELF-ORGANIZATION IN MOTION OF A SET OF LIVING INDIVIDUALS

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Milovan Živanović1,* and Ivan Stojković2, 1

Digital Control Systems Oziris, Sopot, Serbia 2 Mihajlo Pupin Institute, Belgrade, Serbia

RESEARCH SUMMARY This paper discusses self-organized movement of a set of some individuals. It is adopted that individuals perceive reality as its projection on coordinate system that is firmly attached to the individual. Movement of individuals is interpreted as the movement of points in this coordinate system according to the algorithms by which each individual is equipped. The projection of reality and other individuals simultaneously changing the parameters of algorithms and simultaneously impose constraints on the movement of these points. Set of individuals moves so that each individual performs arbitrary motion within the allowed constraints in one of two ways: a) individuals follow one or more leaders, b) individuals preserve system configuration during movement, i.e. not change certain typical magnitude of set. Motion of individuals or set of individuals from one position to another always takes place according to the functions of natural impulses. Shortly we’ll give comparison between function of the natural impulse and other custom-fit functions.

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This chapter was previously published in Self-organization: Theories and Methods, edited by WenJun Zhang, New York: Nova Publishers Inc., 2013. * E-mail address: [email protected].

In: Mathematical Research Summaries. Volume 1 Editor: Matthew A. Rowe

ISBN: 978-1-53612-021-9 © 2017 Nova Science Publishers, Inc.

Chapter 45

A CELLULAR AUTOMATA METHOD FOR SPECIES MIGRATION PROCESS IN A HETEROGENEOUS ENVIRONMENT

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WenJun Zhang*1,2, YanHong Qi1 and ZhiGuo Zhang1 1

2

Sun Yat-sen University, Guangzhou, China International Academy of Ecology and Environmental Sciences, Hong Kong

RESEARCH SUMMARY Habitat diversity is an important mechanism for species migration and distribution. A stochastic model for species migration in a heterogeneous environment is described in this chapter. This model is used to describe various types of dynamics in biological processes, such as periodic oscillation, monotonic increase and decline, and fluctuation. The species extinction likelihood in the migrated area largely determines the dynamics and pattern of species migration. There is a significant difference in species migration between heterogeneous and homogeneous habitats. The increasing fitness of species will lead to a faster migration and higher percentage of migrated areas. Existence of boundary areas may retard species migration.

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This chapter was previously published in Self-organization: Theories and Methods, edited by WenJun Zhang, New York: Nova Publishers Inc., 2013. * E-mail: [email protected], [email protected]

In: Mathematical Research Summaries. Volume 1 Editor: Matthew A. Rowe

ISBN: 978-1-53612-021-9 © 2017 Nova Science Publishers, Inc.

Chapter 46

ROBUST SELF-ADAPTIVE KALMAN FILTER WITH THE R AND Q ADAPTATIONS AGAINST SENSOR/ACTUATOR FAILURES #

Chingiz Hajiyev1 and Halil Ersin Soken2 1

Istanbul Technical University, Aeronautics and Astronautics Faculty, Istanbul, Turkey 2 The Graduate University for Advanced Studies (Sokendai), Department of Space and Astronautical Science, Sagamihara, Kanagawa, Japan

RESEARCH SUMMARY In this chapter a Robust Self-Adaptive Kalman Filter (RSAKF) algorithm with the filter gain correction is developed for the case of sensor/actuator malfunctions. The proposed RSAKF utilizes time variable factors in order to reduce the effect of the faults on the estimation procedure. In this sense, the procedures with single and multiple factors for the adaptation of the filter are presented. In the first case, the filter is adapted by using single adaptive factor as a corrective term on the filter gain while in the second one, an adaptive matrix built of multiple adaptive factors is used to fix the relevant term of the Kalman gain matrix, individually. After choosing the efficient method of adaptation, an overall concept for the RSAKF is proposed. In this concept, the filter detects the type of the fault, either in the sensors or actuators, and after the fault isolation it applies the required adaptation process such that the estimation characteristic is not deteriorated. Effectiveness of the proposed filters is investigated via simulations for the state estimation problem of an UAV. The results of the presented algorithms are compared for different types of sensor/actuator faults and in this context recommendations about their utilization are given.

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This chapter was previously published in Self-organization: Theories and Methods, edited by WenJun Zhang, New York: Nova Publishers Inc., 2013.  Email: [email protected]

In: Mathematical Research Summaries. Volume 1 Editor: Matthew A. Rowe

ISBN: 978-1-53612-021-9 © 2017 Nova Science Publishers, Inc.

Chapter 47

REGULAR APPROXIMATION OF THE STOCHASTIC PUSHDOWN CALCULUS #

Marco Carpentieri* Dipartimento di Matematica ed Informatica, Universitá della Basilicata, Potenza (Pz), Italy

RESEARCH SUMMARY This chapter takes into account the problem of designing regular approximations for the stochastic pushdown computing. I prove that stochastic pushdown automata accepting with finite cut point and for which equivalent non-dirty context-free grammars exist admit arbitrarily accurate regular approximations. I address the problem of designing the uniform representation of the stochastic (context-free/pushdown) computing characterizing it in terms of converging sequences of finite state approximations.

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This chapter was previously published in Self-organization: Theories and Methods, edited by WenJun Zhang, New York: Nova Publishers Inc., 2013. * [email protected].

In: Mathematical Research Summaries. Volume 1 Editor: Matthew A. Rowe

ISBN: 978-1-53612-021-9 © 2017 Nova Science Publishers, Inc.

Chapter 48

LYAPUNOV STABILITY OF NON-AUTONOMOUS DYNAMICAL SYSTEMS #

David N. Cheban* Department of Fundamental Mathematics, State University of Moldova, Republic of Moldova

RESEARCH SUMMARY The foundation of the modern theory of stability was created in the works of A. Poincare and A.M. Lyapunov. The theory of the stability of motion has gained increasing significance in the last decade as is apparent from the large number of publications on the subject. A considerable part of these works are concerned with practical problems, especially problems from the area of controls and servo-mechanisms, and concrete problems from engineering, which first gave the decisive impetus for the expansion and modern development of stability theory. This book contains a systematic exposition of the elements of the asymptotic stability theory of general non-autonomous dynamical systems in metric spaces with an emphasis on the application for different classes of non-autonomous evolution equations (Ordinary Differential Equations (ODEs), Difference Equations (DEs), Functional-Differential Equations (FDEs), Semi-Linear Parabolic Equations etc). The basic results of this book are contained in the courses of lectures which the author has given during many years for the students of the State University of Moldova. This book is intended for mathematicians (scientists and university professors) who are working in the field of stability theory of differential/difference equations, dynamical systems and control theory. It would also be of use for the graduate and post graduate student who is interested in the theory of dynamical systems and its applications. The reader needs no deep knowledge of special branches of mathematics, although it should be easier for readers who #

This chapter was previously published as a book: Lyapunov Stability of Non-Autonomous Dynamical Systems, by David N. Cheban, New York: Nova Publishers Inc., 2013. * email address: [email protected]

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know the fundamentals concepts of the theory of metric spaces, qualitative theory of differential/difference equations and dynamical systems.

In: Mathematical Research Summaries. Volume 1 Editor: Matthew A. Rowe

ISBN: 978-1-53612-021-9 © 2017 Nova Science Publishers, Inc.

Chapter 49

APPLICATIONS OF GRAPH THEORY IN ARCHITECTURAL ANALYSIS: PAST, PRESENT AND FUTURE RESEARCH #

Michael J. Dawes and Michael J. Ostwald School of Architecture and Built Environment, University of Newcastle, Callaghan, Australia

RESEARCH SUMMARY In the 1970s architectural scholars adopted graph theory to support several major analytical approaches to interior and urban design. While the basis for graph theory in architecture is identical to that in mathematics, architects developed several disciplinespecific methods for mapping nodes and edges to various spatial and formal features, and then set out to interpret these maps through a combination of mathematical analysis and observations of human behaviour, social structures and building types. This chapter undertakes a review of architectural applications of graph theory, spanning from its initial use for solving pedestrian circulation problems, through to more recent applications providing insights into access planning, design psychology and way-finding. Through this critical review, three mapping or abstraction techniques, which are a precursor to graph theory analysis, are described and demonstrated. Finally, the chapter identifies three areas that could be the subject of future applications of graph theory in design.

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This chapter was previously published in Graph Theory: New Research, edited by Alessandra Cavalcante, New York: Nova Publishers Inc., 2013.

In: Mathematical Research Summaries. Volume 1 Editor: Matthew A. Rowe

ISBN: 978-1-53612-021-9 © 2017 Nova Science Publishers, Inc.

Chapter 50

MIESIAN INTERSECTIONS: COMPARING AND EVALUATING GRAPH THEORY APPROACHES TO ARCHITECTURAL SPATIAL ANALYSIS #

Michael J. Ostwald and Michael J. Dawes University of Newcastle, New South Wales, Australia

RESEARCH SUMMARY One of the earliest graph theory methods developed for the analysis of spatial relations in architecture is called “convex space” analysis. While more than three decades old, this method is still widely used in architectural and urban planning to analyze the physical connections between architectural spaces. Conversely, one of the least well-known or understood graph theory methods for architectural research is called “intersection point” analysis. Despite offering several potential advantages over classic architectural graph theory approaches, the intersection point method has not convincingly been compared with the more traditional method. Using five houses designed by Modernist architect Mies Van Der Rohe as a sample, this chapter constructs a comparison between the results of the classic convex space method and two variations of the intersection point method; “intersection point” and “end node”. The two variations involve, respectively, the decision to either exclude or include “stubs” in a graph. Stubs are part of the underlying axial line map that is used to generate an intersection point graph and without comparative results there has been no way of evaluating their impact or importance. This chapter concludes that the intersection point method is more capable, than the convex space approach, of identifying the significance of space from the perspective of either navigation or movement. The analysis also shows that the decision to include or exclude stubs has an unexpectedly small impact on integration values and a predictable influence on their distribution within an architectural plan. Finally, while the chapter is #

This chapter was previously published in Graph Theory: New Research, edited by Alessandra Cavalcante, New York: Nova Publishers Inc., 2013.  E-mail address: [email protected] (Corresponding author)

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primarily concerned with the application and evaluation of several variations of graph theory, it concludes with a brief interpretation of what the results suggest about Mies’ early modernist architecture.

In: Mathematical Research Summaries. Volume 1 Editor: Matthew A. Rowe

ISBN: 978-1-53612-021-9 © 2017 Nova Science Publishers, Inc.

Chapter 51

THE ALGEBRAIC STRUCTURE OF GRAPHS

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Antonios Kalampakas1 and Vassilios Tsiantos2 1

Department of Production Engineering and Management, Democritus University of Thrace, Xanthi, Greece 2 Department of Exact Sciences, Technical Institute of Kavala, Kavala, Greece

RESEARCH SUMMARY The importance of magmoids as the appropriate algebraic structure for naturally and effectively generating graphs is demonstrated by illustrating their applicability for finitely axiomatizing graphs, constructing a syntactic recognition mechanism and developing for the first time an unrestricted notion of graph automaton. More precisely, it is known that every graph can be constructed from a set of five elementary graphs inside a magmoid with operations graph composition and graph sum. In this framework we show that two such expressions represent the same graph if and only if one can be transformed in to the other by a set of 15 equations. Magmoids satisfying these equations are called graphoids and the set of all graphs with operation composition and sum is the free graphoid. Automata operating on arbitrary graphs are constructed by virtue of abelian relational graphoids similarly with the well known finite string automata. Automaton recognizability is closed under union, intersection, sum and inverse graph homomorphism but not under complement and composition. In order to construct a graph automaton it is necessary and sufficient that the relations over the Kleene star of the state set constitute a graphoid. In this respect, various different versions of graph automata arise corresponding to the specific relational graphoid that is employed. In particular it is proved that the generation of an abelian graphoid by a set Q implies the partitioning of Q into disjoint abelian groups and vice versa. Syntactic graph recognizability is defined by virtue of the syntactic magmoid, analogously with the syntactic monoid of a word language. In this setup, the syntactic #

This chapter was previously published in Graph Theory: New Research, edited by Alessandra Cavalcante, New York: Nova Publishers Inc., 2013.

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complexity of a given recognizable graph language can be determined, giving rise to a syntactic classification inside the class of recognizable graph languages. The syntactic complexities of the connected and the eulerian graphs are calculated and compared. The class of all syntactically recognizable subsets of a given magmoid is shown to be closed under boolean operations, inverse magmoid morphisms and graph sum. Moreover, the left derivative of a given language L is defined and it is proved to be recognizable, provided that L is recognizable.

In: Mathematical Research Summaries. Volume 1 Editor: Matthew A. Rowe

ISBN: 978-1-53612-021-9 © 2017 Nova Science Publishers, Inc.

Chapter 52

THE COMBINATION OF GRAPH THEORY AND UNSUPERVISED LEARNING APPLIED TO SOCIAL DATA MINING #

Héctor D. Menéndez* and José Luis Llorente Universidad Autónoma de Madrid Escuela Politécnica Superior, Cantoblanco, Madrid, Spain

RESEARCH SUMMARY Over the last few years, Social Data Mining has become an important field inside Data Analysis. These techniques are rapidly finding applications in a variety of domains including artificial intelligence, economics and marketing amongst others. They are based on knowledge extraction from the users, focusing on their behaviour and relationships inside a system which can be modeled as a Social Network where they act independently or establishing relationships. The Social Network studies have been oriented from different points of view, however, the most representatives come from Graph Theory. On the one hand, the Network is usually represented as a Graph where the users are considered nodes and their relationships are the graph edges. Different approximations of Complex Network Analysis are used to described the Network and its features. On the other hand, the Graph Theory can also be used to analyses the behaviour of the users, not only from a relationships point of view, instead, it can be used to analyse the information that they generates, creating an independent profile of the user. A representative selection of these techniques is discussed in detail in this work, showing how different methods extracted from Graph Theory can be combined with different approaches of Unsupervised Learning to analyse Social Behaviour from different perspectives.

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This chapter was previously published in Graph Theory: New Research, edited by Alessandra Cavalcante, New York: Nova Publishers Inc., 2013. * E-mail address: [email protected] (Corresponding author)

In: Mathematical Research Summaries. Volume 1 Editor: Matthew A. Rowe

ISBN: 978-1-53612-021-9 © 2017 Nova Science Publishers, Inc.

Chapter 53

ABOUT ORGANIZING AND STRUCTURING THE CONTENTS OF MATHEMATICAL SUBJECTS USING GRAPH THEORY #

Angélica Martínez-Zarzuelo*,1, Eugenio Roanes-Lozano±,2 and María José Fernández-Díaz†,3 1

Depto. de Evaluación y Analisis de Datos, Instituto Nacional de Evaluación Educativa, Ministerio de Educación, Cultura y Deporte, Madrid, Spain 2 Instituto de Matemática Interdisciplinar (IMI), Depto. de Algebra, Facultad de Educación, Universidad Complutense de Madrid, Madrid, Spain 3 Depto. Métodos de Investigación y Diagnóstico en Educación (MIDE), Facultad de Educación, Universidad Complutense de Madrid, Madrid, Spain

RESEARCH SUMMARY The first two authors are mathematicians and had previously worked in applications of graph theory to transportation engineering. The third author is the Dean of the School of Education of the Universidad Complutense de Madrid. We thought that it would be a good idea to apply graph theory to mathematics teaching. From our point of view, adequately organizing and structuring the contents of a subject are two fundamental issues of the teaching-learning process. We believe that, if the different mathematical contents and the “prerequisite” relation between them are revisited from the point of view of graph theory using graph analysis and visualization software, the analysis of the curricular structures can #

This chapter was previously published in Graph Theory: New Research, edited by Alessandra Cavalcante, New York: Nova Publishers Inc., 2013. * E-mail address: [email protected] ± E-mail address: [email protected] † E-mail address: [email protected]

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A. Martínez-Zarzuelo, E. Roanes-Lozano and M. José Fernández-Díaz

be clearly improved. Mathematics subjects are specially well suited for such an approach, due to their hierarchical structure.

In: Mathematical Research Summaries. Volume 1 Editor: Matthew A. Rowe

ISBN: 978-1-53612-021-9 © 2017 Nova Science Publishers, Inc.

Chapter 54

A MODULARITY BASED FILTERING APPROACH FOR NETWORK IMMUNIZATION #

Tetsuya Yoshida* and Yuu Yamada Graduate Schoolof Information Science and Technology, Hokkaido University, Japan

RESEARCH SUMMARY This chapter presents a modularity based filtering approach, which does not require the community labels of nodes, toward effective network immunization. Various resources are connected to each other and form networks these days. Especially, social media or social networks have been widely used as daily communication media. Links among resources makes it easier to exploit other resources by overcoming geographical or temporal distance. However, fast spreading of information over networks may have negative aspects, such as computer viruses or epidemics of diseases. The spread of epidemics may occur through the interaction between nodes in a network. Since contamination is propagated among communities along links in a network, utilization of community structure in the network seems effective for network immunization. However, although various research efforts have been invested, it is still difficult to identify community labels of nodes in a network. Our approach tries to exploit the community structure of network based on the well-known modularity measure, and construct a vector representation of nodes in the network. Since a vector has both its norm and direction, the presented approach uses not only the norm of the constructed vectors, but also the relation among vectors for calculating node scores. Filtering of nodes is conducted in terms of the inner products of vector representation and mutual angle between vectors. We report the results of experiments to validate our approach. The results indicate that the presented approach is promising and that it is worth pursuing this path.

#

This chapter was previously published in Graph Theory: New Research, edited by Alessandra Cavalcante, New York: Nova Publishers Inc., 2013. * E-mail address: [email protected]

In: Mathematical Research Summaries. Volume 1 Editor: Matthew A. Rowe

ISBN: 978-1-53612-021-9 © 2017 Nova Science Publishers, Inc.

Chapter 55

PARTICLE OF LIFE: MATHEMATICAL ABSTRACTION OR REALITY? #

Michail Zak* Jet Propulsion Laboratory, California Institute of Technology Cypress, CA, USA

RESEARCH SUMMARY The book presents a mathematical answer to the ancient philosophical question “How mind is related to matter”. It proves that in the mathematical world, the bridge from matter to mind requires the extension and modification of quantum physics. The discovery of the Higgs boson and the consequent completeness of the physical picture of our Universe raised many questions, and one of them is the ability to create Life and Mind out of physical matter without any additional entities. This book introduces and discusses a possible expansion of modern physics to include physics of Life since all attempts to create living matter from non-living matter have failed. Prior to the discussion, a life/nonlife criterion is proposed: unlike physical systems, livings can move from disorder to order without an external interference if the model of life concentrates upon the concept of intelligent behavior and does not include such “auxiliary” processes as metabolism and reproduction. A mathematical formalism suggests that a hypothetical “particle of life” (Lparticle) can be represented by a quantum-classical hybrid in which the force following from the quantum potential is replaced by the information force. Besides the capability to move against the second law of thermodynamics, L-particle acquires such properties as self-image, self-awareness, self-supervision, etc., that are typical for living matter. However, since the Lparticle, being a quantum-classical hybrid, acquires non-Newtonian and non-quantum properties, it does not belong to the physics matter as we know it: modern physics should be complemented with the concept of the information force that represents a bridge between #

This chapter was previously published as a book: Particle of Life: Mathematical Abstraction or Reality?, by Michail Zak, New York: Nova Publishers Inc., 2014. * E-mail address: [email protected]

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non-living and living matter. It has been suggested that quantum mechanics and mechanics of livings are sub-classes of a broader physical model, and the difference between them is due to different Liouville feedbacks, i.e. in different information forces. At this stage, L-particle is introduced as an abstract mathematical concept that satisfies only mathematical rules and assumptions, while its physical representation is still an open problem. The first five chapters of the book are concentrated on the derivation and analysis of mathematical models of three versions of L-particles that have identical topology, but different information forces. Special attention is paid to similarity (entanglement, randomness, etc.) and differences (self-image, self-awareness, self-control, etc.) between Lparticles and quantum particles. It is emphasized that the most fundamental property of the L-particle that distinguishes it from both Newtonian and quantum particles is its capability to violate the second law of thermodynamics, i.e. the capability to move from disorder to order without external help, and this autonomy is the crux of intelligence. The next four chapters of the book address applications of L-particles to such human activities that cannot be simulated by Newtonian or quantum physics, and all these activities can be found in the dynamics of social nets. These chapters include models of common sense decision-making processes as well as elements of games with the capability of players to predict the action of adversaries, spontaneous emergence of social sub-structures, as well as the emergence of social catastrophes. Special attention is paid to the problems of artificial life that includes computations, simulations and model discovery, as well as to mathematical model of human mind. The accessible presentation of this book makes it eminently suitable for students and researchers interested in cognition, information processing, theory of stochastic processes, optimization, and modeling life and intelligence. The book will also appeal to researchers in mathematics and biophysical sciences.

In: Mathematical Research Summaries. Volume 1 Editor: Matthew A. Rowe

ISBN: 978-1-53612-021-9 © 2017 Nova Science Publishers, Inc.

Chapter 56

LOCAL FRACTIONAL DERIVATIVES

#

N. C. Dias* and J. N. Prata† Departamento de Matemática Universidade Lusófona de Humanidades e Tecnologias, Lisboa, Portugal and Grupo de Física-Matemàtica Univeridade de Lisboa, Lisboa, Portugal

RESEARCH SUMMARY In the course of history, mathematical models of natural phenomena were based on assumptions of regularity and determinism. It was believed that physical phenomena can, by and large, be represented by analytic functions and the dynamics of physical systems can be adequately described by differential equations. These beliefs were largely supported by the successes of physical theories such as Newton's mechanics, electromagnetic theory, acoustics, heat transport, along with diffusion, quantum mechanics and relativity in the 20th century. However, it became clear in more recent years that such phenomena as phase transitions, turbulence, and the rheology of polymeric materials could not be explained using such an approach. In Mandelbrot's own words, "clouds are not spheres, mountains are not cones, coastlines are not circles, and bark is not smooth, nor does lightning travel in a straight line". In his renowned essay, Mandelbrot advocated a departure from this tradition of smoothness, regularity and determinism, to one where roughness, irregularity and randomness are prevalent. It is not just the fact that natural phenomena are more accurately described by the latter characteristics, but also from a mathematical standpoint, sets and structures which were reputed as exceptional or aberrant should in a sense be the rule. We will recapitulate two notable theorems which prove that, from a topological point of view, the sets of continuous functions and of infinitely differentiable functions are much more profligate at providing functions which are nowhere differentiable or nowhere analytic than the opposite. #

This chapter was previously published in Fractional Calculus in Analysis, Dynamics and Optimal Control, edited by Jacky Cresson, New York: Nova Publishers Inc., 2014. * E-mail address: [email protected] †

E-mail address: [email protected]

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A paramount example of randomness and non-differentiability is Brownian motion. The typical path of the Brownian particle is nowhere differentiable. Unlike ordinary Newtonian motion, one cannot write down differential equations for such processes. There is an old answer to this problem, called fractional calculus. Fractional derivatives generalize the notion 𝑑𝑛 𝑓

𝑑𝛼 𝑓

of derivative of order 𝑛 ∈ of a function 𝑑𝑥 𝑛 to non-integer orders 𝑑𝑥 𝛼 , 𝛼 ∈ +. One of the truly remarkable properties of fractional derivatives is the fact that a non-differentiable function f may nevertheless admit a fractional derivative of some order 0 < α < 1. It is by now widely acknowledged that there are numerous situations were fractional differential equations are very effective at describing the situation at hand. It is not just the fact that nondifferentiable (fractal) functions may emerge as solutions to fractional differential equations, also the highly non-local nature of fractional derivatives is very useful at addressing systems with long range interactions or prolonged memory effects. On the other hand, this non-locality prevents the same kind of local description of the geometry of the graph of a function that one has from traditional calculus of differentiable functions. This prompted the search for local versions of fractional derivatives. The first attempts were put forward by Kolwankar and Gangal and several authors then worked on the main mathematical properties of such derivatives and applications. The local fractional derivatives are themselves (as are the non-differentiable functions on which they act) fractallike. There is a critical order of differentiability below which the derivative vanishes, and above which it diverges. This is strongly reminiscent of the Hausdorff-dimension as one computes the Hausdorff measure of a set below and above its dimension. And indeed the two concepts are inextricably linked. The critical order of differentiability is related to the fractal dimension of the graph of the function. A structure theorem due to Chen, Yan and K. Zhang proves that if the local fractional derivative of some order 0 < α < 1 of a function exists in an interval, then it is zero, except possibly in a set of vanishing Lebesgue measure. The interest in local fractional derivatives, then becomes restricted to the following situations. (i) The function is multi-fractal, and hence the critical order of differentiability varies in the interval. This weakens the conditions of the Chen-Yan-Zhang Theorem and permits the fractional derivative (of varying order) to be finite and non-zero. In this context, various techniques in the framework of wavelet theory have been developed. (ii) The set of zero Lebesgue measure on which the fractional derivative is non-vanishing cannot be discarded as it has non-vanishing and finite Hausdorff measure of dimension 0 log 2

< s < 1 (e.g. the devil staircase function for the Cantor set for s=log 3). This situation could be a physical model for a particle interacting at a set of instants which is a fractal set (e.g. Cantor's set). In such a case the particle's trajectory is certainly not a straight line, which is what one obtains if one neglects the set of vanishing Lebesgue measure where the interactions occur. For this situation a certain type of fractal calculus developed by Parvate and Gangal is more useful. Certain fractal sets display a vanishing or divergent Hausdorff measure for all dimensions s > 0. This is because the functions that one uses to "resolve" these sets - the powers xs - are not tailored for such sets. It is well known that other functions (called dimension functions) may be more appropriate. By the same token, the fact that (in accordance with the Chen-YanZhang Theorem) the local fractional derivatives vanish almost everywhere may in certain

Local Fractional Derivatives

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cases just be an indication that fractional derivatives of order α are not appropriate and a finetuning using orders other than the powers may be more effective. As we will see this is what happens for instance in the case of the Takagi function. In this work we will follow this point of view. Our strategy to circumvent the Chen-YanZhang Theorem is then to develop a local fractional calculus of orders other than the positive reals. We will develop the main properties of this type of calculus, which we dubbed ψ-calculus. The fractal nature of the ψ-local fractional derivative manifests itself again. Indeed, if it vanishes nowhere in an interval, then the set of points where it is positive and where it is negative are both dense everywhere in that interval. Moreover, if one draws the graph of the points where the ψ-derivative is positive (or negative) versus the value of the ψ-derivative one obtains a dust-like structure. Here is a brief outlook of the paper. In the next section we dwell on the concept of negligible set from a topological point of view. We revise the categories of Baire and Baire's Theorem. We apply Baire's Theorem in the proofs of the Banach-Mazurkiewicz Theorem and of the Cater Theorem. The BanachMazurkiewicz Theorem says that the set of functions that admit a finite (right) derivative at a point in some interval is a negligible subset of the space of continuous functions on that interval. We consider the Weierstrass and the Takagi functions as examples of functions which are continuous but nowhere differentiable in an interval. The Cater Theorem, on the other hand, states that the set of functions which are analytic somewhere in an interval are a negligible subset of the space of infinitely differentiable functions on that interval. We also give an example by Cater of a function which is infinitely differentiable but nowhere analytic in an interval. In section 3 we develop the concept of dimension function, a generalization of the topological and the fractal notions of dimension. As an application, we discuss various types of Hölder continuity with respect to dimension functions. The Takagi function constitutes an example of a function displaying a Hölder continuity with respect to one of such functions. The Hausdorff measure and Hausdorff dimension are then presented in connection with the dimension functions. The main result here is the relation between the Hölder behavior of a function and the fractal dimension of its graph. Section 4 presents our main results: a generalization of local fractional derivatives by using generalized dimension functions as the order of differentiability instead of the more widely used powers. We develop the complete calculus for such derivatives. Finally in section 5, we consider some possible generalizations, such as Cresson and Nottale's quantum difference operators, the local fractional calculus in several dimensions, and a generalization of Clarke's derivative to fractional order.

In: Mathematical Research Summaries. Volume 1 Editor: Matthew A. Rowe

ISBN: 978-1-53612-021-9 © 2017 Nova Science Publishers, Inc.

Chapter 57

FRACTIONAL VARIATIONAL EMBEDDING AND LAGRANGIAN FORMULATIONS OF DISSIPATIVE PARTIAL DIFFERENTIAL EQUATIONS #

Jacky Cresson* Laboratoire de Mathématiques et de leurs Applications de Pau, Universit´e de Pau et des Pays de l’Adour, Pau Cedex, France

RESEARCH SUMMARY Many problems of physics cannot be formalized using the usual Lagrangian or Hamiltonian formalisms. This is in particular the case for dissipative systems. Many authors have tried to overcome this difficulty. The main reason behind these generalizations is that the Lagrangian formalism provides efficient tools to study the dynamics and properties of the underlying equations as well as an intrinsic structure (i.e. not depending on coordinates systems) related to a first principle of physic by the least action principle. As examples of previous attempts we can cite:    

Bateman which constructs a mirror dynamics assuming that the description of dissipative systems is physically incomplete. Tveter formalism which preserves the form of the Hamiltonian equations. Riewe's approach using fractional variational calculus. Stochastic differential equations whose mean behaviour corresponds to a dissipative systems.

This list is far from being exhaustive. All of these tentative are based on a particular assumption. The formalism of Tveter is dedicated to the preservation of a Hamiltonian like

#

This chapter was previously published in Fractional Calculus in Analysis, Dynamics and Optimal Control, edited by Jacky Cresson, New York: Nova Publishers Inc., 2014. * E-mail address: [email protected]

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structure. This mathematical demand is not supported by any physic idea and the interpretation of the new structure is not clear. The stochastic approach is not sufficiently general due to mathematical difficulties in the effective computation of the mean dynamics. The idea is to see dissipative phenomenon as the trace of an irreversible dynamics conducted by a stochastic differential equation. Bateman's work is also supported by a physic idea related to the irreversibility of the equation but his construction appears as purely formal: the construction of the mirror dynamics is not fixed by the theory. One must construct the equation for each case. Finally, Riewe's approach is supported by physic. The dissipative phenomenon induces forces which are of fractional nature and which appear in the Lagrangian formalism via fractional derivatives. His tentative fails for technical reasons which are discussed in details in Section 2.5 and cannot be used in its present form. In this chapter we follow Riewe's idea and provide a fractional variational framework for dissipative systems. The main advantage of this formulation is that dissipative terms are then connected to the emergence of fractional terms in the Lagrangian formulation. As a consequence, the interpretation of our formalism is clear. Most of the material contains in this chapter can be found in many different articles during the last years. As a consequence, it is difficult for the readers to have a global view of the tools we have developed and the results we have obtained. This chapter can be considered as an overview of our contributions in the direction of fractional calculus of variations. Our work in fractional calculus is part of a general program to study generalization of ordinary or partial differential equations called embedding formalisms. Although this formalism is continuously developed and modified we provide in Section 3 a general introduction to this idea. We can formally resume this point of view as follows: try to find functorial or categorical ways to generalize ODEs and PDEs and classify all the existing generalizations using this formalism. Although this program is not completely fulfilled, we provide a first tentative in this direction.

In: Mathematical Research Summaries. Volume 1 Editor: Matthew A. Rowe

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Chapter 58

A CLASS OF FRACTIONAL OPTIMAL CONTROL PROBLEMS AND FRACTIONAL PONTRYAGIN'S SYSTEMS. VARIATIONAL INTEGRATOR AND EXISTENCE OF CONTINUOUS/DISCRETE NOETHER'S THEOREMS #

Loïc Bourdin* Laboratoire de Mathématiques et de leurs Applications de Pau, Université de Pau et des Pays de l’Adour, Pau Cedex, France

RESEARCH SUMMARY Recently, a subtopic of the fractional calculus gains importance: it concerns the variational principles on functionals involving fractional derivatives. This leads to the statement of fractional Euler-Lagrange equations. A direct consequence is the emergence of works concerning a particular class of fractional optimal control problems. These studies usually use a Lagrange multiplier technique allowing to write these problems as problems of optimization without constraint of augmented functionals. With a calculus of variations, authors then obtain a necessary condition for the existence of an optimal control. This condition is commonly given as the existence of a solution of a system of fractional differential equations called fractional Pontryagin’s system. In this chapter, we first give a new presentation of this result. Precisely, making an additional assumption (see Condition (fx lip)), we rewrite directly these fractional optimal control problems as simpler problems of optimization without constraint of functionals depending only on the control. Although the method used is considerably inspired by the Lagrange multiplier technique, it allows us to give a complete proof of this result using only classical mathematical tools adapted to the fractional case: calculus of variations, Gronwall’s #

This chapter was previously published in Fractional Calculus in Analysis, Dynamics and Optimal Control, edited by Jacky Cresson, New York: Nova Publishers Inc., 2014. * E-mail address: [email protected]

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Loïc Bourdin

Lemma, Cauchy-Lipschitz Theorem and stability of differential equations under perturbations. Nevertheless, the explicit computation of controls satisfying the above necessary condition needs the resolution of a fractional Pontryagin’s system which is a main drawback. Indeed, solving a fractional differential equation is in general very difficult. Consequently, in this chapter, we suggest two deviously ways in order to get information on the solutions of a fractional Pontryagin’s system. Firstly, we study the existence of classical conservation laws, i.e. functions which are constant on each solution. Indeed, constants of motion, generally associated to physical quantities, give strong information on the solutions in the phase space for example. Moreover, they also can be used in order to reduce or integrate the equation by quadrature. Previous results in this direction have been obtained by Torres and Frederico. However, in each of these papers, the conservation law is not explicit but implicitly defined by a functional relation. In this chapter, we prove a fractional Noether’s theorem providing an explicit conservation law for fractional Pontryagin’s systems exhibiting a symmetry. The second idea is to suggest a numerical approach. In this chapter, we construct a numerical scheme preserving the variational structure of the fractional Pontryagin’s systems. Indeed, this variational structure is intrinsic and induces strong constraints on the qualitative behaviour of the solutions. It seems then important to preserve it at the discrete level. A variational integrator is a numerical scheme preserving the variational structure at the discrete level. We refer to Section 2 for more details concerning the construction of a variational integrator and let us remind that the variational integrators are well-developed in [36, 46] for classical Euler-Lagrange equations and for fraction alones. In this chapter, we construct a variational integrator for fractional Pontryagin’s systems and it is called shifted discrete fractional Pontryagin’s system. Finally, adapting the strategy from the continuous level to the discrete one, we prove a discrete fractional Noether’s theorem providing an explicit discrete conservation law for shifted discrete fractional Pontryagin’s systems exhibiting a discrete symmetry.

In: Mathematical Research Summaries. Volume 1 Editor: Matthew A. Rowe

ISBN: 978-1-53612-021-9 © 2017 Nova Science Publishers, Inc.

Chapter 59

FRACTAL TRAPS AND FRACTIONAL DYNAMICS

#

Pierre Inizan* Institut de Mécanique Céleste et de Calcul des Éphémérides, Observatoire de Paris, Paris, France

RESEARCH SUMMARY Anomalous diffusion may arise in typical chaotic Hamiltonian systems. According to G.M. Zaslavsky’s analysis, this behavior is induced by sticky zones within the phase space, which may trap trajectories for a long time. A description can be done by means of fractional kinetics equations. However, the dynamical origin of those fractional derivatives is still unclear. We provide in this article an attempt for a possible explanation. Starting from R. Hilfer’s work, an expression for the average infinitesimal evolution of trajectories sets is given by using Poincaré recurrence times. The fractal structures of the traps, described by G.M. Zaslavsky, are then taken into account, and it is shown that in this case, the derivative associated to this evolution may become fractional, with order equal to the transport exponent of the diffusion process.

#

This chapter was previously published in Fractional Calculus in Analysis, Dynamics and Optimal Control, edited by Jacky Cresson, New York: Nova Publishers Inc., 2014. * E-mail address: [email protected]

In: Mathematical Research Summaries. Volume 1 Editor: Matthew A. Rowe

ISBN: 978-1-53612-021-9 © 2017 Nova Science Publishers, Inc.

Chapter 60

NUMERICAL APPROXIMATIONS TO FRACTIONAL PROBLEMS OF THE CALCULUS OF VARIATIONS AND OPTIMAL CONTROL #

Shakoor Pooseh*, Ricardo Almeida† and Delfim F. M. Torres‡ Center for Research and Development in Mathematics and Applications (CIDMA) Department of Mathematics, University of Aveiro, Aveiro, Portugal

RESEARCH SUMMARY A fractional problem of the calculus of variations and optimal control consists in the study of an optimization problem in which the objective functional or constraints depend on derivatives and integrals of arbitrary, real or complex, orders. This is a generalization of the classical theory, where derivatives and integrals can only appear in integer orders.

#

This chapter was previously published in Fractional Calculus in Analysis, Dynamics and Optimal Control, edited by Jacky Cresson, New York: Nova Publishers Inc., 2014. * E-mail address: [email protected] † E-mail address: [email protected] ‡ E-mail address: [email protected]

In: Mathematical Research Summaries. Volume 1 Editor: Matthew A. Rowe

ISBN: 978-1-53612-021-9 © 2017 Nova Science Publishers, Inc.

Chapter 61

SELECTED TOPICS OF INVARIANT MEASURES IN POLISH GROUPS #

Gogi Pantsulaia* Department of Mathematics, Georgian Technical University, Tbilisi, Georgia

RESEARCH SUMMARY This book explores a number of new applications of invariant quasi-finite diffused Borel measures in Polish groups for a solution of various problems stated by famous mathematicians (for example, Carmichael, Erdos, Fremlin, Darji and so on). By using natural Borel embeddings of an infinite-dimensional function space into the standard topological vector space of all real-valued sequences (endowed with the Tychonoff topology), a new approach for the construction of different translation-invariant quasi-finite diffused Borel measures with suitable properties and for their applications in a solution of various partial differential equations in an entire vector space is proposed.

#

This chapter was previously published as a book: Selected Topics of Invariant Measures in Polish Groups, by Gogi Pantsulaia, New York: Nova Publishers Inc., 2014. * e-mail address: [email protected]

In: Mathematical Research Summaries. Volume 1 Editor: Matthew A. Rowe

ISBN: 978-1-53612-021-9 © 2017 Nova Science Publishers, Inc.

Chapter 62

FOUNDATIONS OF ISO-DIFFERENTIAL CALCULUS. VOLUME 2 #

Svetlin Georgiev* Faculty of Mathematics and Informatics, Department of Differential Equations, Sofia University, Sofia, Bulgaria

RESEARCH SUMMARY This book introduces the main ideas and the fundamental methods of iso-differential calculus for the iso-functions of several variables. In Chapter 1, the structure of iso-Euclidean spaces; the main conceptions for the isofunctions of the first, the second, the third, the fourth, and the fifth kind of n - variables; the limits of the iso-real iso-valued iso-functions of several variables; the continuous isofunctions; and the main ideas for the iso-partial derivatives of the first, the second, the third, the fourth, the fifth, the sixth, and the seventh kind of the iso-functions of several variables are discussed. They are introduced along with the main approaches for finding the minima and the maxima of the iso-functions of n variables. In Chapter 2, some of the most relevant results of the iso-integration theory are represented. The aim is to provide the reader with all that is needed to harness the power of iso-integration. In Chapter 3 we deal with the line and surface iso-integrals. Chapter 4 provides a sufficiently wide introduction to the theory of the iso-Fourier integral. Chapter 5 is dedicated to some concepts connected with iso-Hilbert spaces. Some classes of iso-operators in the iso-Hilbert spaces are defined and their properties are presented. In Chapter 6 a definition for the Santilli-Lie-isotopic power series is given and some of its properties are deducted. #

This chapter was previously published as a book: Foundations of Iso-Differential Calculus. Volume 2, by Svetlin Georgiev, New York: Nova Publishers Inc., 2014 * E-mail: [email protected] or [email protected]

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I think, in fact, that it is useful for the reader to have a wide spectrum of context in which these ideas play an important role and wherein even the technical and formal aspects play a role. However, I have tried to keep the same spirit, always providing examples and exercises to clarify the main presentation.

In: Mathematical Research Summaries. Volume 1 Editor: Matthew A. Rowe

ISBN: 978-1-53612-021-9 © 2017 Nova Science Publishers, Inc.

Chapter 63

HYPERGRAPHS AND DESIGNS

#

Mario Gionfriddo1, Lorenzo Milazzo1 and Vitaly Voloshin2,* 1

Department of Mathematics and Computer Science, University of Catania, Italy 2 Department of Mathematics, Troy University, AL, US

RESEARCH SUMMARY Combinatorial designs represent an important area of contemporary discrete mathematics closely related to such fields as finite geometries, regular graphs and multigraphs, factorizations of graphs, linear algebra, number theory, finite fields, group and quasigroup theory, Latin squares, and matroids. It has a history of more than 150 years when it started as a collection of unrelated problems. Nowadays the field is a well developed theory with deep mathematical results and a wide range of applications in coding theory, cryptography, computer science, and other areas. In the most general setting, a combinatorial design consists of a ground set of elements and a collection of subsets of these elements satisfying some specific restrictions; the latter are often expressed in the language of graphs. On the other side, hypergraph theory is a relatively new field which started in early 60s of the last century as a generalization of graph theory. A hypergraph consists of a ground set of elements and a collection of subsets of these elements without any specific restrictions. In this sense the concept of hypergraph is more general than the concept of combinatorial design. While it started as a generalization of graph theory, hypergraph theory soon became a separate subject because many new properties have been discovered that miss or degenerate in graphs. Compared to graph theory, the language of hypergraphs not only allows us to formulate and solve more general problems, it also helps us to understand and solve several graph theory problems by simplifying and unifying many previously unrelated concepts. The main feature of this book is applying the hypergraph approach to the theory of combinatorial designs. An alternative title of it could be “Combinatorial designs as hypergraphs”. There is no analogue to this book on the market. Its primary audience are #

This chapter was previously published as a book: Hypergraphs and Designs, by Mario Gionfriddo, Lorenzo Milazzo and Vitaly Voloshin, New York: Nova Publishers Inc., 2014. * E-mail addresses: [email protected]; [email protected]

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researchers and graduate students taking courses in design theory, combinatorial geometry, finite geometry, discrete mathematics, graph theory, combinatorics, cryptography, information and coding theory, and similar areas. The aim of this book is to show the connection and mutual benefit between hypergraph theory and design theory. It does not intend to give a survey of all important results or methods in any of these subjects. In Chapter 1, we provide basic definitions from graph theory which we use throughout the book. Chapter 2 contains definitions and introductory concepts from hypergraph theory. We discuss regular and uniform hypergraphs, linear and k-linear hypergraphs, stars and intersecting families, transversals and blocking sets, and finally introduce Steiner systems as hypergraphs. Chapters 3 and 4 are devoted to vertex and edge colorings of hypergraphs. We examine basic concepts and results about equicolorings, color distributions, blocking sets and 2colorings. Special attention is given to Berge’s conjecture for linear hypergraphs. In Chapter 5, we survey basic facts about quasigroups and Latin squares due to their importance in describing further properties of designs. Finally, in Chapter 6, we begin study of combinatorial designs called Steiner Triple systems (STS) as special cases of hypergraphs: Kirkman triple systems, triple systems with l = 1, 2, 3, 4, 5, 6, and cyclic Steiner triple systems. Steiner quadruple systems (SQS) is the topic of Chapter 7. It includes systems of type S(2, 4, v), S(3, 4, v), resolvable S(2, 4, v), and the problem of parallelism in SQS. General Steiner systems are discussed in Chapter 8. Besides historical introduction, we describe some important particular cases and provide general theorems about the existence of the systems. Different types of constructions of Steiner systems are described in Chapter 9, and blocking sets in different systems are discussed in Chapter 10. The basic results about balanced incomplete block designs are contained in Chapter 11. The last chapter, Chapter 12, is dedicated to G-designs. After defining G decomposition, we discuss balanced and strongly balanced G-designs, and G-designs where G is a path, a star, or a cycle on small number of vertices. The book contains a significant number of detailed examples and figures which help in understanding mathematical concepts and theorems and may serve as useful exercises. The content of this book represents the material taught by the first author in Catania University during more than 30 years in courses such as combinatorial geometry and design theory.

In: Mathematical Research Summaries. Volume 1 Editor: Matthew A. Rowe

ISBN: 978-1-53612-021-9 © 2017 Nova Science Publishers, Inc.

Chapter 64

ANALYSIS OF THE CAPUTO DERIVATIVE AND PSEUDO STATE REPRESENTATION WITH THE INFINITE STATE APPROACH #

Jean-Claude Trigeassou1,, Nezha Maamri2,† and Alain Oustaloup3,‡ 1

Laboratory IMS, UMR 5218 CNRS, University of Bordeaux, INP Bordeaux, Talence Cedex, France 2 LIAS, University of Poitiers, Poitiers Cedex, France 3 Institut National Polytechique de Bordeaux (INPB), ENSEIRB-MATMECA, France

RESEARCH SUMMARY This paper presents the interpretation of the Caputo derivative with the help of the infinite state approach, also known as the fractional integrator approach. After presentation of the modified Laplace transform equations, definition of state variables is discussed, as well as its application to the characterization of fractional system energy. Then, the infinite state approach is used to analyze system simulation based on usual Caputo initial conditions. Finally, a new formulation of the transition matrix is proposed, to take into account the true initial state of a fractional system.

#

This chapter was previously published in Fractional Calculus: Theory, edited by Roy Abi Zeid Daou and Xavier Moreau, New York: Nova Publishers Inc., 2014.  E-mail address: [email protected]; Address: IMS-LAPS, University of Bordeaux I, 351 Avenue de la Liberation, 33405 Talence cedex, France. † E-mail address: [email protected]; Address: LIAS, University of Poitiers, 40 Avenue du Recteur Pineau, 86022 Poitiers cedex, France. ‡ E-mail address: [email protected]; Institut National Polytechique de Bordeaux (INPB), ENSEIRB-MATMECA, France

In: Mathematical Research Summaries. Volume 1 Editor: Matthew A. Rowe

ISBN: 978-1-53612-021-9 © 2017 Nova Science Publishers, Inc.

Chapter 65

STABILITY OF A CLASS OF FRACTIONAL CAUCHY PROBLEM

#

Rabha W. Ibrahim* Institute of Mathematical Sciences, University Malaya, Kuala Lumpur, Malaysia

RESEARCH SUMMARY In this work, we utilize the method of non-expansive operators to more general iterative and non-iterative fractional differential equations (Cauchy type) in sense of the Krasnoselskij iterations. The non-integer case is taken in sense of Riemann-Liouville fractional operators. Applications are illustrated. Ulam-Hyers stability for iterative fractional differential equation is defined and studied.

# *

This chapter was previously published in Fractional Calculus: Theory, edited by Roy Abi Zeid Daou and Xavier Moreau, New York: Nova Publishers Inc., 2014. E-mail address: [email protected]; Address: Institute of Mathematical Sciences, University Malaya, 50603, Kuala Lumpur, Malaysia.

In: Mathematical Research Summaries. Volume 1 Editor: Matthew A. Rowe

ISBN: 978-1-53612-021-9 © 2017 Nova Science Publishers, Inc.

Chapter 66

NUMERICAL SOLUTION OF FRACTIONAL ORDER DIFFERENTIAL EQUATIONS VIA MATRIX-BASED METHODS #

Matthew Harker* and Paul O’Leary University of Leoben, Institute for Automation, Leoben, Austria

RESEARCH SUMMARY This chapter presents a new matrix-based method for the numerical solution of fractional order differential equations (FDE). A new discretization of fractional order derivatives is presented, based on integer order numerical differentiation, and fractional order numerical integration. The discretized FDE and its associated initial-, boundary-, or interior-values are formulated as a linear constrained least squares optimization problem; with the proposed approach, the discretization of FDE becomes a straightforward one-to-one mapping of symbols. In this vein, a large class of linear FDE can be solved under the proposed framework. The method is demonstrated on common examples such as the Bagley-Torvik Equation, and the Relaxation-Oscillation Equation.

#

This chapter was previously published in Fractional Calculus: Theory, edited by Roy Abi Zeid Daou and Xavier Moreau, New York: Nova Publishers Inc., 2014. * E-mail address: [email protected]

In: Mathematical Research Summaries. Volume 1 Editor: Matthew A. Rowe

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Chapter 67

ON ANALYTICAL METHODS FOR DIFFERENTIAL EQUATIONS WITH LOCAL FRACTIONAL DERIVATIVE OPERATORS #

Xiao-Jun Yang1,*, Dumitru Baleanu2,3,4 and J. A. Tenreiro Machado5 1

Department of Mathematics and Mechanics, China University of Mining and Technology, Xuzhou Campus, Xuzhou, Jiangsu, China 2 Department of Chemical and Materials Engineering, Faculty of Engineering, King Abdulaziz University, Jeddah, Saudi Arabia 3 Institute of Space Sciences, Magurele, RO, Bucharest, Romania 4 Department of Mathematics and Computer Sciences, Faculty of Arts and Sciences, Cankaya University, Ankara, Turkey 5 Department of Electrical Engineering, Institute of Engineering, Polytechnic of Porto, Rua Dr. Antonio Bernardino de Almeida, Porto, Portugal

RESEARCH SUMMARY This chapter reviews new analytical methods for a family of differential equations with local fractional derivatives. We concentrate mainly on Fourier series, and Fourier and Laplace transforms with local fractional operators. The potential applications of the reported results are discussed.

#

This chapter was previously published in Fractional Calculus: Theory, edited by Roy Abi Zeid Daou and Xavier Moreau, New York: Nova Publishers Inc., 2014. * E-mail address: [email protected]; Address: Department of Mathematics and Mechanics, China University of Mining and Technology, Xuzhou Campus, Xuzhou, Jiangsu 221008, China (Corresponding author)

In: Mathematical Research Summaries. Volume 1 Editor: Matthew A. Rowe

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Chapter 68

EXTENDED BOREL TRANSFORM AND FRACTIONAL CALCULUS #

Akira Asada Sinsyu University, Japan

RESEARCH SUMMARY We have introduced an integral transform of R; ∞

𝑥𝑠

R[f(s)](x) = ∫−∞ f(s)ds that intertwines fractional order differentiation with the Γ(1+s) parallel transform of a variable: 𝑑𝑎 𝑅[𝑓(𝑠)](𝑥) = 𝑅[𝑓(𝑠 + 𝑎)](𝑥) 𝑑𝑥 𝑎 It is recognized that the suitable choice of domains for R are spaces of discrete support distributions or ultra distributions. In these cases, R is decomposed as B ○ N, where B is the extended Borel transform and N is closely related to the Mellin transform. In this paper, we explain these relations, mainly focusing on the interpretation of an extended Borel transform that is the extension of the Borel transform to functions expressed by power series of log x. Then we will discuss the applications of R to fractional differential equations.

#

This chapter was previously published in Fractional Calculus: Theory, edited by Roy Abi Zeid Daou and Xavier Moreau, New York: Nova Publishers Inc., 2014.

In: Mathematical Research Summaries. Volume 1 Editor: Matthew A. Rowe

ISBN: 978-1-53612-021-9 © 2017 Nova Science Publishers, Inc.

Chapter 69

INTRODUCTION TO STABILITY THEORY OF LINEAR FRACTIONAL DIFFERENCE EQUATIONS #

Jan Čermák and Tomáš Kisela* Institute of Mathematics, Brno University of Technology Brno, Czech Republic

RESEARCH SUMMARY One of the important aspects of the current development of fractional calculus is its expansion to various discrete settings. Foundations of discrete fractional calculus were set in 1960s and 1970s, but its systematic study started only recently. This research is carried out especially in two main directions: discrete fractional calculus as a special branch of discrete analysis, and as a tool of numerical investigations of underlying continuous fractional problems. In this chapter, we will summarize and develop some recent results achieved in the field of discrete fractional calculus, with a special attention devoted to fractional difference equations and essentials of their qualitative theory. First we will recall some basic definitions and properties of discrete fractional calculus, which are useful in the following investigations. Then we will introduce the notion of linear fractional difference equation considered on a uniform mesh of points, investigate the well-posedness of the corresponding initial value problem and discuss the structure of the solution space. Also, an explicit form of the general solution will be described via discrete analogues of the Mittag-Leffler type functions. As the main results, basic qualitative properties of some test equations will be stated, with emphasis on their stability and asymptotics. Finally, several notes will discuss connections of these results to numerical analysis of underlying fractional differential equations and we will also outline their possible extensions to other (non-uniform) discrete settings.

#

This chapter was previously published in Fractional Calculus: Theory, edited by Roy Abi Zeid Daou and Xavier Moreau, New York: Nova Publishers Inc., 2014. * E-mail address: [email protected] (Corresponding author)

In: Mathematical Research Summaries. Volume 1 Editor: Matthew A. Rowe

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Chapter 70

USING THE HANKEL OPERATOR TO INITIALIZE FRACTIONAL-ORDER SYSTEMS #

Jay L. Adams*, Robert J. Veillette and Tom T. Hartley The University of Akron, Akron, Ohio, US

RESEARCH SUMMARY This chapter presents a comprehensive discussion of using the Hankel operator to characterize the initial-condition response of a fractional-order system. Using the Hankel operator when either the input to the system for t < 0 or the output of the system for t < 0 is known is discussed. Sufficient conditions under which output-based initialization can be done via the Hankel operator are developed for a class of fractional-order systems. The error bounds when using the Hankel-operator of a reduced-order approximation to the fractionalorder system to approximate the initial-condition response are discussed. The Hankeloperator technique is applied to examples, illustrating the results.

#

This chapter was previously published in Fractional Calculus: Theory, edited by Roy Abi Zeid Daou and Xavier Moreau, New York: Nova Publishers Inc., 2014. * E-mail address: [email protected]

In: Mathematical Research Summaries. Volume 1 Editor: Matthew A. Rowe

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Chapter 71

FRACTIONAL REACTION-TRANSPORT EQUATIONS ARISING FROM EVANESCENT CONTINUOUS TIME RANDOM WALKS #

E. Abad1,* , S. B. Yuste2, and K. Lindenberg3 1

Departamento de Física Aplicada and Instituto de Computación Científica Avanzada (ICCAEX) Centro Universitario de Mérida Universidad de Extremadura, Mérida, Spain 2 Departamento de Física and Instituto de Computación Científica Avanzada (ICCAEX) Universidad de Extremadura, Badajoz, Spain 3 Department of Chemistry and Biochemistry and BioCircuits Institute University of California San Diego, La Jolla, California, US

RESEARCH SUMMARY Continuous time random walks (CTRWs) describe a particular class of renewal processes used to model a wide variety of phenomena such as the motion of charge carriers in disordered systems, the dynamics of financial markets, the motion of diffusing particles in crowded environments, and certain anomalous relaxation phenomena in dielectric systems. It is well known that, on long time scales, a CTRW described by a separable probability density function (pdf) for the jump length of a particle and its waiting time between consecutive jumps yields a variety of fractional diffusion equations for suitable (and yet rather general) choices of both pdfs. Such fractional diffusion equations give rise to a broad range of behaviors for the mean square displacement of the particle, ranging from subdiffusive to superdiffusive. In this work we show that fractional equations with interesting solutions may #

This chapter was previously published in Fractional Calculus: Theory, edited by Roy Abi Zeid Daou and Xavier Moreau, New York: Nova Publishers Inc., 2014. * E-mail address: [email protected]

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also be obtained when the above CTRW is combined with a rather general class of death processes (evanescence), including a simple first-order process typical of radioactive decay. A general feature of the resulting fractional equations is that the parameters describing the decay process explicitly appear in the transport term, as opposed to heuristic fractional equations lacking a rigorous mesoscopic justification. In the subdiffusive case, we consider two applications of interest. First, we compute the survival probability of an immobile target surrounded by one or more subdiffusive traps that may spontaneously disappear in the course of their motion. The second example concerns a biologically relevant problem, namely, the formation of stationary morphogen concentration gradients by means of morphogen synthesis, anomalous diffusion, and degradation.

In: Mathematical Research Summaries. Volume 1 Editor: Matthew A. Rowe

ISBN: 978-1-53612-021-9 © 2017 Nova Science Publishers, Inc.

Chapter 72

EXPONENTIAL INTEGRATORS FOR FRACTIONAL DIFFERENTIAL EQUATIONS #

Roberto Garrappa1,* and Marina Popolizio2,† 1 2

Department of Mathematics, University of Bari, Bari, Italy Department of Mathematics and Physics “Ennio De Giorgi” University of Salento, Lecce, Italy

RESEARCH SUMMARY Exponential integrators are a well–established class of effective methods for the numerical integration of systems of differential equations of large dimension, especially in the presence of stiffness. Problems of this kind are common in several applications and usually come from semi–discretization of partial differential equations. The main idea behind exponential integrators is to solve in an exact way the stiff term of the problem and hence apply a time–step integration to the non–stiff term, thus to allow to use less expensive explicit schemes and obtain, at the same time, good stability properties. Recently, the investigation of exponential integrators has been generalized to differential equations of fractional order (FDEs). In this context exponential integrators turn out to be very effective since they overcome some of the typical weak points of numerical methods for FDEs: indeed, it is possible to derive methods with excellent stability properties and, when working with linear problems, to surmount some limitations in accuracy and order of convergence which represent a severe constriction for common methods for FDEs. In this chapter we illustrate the main aspects concerning the derivation of some families of exponential integrators for FDEs and we study the convergence properties.

#

This chapter was previously published in Fractional Calculus: Theory, edited by Roy Abi Zeid Daou and Xavier Moreau, New York: Nova Publishers Inc., 2014. * E-mail address: [email protected] † E-mail address: [email protected]

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Roberto Garrappa and Marina Popolizio

Moreover, we address their numerical implementation with special attention to some peculiar aspects as, for example, the evaluation of Mittag–Leffler functions, with scalar and/or matrix arguments; this is a central feature in the implementation of exponential integrators for fractional order problems. The application to some time– fractional partial differential equations is also presented by means of some numerical examples.

In: Mathematical Research Summaries. Volume 1 Editor: Matthew A. Rowe

ISBN: 978-1-53612-021-9 © 2017 Nova Science Publishers, Inc.

Chapter 73

NON-FRAGILE TUNING OF FRACTIONAL-ORDER PD CONTROLLERS FOR INTEGRATING AND DOUBLE INTEGRATING TIME-DELAY SYSTEMS #

MirSaleh Bahavarnia and Mohammad Saleh Tavazoei* Electrical Engineering Department, Sharif University of Technology, Tehran, Iran

RESEARCH SUMMARY In this chapter, non-fragile algebraic tuning rules are proposed for fractional-order PD controllers in order to be used in control of integrating time-delay systems. It is assumed that these systems are described by Integrating Plus Time Delay (IPTD) or Double Integrating Plus Time Delay (DIPTD) models. The tuning rules are derived based on a recently introduced approach, known as the centroid approach, which leads to designing non-fragile controllers. Considering this approach, it is found out that the centroids of two-parameter admissible regions or the center of mass of three-parameter admissible regions in the controller parameter space provide non-fragile choices for choosing controller parameters.

#

This chapter was previously published in Fractional Calculus: Theory, edited by Roy Abi Zeid Daou and Xavier Moreau, New York: Nova Publishers Inc., 2014. * E-mail address: [email protected]. A part of this chapter has been presented in the 6th IFAC Workshop on Fractional Differentiation and its Applications, Grenoble, France, February 4-6, 2013.

In: Mathematical Research Summaries. Volume 1 Editor: Matthew A. Rowe

ISBN: 978-1-53612-021-9 © 2017 Nova Science Publishers, Inc.

Chapter 74

ON DISCRETE, FINITE-DIMENSIONAL APPROXIMATION OF LINEAR, INFINITE DIMENSIONAL SYSTEMS #

Milan R. Rapaić1,*, Tomislav B. Šekara2 and Mihailo P. Lazarević3 1

Faculty of Technical Sciences, University of Novi Sad, Novi Sad, Serbia Faculty of Electrical Engineering, University of Belgrade, Belgrade, Serbia 3 Faculty of Mechanical Engineering, University of Belgrade, Belgrade, Serbia 2

RESEARCH SUMMARY Many phenomena are naturally described in terms of dynamical systems of infinite order. Such phenomena cannot be adequately described by an interconnection of a finite number of accumulating elements, i.e., by means of differential or difference equations of finite order. Among the well-known examples are distributed parameter systems, which are usually described by partial differential equations, and fractional order systems, which are described by fractional differential equations. In order for an infinite-dimensional system to be simulated or implemented using a digital computer, it must be approximated by a finitedimensional model. Numerous methods for finite-dimensional approximations of infinite dimensional systems have been considered in literature. If spatial distribution of variables is of interest, distributed parameter systems are often simulated by means of the finite elements method (FEM). If the spatial distribution of variables is not of interest, as it is the case with fractional order models, an approximating ordinary differential equation of sufficiently high order is used for approximation. A novel, flexible and numerically efficient method for rational, finite-dimensional approximation of linear, infinite-dimensional systems is presented in the current chapter. The proposed method uses the least-squares (LS) procedure to interpolate frequency domain response of a fractional order system using a finite number of # *

This chapter was previously published in Fractional Calculus: Theory, edited by Roy Abi Zeid Daou and Xavier Moreau, New York: Nova Publishers Inc., 2014. E-mail address: [email protected]; Address: Faculty of Technical Sciences, University of Novi Sad, Novi Sad, Serbia (Corresponding author)

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Milan R. Rapaić, Tomislav B. Šekara and Mihailo P. Lazarević

incident frequencies. An adequate comparative analysis has also been carried out through corresponding examples by applying several other known approximation methods.

In: Mathematical Research Summaries. Volume 1 Editor: Matthew A. Rowe

ISBN: 978-1-53612-021-9 © 2017 Nova Science Publishers, Inc.

Chapter 75

ADVANCED FRACTIONAL DIFFERENTIAL AND INTEGRAL EQUATIONS #

Said Abbas1, Mouffak Benchohra2,* and Gaston Mandata N'Guerekata3,† 1

University of Saida, Saïda, Algeria 2 University of Sidi Bel Abbes King Abdulaziz University in Jeddah, Sidi Bel Abbes, Algeria Jeddah, Saudi Arabia 3 Morgan State University, Baltimore, MD, US

RESEARCH SUMMARY The fractional calculus deals with extensions of derivatives and integrals to non-integer orders. It represents a powerful tool in applied mathematics to study a myriad of problems from different fields of science and engineering, with many break-through results found in mathematical physics, finance, hydrology, biophysics, thermodynamics, control theory, statistical mechanics, astrophysics, cosmology and bioengineering. This book is devoted to the existence and uniqueness of solutions and some Ulam’s type stability concepts for various classes of functional differential and integral equations of fractional order. Some equations present delay which may be finite, infinite or state-dependent. Others are subject to multiple time delay effect. The tools used include classical fixed points theorems. Other tools are based of the measure of non-compactness together with appropriates fixed point theorems. Each chapter concludes with a section devoted to notes and bibliographical remarks and all abstract results are illustrated by examples. The content of the book is new and complements the existing literature in Fractional Calculus. It is useful for researchers and graduate students for research, seminars and #

This chapter was previously published as a book: Advanced Fractional Differential and Integral Equations, by Said Abbas, Mouffak Benchohra and Gaston Mandata N'Guerekata, New York: Nova Publishers Inc., 2015. * [email protected] † gaston.n'[email protected]

162

Said Abbas, Mouffak Benchohra and Gaston Mandata N'Guerekata

advanced graduate courses, in pure and applied mathematics, engineering, biology and all other applied sciences.

In: Mathematical Research Summaries. Volume 1 Editor: Matthew A. Rowe

ISBN: 978-1-53612-021-9 © 2017 Nova Science Publishers, Inc.

Chapter 76

THE HEURISTIC POWER OF THE NON INTEGER DIFFERENTIAL OPERATOR IN PHYSICS: FROM CHAOS TO EMERGENCE, AUTO-ORGANISATIONS AND HOLISTIC RULES #

Alain Le Méhauté Physics Department, Kazan Federal University, Kazan, Russia

RESEARCH SUMMARY The use of fractional differential equations raises a paradox due to the non-respect of the space time noetherian axioms. In environments characterized by scaling laws (hyperbolic geometry associated with fractional diff-integral) energy is no more the invariant of the dynamics. Nevertheless the experimental action requiring the use of energy, the relevant representation of the fractional-process, must be extended. The extension is carried out using the canonical transfer functions in Fourier space and explained by their links with the Riemann zeta function. Category theory informs the extension problem. Ultimately the extension can be expressed by a simple change of referential. It leads to embed the time in the complex space. This change unveils the presence of a time singularity at infinity. The paradox of the energy in the fractality illuminates the heuristic power of the fractional differential equations. In this mathematical frame, it is shown that the dual requirement of the frequency response to differential equations of non-integer order and of the noetherian constraints make gushing out a source of negentropique likely to formalize the emergence of macroscopic correlations into self-organized structures as well as holistic rules of behaviour.

#

This chapter was previously published in Fractional Calculus: Applications, edited by Roy Abi Zeid Daou and Xavier Moreau, New York: Nova Publishers Inc., 2015.  E-mail address: [email protected]

In: Mathematical Research Summaries. Volume 1 Editor: Matthew A. Rowe

ISBN: 978-1-53612-021-9 © 2017 Nova Science Publishers, Inc.

Chapter 77

DYNAMICS OF FRACTIONAL ORDER CHAOTIC SYSTEM #

Sachin Bhalekar* Department of Mathematics, Shivaji University, Kolhapur, India

RESEARCH SUMMARY This chapter deals with the fractional order generalization of the chaotic system proposed by Li et al [Nonlinear Analysis: Modelling & Control, 18 (2013) 66-77]. We discuss the dynamical properties such as symmetry, dissipativity, stability of equilibrium points and chaos. Further we control the chaos in proposed system and present the synchronization phenomenon.

#

This chapter was previously published in Fractional Calculus: Applications, edited by Roy Abi Zeid Daou and Xavier Moreau, New York: Nova Publishers Inc., 2015. * E-mail addresses: sbb [email protected], [email protected]

In: Mathematical Research Summaries. Volume 1 Editor: Matthew A. Rowe

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Chapter 78

PRESSURE CONTROL OF CNG ENGINES BY NON-INTEGER ORDER CONTROLLERS: A NEW TREND IN APPLICATION OF FRACTIONAL CALCULUS TO AUTOMOTIVE SYSTEMS #

Paolo Lino* and Guido Maione† Dipartimento di Ingegneria Elettrica e dell’Informazione, Politecnico di Bari, Bari, Italy

RESEARCH SUMMARY The massive use of electronic control in automotive vehicles improved performance, comfort, safety and reduced pollutant emissions and consumption. In particular, the accurate control of the fuel injected into cylinders allowed the common rail fuel injection system to increase engine performance while reducing emissions, noise and fuel consumption. In this context, compressed natural gas (CNG) engine systems can further reduce emissions to adhere to environmental policy regulations. However, the injection process is strongly nonlinear, time-variant and highly coupled, so suitable control systems must be designed to guarantee the desired performance. This chapter describes how to synthesize and realize non-integer order controllers for pressure control in common rail injection systems of CNG engines. The realization is relatively simple and cheap, as required by the industrial application. Namely, not only low sensitivity to parameter variations and load disturbances must be achieved, but also a limited cost with respect to implementation by consolidated PID controllers. The CNG common rail injection system includes: a tank storing high pressure gas; a main chamber and a control chamber; a solenoid valve; an electronic control unit; a common rail #

This chapter was previously published in Fractional Calculus: Applications, edited by Roy Abi Zeid Daou and Xavier Moreau, New York: Nova Publishers Inc., 2015. * E-mail address: [email protected] † E-mail address: [email protected]

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Paolo Lino and Guido Maione

and electro-injectors. The tank feeds the downstream circuit. The main and control chambers are separated by a moving piston. Both chambers receive fuel from the tank and send it to the common rail, which is a constant volume accumulator connected to the electro-injectors. The inlet flow to the main chamber is regulated by a shutter that is integral with the piston, whose position depends on the equilibrium of the pressures acting on its surfaces. Adjusting the pressure in the control circuit by the solenoid valve regulates the main chamber inflow. Moreover, as the main chamber and the common rail have almost equal pressures, accurate metering of the injected fuel is allowed by setting the injection timings at the same time. This work reports recent advancements in the design and simulation of switched fractional order PI controllers, in which the integral action is of non-integer order. Performance, robustness and disturbance rejection are tested by simulation of virtual prototypes based on non-linear models. The basic idea is to perform a loop-shaping of the open-loop transfer function to obtain frequency domain performance specifications and achieve an optimal feedback system. To this aim, the fractional integrator is profitably used and robust stability of the closed-loop system is guaranteed by a D-decomposition method. There are several benefits of the design approach. Closed formulas determine the controller gains by frequency domain specifications and can be used for an automatic synthesis of the controller. Moreover, the realization of the noninteger operator is by an efficient approximation method that prevents numerical problems and leads to a rational transfer function characterized by interlaced minimum phase zeros and stable poles, so that a reduced approximation error is obtained and easy implementation is possible. To conclude, the noninteger order controllers allow higher accuracy in metering the injected fuel and promptness in setting the rail pressure to the desired reference values.

In: Mathematical Research Summaries. Volume 1 Editor: Matthew A. Rowe

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Chapter 79

LINEAR INTEGER ORDER SYSTEM CONTROL BY FRACTIONAL PI-STATE FEEDBACK #

Rachid Mansouri1, Maamar Bettayeb2,3, Chahira Boussalem1 and Ubaid M. Al-Saggaf 3 1

L2CSP Laboratory, University Mouloud Mammeri of Tizi-Ouzou, Algeria Electrical & Computer Engineering Department, University of Sharjah, UAE 3 Center of Excellence in Intelligent Engineering Systems (CEIES), King Abdulaziz University, Jeddah, KSA

2

RESEARCH SUMMARY This book chapter deals with a linear non-fractional order system control by a PI-state feedback fractional-controller. The fractional aspect of the control law is introduced by a dynamic state feedback as 𝑢(𝑡) = 𝐾𝑝 𝑥(𝑡) + 𝐾𝐼 ℐ𝛼 (𝑥(𝑡)). Two methods, based on pole placement principle, are then proposed to design the feedback vector gains 𝐾𝑝 and 𝐾𝐼 . The first one uses the augmented system method. In this case, the closed-loop characteristic polynomial is of order (𝑞𝑛 + 𝜇) where 𝑛 is the order of the integer system and 𝑞 is the fractional ratio of the non integer order 𝛼 (𝛼 = 𝜇/q). The second proposed method allows to decompose the closed-loop characteristic polynomial into a fractional polynomial of order 𝛼, (0 < 𝛼 < 2) and an integer order polynomial of order 𝑛 − 1. In this case, a suitable choice of the poles provides to obtain, in closed-loop, the Bode's ideal transfer function. These two methods are then applied to stabilize an inverted pendulum-car system and the effectiveness and robustness of the proposed controllers are examined by experiments on a real system.

#

This chapter was previously published in Fractional Calculus: Applications, edited by Roy Abi Zeid Daou and Xavier Moreau, New York: Nova Publishers Inc., 2015.

In: Mathematical Research Summaries. Volume 1 Editor: Matthew A. Rowe

ISBN: 978-1-53612-021-9 © 2017 Nova Science Publishers, Inc.

Chapter 80

FROM THE FORMAL CONCEPT ANALYSIS TO THE NUMERICAL SIMULATION OF THE THERMAL DIFFUSION PHENOMENA IN A FINITE MEDIUM #

Riad Assaf1,2,, Roy Abi Zeid Daou2,†, Xavier Moreau1,‡ and Fady Christophy1,2,# 1

University of Bordeaux, IMS Laboratory, Talence, Bordeaux, France 2 Lebanese German University, Faculty of Public Health, Biomedical Technologies department, Sahel Alma, Jounieh, Lebanon

RESEARCH SUMMARY This chapter shows the use of the fractional order approach in the study of the thermal interface behavior in view to facilitate the identification of this phenomenon and the optimization of its process control. After a short introduction, the main parameters are defined then the semi-infinite plane case study is considered. A representative model is developed based on the system equations. The operational, frequency and time responses are studied. The case study of a finite plane follows using the same methodology, nevertheless exact analytical solutions in the time domain don’t exist; their approximations will be treated in other publications.

#

This chapter was previously published in Fractional Calculus: Applications, edited by Roy Abi Zeid Daou and Xavier Moreau, New York: Nova Publishers Inc., 2015.  E-mail addresses: [email protected]; [email protected]. † E-mail address: [email protected]. ‡ E-mail address: [email protected]. # E-mail addresses: [email protected]; [email protected].

In: Mathematical Research Summaries. Volume 1 Editor: Matthew A. Rowe

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Chapter 81

TEMPERATURE CONTROL OF A DIFFUSIVE MEDIUM USING THE CRONE APPROACH #

Fady Christophy1,2,, Xavier Moreau1,†, Roy Abi Zeid Daou2 and Riad Assaf1,2,‡ 1

University of Bordeaux, Laboratory IMS, Talence, Bordeaux, France 2 Lebanese German University, Faculty of Public Health, Biomedical Technologies department, Sahel Alma, Jounieh, Lebanon

RESEARCH SUMMARY This chapter presents the design of the temperature control of a diffusive medium by using a unique robust controller for three different materials: aluminum, copper and iron. For the control-system design, the aluminum is selected as the material defining the nominal model. Then, the second generation CRONE control is used because the parametric uncertainty (due to the copper and the iron) leads to variations of open-loop gain. Finally, the responses in frequency-domain and in time-domain illustrate the influence of the position of the sensor versus the actuator on the stability degree robustness.

#

This chapter was previously published in Fractional Calculus: Applications, edited by Roy Abi Zeid Daou and Xavier Moreau, New York: Nova Publishers Inc., 2015.  E-mail address: [email protected]. † E-mail address: [email protected]. ‡ E-mail address: [email protected].

In: Mathematical Research Summaries. Volume 1 Editor: Matthew A. Rowe

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Chapter 82

ADAPTIVE SECOND-ORDER FRACTIONAL SLIDING MODE CONTROL WITH APPLICATION TO WATER TANKS LEVEL CONTROL #

Danial Senejohnny1,, Mohammadreza Faieghi2,† and Hadi Delavari 3,‡ 1

School of Electrical Engineering, Sharif University of Technology, Tehran, Iran 2 School of Electrical Engineering, Iran University of Science and Technology, Tehran, Iran 3 Faculty of Electrical Engineering, Hamedan University of Technology, Hamedan, Iran

RESEARCH SUMMARY Combining the fractional calculus with second-order sliding mode control, a novel type of control strategy called second order fractional sliding mode control is introduced for a class of nonlinear dynamical systems subject to uncertainty. A fractional-order switching manifold is proposed and the corresponding control law is formulated based on the Lyapunov stability theory to guarantee the sliding condition. A novel adaptation algorithm is derived to ensure perfect tracking, diminish chattering effect and steady state error by estimating switching controller parameters. Finally, numerical simulation results utilizing the dynamic model of interconnected twin tank system are presented to illustrate the effectiveness of the proposed method.

#

This chapter was previously published in Fractional Calculus: Applications, edited by Roy Abi Zeid Daou and Xavier Moreau, New York: Nova Publishers Inc., 2015.  E-mail address: [email protected] (Corresponding author). † E-mail address: [email protected]. ‡ E-mail address: [email protected].

In: Mathematical Research Summaries. Volume 1 Editor: Matthew A. Rowe

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Chapter 83

FEATURES OF FRACTIONAL OPERATORS INVOLVING FRACTIONAL DERIVATIVES AND THEIR APPLICATIONS TO THE PROBLEMS OF MECHANICS OF SOLIDS #

Yury A. Rossikhin* and Marina V. Shitikova† Research Center on Dynamics of Solids, Voronezh State University of Architecture and Civil Engineering, Voronezh, Russia

RESEARCH SUMMARY The given chapter consists of Introduction, 8 paragraphs and Conclusion. The state-ofthe-art review of papers devoted to the fractional derivatives, fractional operators and their applications is presented in paragraph 1. In first four original paragraphs, from 2 to 5, the theoretical foundations of Rabotnovs fractional operators are presented, namely: the definition of the fractional operators, their connection with fractional derivatives, the multiplication theorem of fractional operators, the class of resolvent operators originated by Rabotnov operator. Besides, the definitions of the generalized Rabotnov operators are formulated, which are represented in terms of finite sums of the fractional Rabotnov operators with one and the same fractional parameter. The class of the resolvent operators, which are originated by the generalized Rabotnov operator, has been constructed. The main viscoelastic operators of frequent use in applications, and particularly, the operator of cylindrical rigidity, are calculated under two assumptions: (1) when the operator of volume expansioncompression is constant, and (2) when it is an operator involving the Rabotnov fractional operator. The connection between the Rabotnov fractional operator and Koellers operators is shown in paragraph 5. The applications of the presented theories to the problems of vibrations #

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of oscillators, propagation of stationary shock waves in hereditarily elastic media, and of impact interaction of an elastic sphere with viscoelastic beams are given, respectively, in paragraphs from 6 to 8.

In: Mathematical Research Summaries. Volume 1 Editor: Matthew A. Rowe

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Chapter 84

THEORY OF DIFFUSIVE STRESSES BASED ON THE FRACTIONAL ADVECTION-DIFFUSION EQUATION

#

Yuriy Povstenko* Institute of Mathematics and Computer Science Jan Długosz University in Czȩstochowa, Poland

RESEARCH SUMMARY Conventional theory of diffusive stresses is based on the principles of the classical theory of diffusion, specifically on the classical Fick law, which relates the matter flux to the concentration gradient. In combination with the balance equation for mass, this law leads to the classical diffusion equation. We study time-nonlocal generalizations of the diffusive flux governed by the Fick law and of the advection flux associated with the velocity field. The nonlocal constitutive equations with the long-tail power memory kernel result in the timefractional advection-diffusion equation. The nonlocal constitutive equations with the middletail memory kernel expressed in terms of the Mittag-Leffler function lead to the fractional advection-diffusion equation of the Cattaneo type. The theory of diffusive stresses based on the fractional advection-diffusion equation is formulated.

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This chapter was previously published in Fractional Calculus: Applications, edited by Roy Abi Zeid Daou and Xavier Moreau, New York: Nova Publishers Inc., 2015. * E-mail address: [email protected]

In: Mathematical Research Summaries. Volume 1 Editor: Matthew A. Rowe

ISBN: 978-1-53612-021-9 © 2017 Nova Science Publishers, Inc.

Chapter 85

MODELLING DRUG EFFECT USING FRACTIONAL CALCULUS #

Clara M. Ionescu* Ghent University, Department of Electrical Energy, Systems and Automation, Zwijnaarde, Belgium

RESEARCH SUMMARY Closed loop control of depth of anesthesia (DOA) implies a good knowledge of the patient pharmaco-kinetics and -dynamics, i.e., the availability of a reliable model of the patient. This is necessary since prediction of drug effect in the body is essentially the main component of regulating DOA. Hitherto, this is done in a complex clinical environment, involving the anesthesiologist as a main decision-maker element. Obviously, the decision of administrating hypnotic and opioid drugs is a difficult one, since over- and under-dosing are a peril for patient’s wellbeing and recovery. The expertise of the anesthesiologist and human factor make this decision a subjective one and may be difficult to justify in a mathematical framework. This chapter introduces emerging tools available on the 'engineering market' imported from the area of fractional calculus. Drug diffusion compartmental models are introduced and a novel interpretation of the classical drug-effect curve given. By employing tools from fractional calculus, model nonlinearity is avoided, allowing linear control strategies for automatic control of DOA systems.

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This chapter was previously published in Fractional Calculus: Applications, edited by Roy Abi Zeid Daou and Xavier Moreau, New York: Nova Publishers Inc., 2015. * Corresponding Author address: Email: [email protected].

In: Mathematical Research Summaries. Volume 1 Editor: Matthew A. Rowe

ISBN: 978-1-53612-021-9 © 2017 Nova Science Publishers, Inc.

Chapter 86

FUZZY FRACTIONAL PID CONTROLLERS: ANALYSIS, SYNTHESIS AND IMPLEMENTATION

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Ramiro S. Barbosa* and Isabel S. Jesus† GECAD − Knowledge Engineering and Decision Support Research Center Institute of Engineering / Polytechnic of Porto (ISEP/IPP) Dept. of Electrical Engineering, Porto, Portugal

RESEARCH SUMMARY Fuzzy logic controllers (FLC) have developed greatly in recent years. They offer easy and robust solutions to complex problems, allowing human reasoning to be applied to the control of systems. This chapter introduces the concepts of fractional calculus in FLC. The resulting fuzzy fractional PID controllers are investigated in terms of their structures and respective digital implementations. In the first part of chapter, a simple and effective tuning methodology is proposed and compared with traditional approaches. The methodology for tuning the fuzzy controllers is based on the prior knowledge of integer/fractional-order control strategy, making the procedure adequate to replace an existent controller in order to improve the system control performance. In the second part of chapter, are devised optimal fuzzy fractional PID controllers by using a particle swarm optimization algorithm. A comparative study between fuzzy integer and fractional PID controllers is presented. The feasibility and effectiveness of the proposed controllers are tested on several benchmark systems that are representative of industrial processes. The simulation results show the better performance of fractional controllers over the conventional PID or fuzzy PID controllers.

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This chapter was previously published in Fractional Calculus: Applications, edited by Roy Abi Zeid Daou and Xavier Moreau, New York: Nova Publishers Inc., 2015. * E-mail address: [email protected] † E-mail address: [email protected]

In: Mathematical Research Summaries. Volume 1 Editor: Matthew A. Rowe

ISBN: 978-1-53612-021-9 © 2017 Nova Science Publishers, Inc.

Chapter 87

FOUNDATIONS OF ISO-DIFFERENTIAL CALCULUS. VOLUME 3: ORDINARY ISO-DIFFERENTIAL EQUATIONS #

Svetlin Georgiev* Faculty of Mathematics and Informatics, Department of Differential Equations, Sofia University, Sofia, Bulgaria

RESEARCH SUMMARY This book is intended for readers who have had a course in iso-differential calculus and it can be used for a senior undergraduate course. Chapter 1 deals with exact iso-differential equations, while first-order iso-differential equations are studied in Chapter 2 and Chapter 3. Chapter 4 discusses iso-integral inequalities. Many iso-differential equations cannot be solved as finite combinations of elementary functions. Therefore, it is important to know whether a given iso-differential equation has a solution and if it is unique. These aspects of the existence and uniqueness of the solutions for first-order initial value problems are considered in Chapter 5. Iso-differential inequalities are discussed in Chapter 6. Continuity and differentiability of solutions with respect to initial conditions are examined in Chapter 7. Chapter 8 extends existence-uniqueness results and continuous dependence on initial data for linear iso-differential systems. Basic properties of solutions of linear iso-differential systems are given in Chapter 9. Chapter 10 deals with the fundamental matrix solutions. In Chapter 11 necessary and sufficient conditions are provided so that a linear iso-differential system has only periodic solutions. The asymptotic behaviour of the solutions of linear systems is investigated in Chapter 12. Chapters 13 and 14 are devoted on some aspects of the stability of solutions of iso-differential systems.

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This chapter was previously published as a book: Foundations of Iso-Differential Calculus. Volume 3: Ordinary Iso-Differential Equations, by Svetlin Georgiev, New York: Nova Publishers Inc., 2015. * Email: [email protected] or [email protected]

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The last major topic covered in this book is that of boundary value problems involving second-order iso-differential equations. After linear boundary value problems are introduced in Chapter 15, Green’s function and its construction is discussed in Chapter 16.

In: Mathematical Research Summaries. Volume 1 Editor: Matthew A. Rowe

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Chapter 88

THE ATOMIC STRUCTURE AND LAW

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Kunming Xu* College of Ocean & Earth Sciences Xiamen University, China

RESEARCH SUMMARY This book discovers four-dimensional space within a sphere with the instantiation of the 2s2p electron octet in a neon shell. Four space dimensions correspond to points, lines, planes, and solids geometrically. This book develops the idea of dynamic calculus that is implemented by circular functions instead of infinitesimal limits. As the law of nature, dynamic calculus of spherical quantities describes harmonic oscillations of electrons in atoms by dimension transformation rather than kinematic movement. In particular, electronic orbitals of 1s2s2p within a neon atom are defined in calculus, trigonometry, and geometry rigorously. A fresh theory of the atomic structure and law is established from scratch that eventually changes the traditional spacetime worldview. The theory derived from atomic spacetime may be extended to the description of molecules, cells, and organisms. For example, both electrons within a helium atom constitute a two-dimensional system, which provides a mathematical model for life phenomena. A husband and a wife are two dimensions of the family; plants and animals are two kingdoms of the advanced lives. The interplay and transformation between both dimensions are the eternal theme of nature. A DNA molecule, composed of space and time strands, is a stepwise LC oscillatory circuitry where each base pair is a capacitor, each phosphate bridge is an inductor, and each deoxyribose is a charge router directed by chiral carbons with anisotropic 2p electronic orbitals. All physical quantities are ordered into a periodic table according to their spacetime dimensions. This original approach provides sharp insight into the properties of and relationships between various physical quantities, paving the way toward the formulation of a #

This chapter was previously published as a book: The Atomic Structure and Law, by Kunming Xu, New York: Nova Publishers Inc., 2015 * E-mail: [email protected]

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Kunming Xu

grand unification theory. Spherical quantities in dynamic calculus complement physical quantities in linear algebra, comply with the Pythagorean theorem and the general Stokes’ theorem, observe Maxwell’s equations, and characterize the rhythms of entities and life essentially. The spherical view also endorses the core concepts of traditional Chinese medicine, such as yin and yang theory, five element theory, and eight trigram philosophy. A previous book under the title “The law of nature: spherical quantity in dynamic calculus” revealed my exciting discovery of four-dimensional space and inspiring invention of dynamic calculus, but left many loose ends to be tied up and many avenues to be explored. After five years of deliberation on the platform, I have developed a more mature thought over many aspects of the book, as if a man strolling in a mountain to and fro for so many times would gain a better knowledge of the landform than before. Hence the objective of this revision is not to extend the scope of the book but to dwell on existing subjects more thoroughly in a more lucid language. For example, how to explain the usage of angular velocity as a complex function identifier (Chapter 1)? How do dimensions in spherical quantities correspond to dimensions in physical quantities (Chapter 1)? How to explain the symmetry and complementarity of electronic orbitals within an argon atom (Chapters 1 and 5)? How to explain the significance of cosine operators casting upon spherical quantities in dimension encapsulation mechanism (Chapters 2 and 5)? What does a curl operator in vector differential calculus mean under quaternity space (Chapter 3)? What is the connection between space and time in spherical quantities and those in physical quantities (Chapter 4)? Why are anisotropic 2p orbitals in a carbon atom the origin of molecular chirality (Chapter 6)? How to explain the physical meaning of the centripetal force deduced from the primary wave function of an electron in a helium atom (Chapter 9)? Why is the duality equation equivalent to Maxwell’s equations in free space (Chapter 10)? Without long time meditations on these fundamental questions, a clear exposition of the topics would not have been possible. The central theme of dynamic calculus is strengthened throughout the text. The principle of a rotatory operation that involves a differential operation with respect to a time dimension and an integral operation over a space dimension is equivalent to Faraday’s law in electromagnetism. A curl operator is equivalent to a dynamic differential operator or a cosine operator. And the complementarity of two orthogonal spherical quantities agrees with the Pythagorean theorem. This dynamic calculus paradigm is repeatedly illustrated by dimension diagrams throughout the whole book. A glimpse of Appendix III will reveal how the law of nature in dynamic calculus is omnipresent and compatible with established physical and mathematical laws.

In: Mathematical Research Summaries. Volume 1 Editor: Matthew A. Rowe

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Chapter 89

COMPUTING ALGORITHMS FOR SOLUTIONS OF PROBLEMS IN APPLIED MATHEMATICS AND THEIR STANDARD PROGRAM REALIZATION. PART 1: DETERMINISTIC MATHEMATICS AND PART 2: STOCHASTIC MATHEMATICS #

K. J. Kachiashvili1, D. YU. Melikdzhanian2 and A. I. Prangishvili3 1

Full Professor of Georgian Technical University, Main Scientific Worker of the I. Vekua Institute of Applied Mathematics of the Tbilisi State University, Tbilisi, Georgia 2 Associated Professor of Georgian Technical University, Tbilisi, Georgia 3 Professor, Rector of Georgian Technical University, Tbilisi, Georgia

RESEARCH SUMMARY Algorithms were always an important part of many branches in the sciences. In many manuals and handbooks, algorithms of problems of computational mathematics are focused on the manual performance or by means of a calculator. In these books, descriptions of algorithms, their solutions and main characteristics are discussed. The present works are the outcome of many years of the authors’ work on solving different problems and tasks from domains of instruction making, metrology, system analysis, ecology, data analysis from ecology, agriculture, medicine and creation of corresponding universal computer packages and systems.

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This chapter was previously published as a book: Computing Algorithms For Solutions of Problems in Applied Mathematics and their Standard Program Realization. Part 1: Deterministic Mathematics and Part 2: Stochastic Mathematics, by K. J. Kachiashvili, D. YU. Melikdzhanian and A. I. Prangishvili, New York: Nova Publishers Inc., 2015.

In: Mathematical Research Summaries. Volume 1 Editor: Matthew A. Rowe

ISBN: 978-1-53612-021-9 © 2017 Nova Science Publishers, Inc.

Chapter 90

FOUNDATIONS OF ISO-DIFFERENTIAL CALCULUS. VOLUME 4: ISO-DYNAMIC EQUATIONS #

Svetlin Georgiev* Faculty of Mathematics and Informatics, Department of Differential Equations, Sofia University, Sofia, Bulgaria

RESEARCH SUMMARY This book is intended for readers who have had a course in difference equations, isodifferential calculus and it can be used for a senior undergraduate course. Chapter 1 deals with the linear first-order iso-difference equations, equilibrium points, eventually equilibrium points, periodic points and cycles. In Chapter 2 are introduced the iso-difference calculus and the general theory of the linear homogeneous and nonhomogeneous iso-difference equations. In Chapter 3 are studied the systems of linear iso-difference equations and the linear periodic systems. Chapter 4 is devoted to the stability theory. They are considered the nonautonomous linear systems, Lyapunov’s direct method, stability by linear approximation. In Chapter 5 is considered the oscillation theory. They are defined the iso-self-adjoint second-order iso-difference equations and they are given some of their properties. They are considered some classes nonlinear iso-difference equations. In Chapter 6 is studied the asymptotic behavior of some classes iso-difference equations. Time scales iso-calculus is introduced in Chapter 7. They are given the main properties of the backward and forward jump iso-operators. They are considered the iso-differentiation and iso-integration. They are introduced the iso-Hilger’s complex plane and the iso-exponential function.

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This chapter was previously published as a book: Foundations of Iso-Differential Calculus. Volume 4: IsoDynamic Equations, by Svetlin Georgiev, New York: Nova Publishers Inc., 2015. * Email: [email protected] or [email protected]

In: Mathematical Research Summaries. Volume 1 Editor: Matthew A. Rowe

ISBN: 978-1-53612-021-9 © 2017 Nova Science Publishers, Inc.

Chapter 91

A PROPOSED CLOUD COMPUTING BUSINESS FRAMEWORK #

Victor Chang* PhD, Senior Lecturer in Computing Leeds Beckett University, School of Computing Creative Technologies and Engineering, Headingley Campus, Leeds, UK

RESEARCH SUMMARY This book gives an overview of Cloud Computing (CC) and presents a literature review explaining the development of CC. Selected frameworks are discussed, including those suitable for this research. Technical and organisational challenges for CC are also identified which include: Technical:   

Vendors' lock-in; Security; Interoperability.

Organisational:   

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No connections between different services; Do not have a structured measurement of Cloud business performance; Portability.

This chapter was previously published as a book: A Proposed Cloud Computing Business Framework, by Dr. Victor Chang, New York: Nova Publishers Inc., 2015. * [email protected]

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Victor Chang

This book focuses on organisational challenges and recommendation to address organisational challenges. Research questions and key areas of research are focused on organisational challenges in this book. To help organisations to achieve good Cloud design, deployment and services, there is a need for the proposal and development of a framework, the Cloud Computing Business Framework (CCBF), which explains how three research questions are connected together. These issues are: (i) Organisational Sustainability: How do you measure cloud business performance accurately? (ii) Portability: How do you demonstrate Cloud portability? (iii) Linkage: How do you link and integrate different services? The CCBF is a conceptual and an architectural framework to be validated through modelling, simulation, experiments and hybrid case studies. The architecture of the CCBF is presented to explain how different key areas can relate to each other and fit into the framework. Major research contributions include: (i) Organisational Sustainability: It introduces Organisational Sustainability Modelling (OSM), which is the improvement of a Nobel-prized model, Capital Asset Pricing Model (CAPM) and presents the result in 3D Visualisation with Quality Assurance in place. It is a unique way to present ROI and has eight case studies to support. (ii) Portability: The Financial Software as a Service (FSaaS) is demonstrated which uses Monte Carlo Methods (MCM) and 3D black Scholes Model (BSM) to quantify and visualise risks, including 2008 and 2011 financial crisis simulations. (iii) Linkage: An innovative approach, Business Integration as a Service (BIaaS), demonstrates how different services can be connected and integrated as a single service. Results of case studies, simulations, modelling and experiments are used to validate CCBF and are discussed in details which collaborators find results of CCBF useful for their Cloud adoption. Selected results have been published including four journals and one book chapter. Finally, future work plans are proposed and followed-up steps are explained.

In: Mathematical Research Summaries. Volume 1 Editor: Matthew A. Rowe

ISBN: 978-1-53612-021-9 © 2017 Nova Science Publishers, Inc.

Chapter 92

THE COMPLEXITIES OF MATH SKILLS DEVELOPMENT #

Robert Perna and Ashlee R. Loughan Neurobehavioral Associates, Augusta GA

RESEARCH SUMMARY People differ dramatically in their ability to perform different kinds of math operations. It is estimated that approximately 5% of children have a diagnosable math weakness, another 47% have a math weakness relative to their general intellectual ability, and over 50% of students with individualized education programs require specific mathematic goals. Based on learning theories and research showing that depth of information processing is important for effective learning, math learning is best if it is made meaningful. Real life examples and hands-on approaches may be beneficial for most people learning math. These practices also will likely change the evolving pattern of people feeling math is a nonessential subject. Mathematics is often thought of as a subject that a person is either innately proficient at or not, with little room for fluctuation in-between. When in reality, the development and performance mathematics incorporates an extensive array of cognitive skills and abilities. Because different types of math necessitate different cognitive skills, a person may be very good at some types of math and far less proficient at other types of math. At least conceptually, if the effective development of math skills are contingent on certain foundational cognitive skills, such as visuospatial skills, working memory, or other skills, it may be important that students receive appropriate exercises and remediation in those cognitive domains as well as typical mathematic skill exercises. All of this needs to be built on a strong number sense and basic math skills foundation. Some researchers have gone so far as to try and find variables predictive of future math performance. Research has found that an identified mathematics learning disability in the third grade can be accurately predicted from difficulty on several mathematics tasks at kindergarten, such as reading numerals, applying #

This chapter was previously published in Advances in Mathematics Research. Volume 19, edited by Albert R. Baswell, New York: Nova Publishers Inc., 2015.

196

Robert Perna and Ashlee R. Loughan

counting principles, number line concepts, and mental addition. Aiding in the investigation of math development are the studies focusing on children who are exceptionally talented in math, thus examining and correlating math strengths and the cognitive processes facilitating this aptitude. This chapter will review math development throughout the educational process and discuss why certain individual differ in their math skills and other relevant factors at each stage of learning math, will be discussed.

In: Mathematical Research Summaries. Volume 1 Editor: Matthew A. Rowe

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Chapter 93

CONSTRUCTION OF AN NP PROBLEM WITH AN EXPONENTIAL LOWER BOUND

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Roman V. Yampolskiy Computer Engineering and Computer Science, University of Louisville

RESEARCH SUMMARY In this paper we present a Hashed-Path Traveling Salesperson Problem (HPTSP), a new type of problem which has the interesting property of having no polynomial time solutions. Next we show that HPTSP is in the class NP by demonstrating that local information about sub-routes is insufficient to compute the complete value of each route. As a consequence, via Ladner’s theorem, we show that the class NPI is non-empty.

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This chapter was previously published in Advances in Mathematics Research. Volume 19, edited by Albert R. Baswell, New York: Nova Publishers Inc., 2015.  Email: [email protected].

In: Mathematical Research Summaries. Volume 1 Editor: Matthew A. Rowe

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Chapter 94

MISCONCEPTIONS AND MISUNDERSTANDINGS (M&M) OF EXPLORATORY FACTOR ANALYSIS: SOME CLARIFICATIONS #

Eddie T. C. Lam1*, PhD, and Anita N. Lee2, DPE 1

Department of Health and Human Performance, Cleveland State University, OH, US 2 Department of Health and Physical Education, Eastern Connecticut State University, CT, US

RESEARCH SUMMARY Exploratory factor analysis (EFA) is a popular statistical technique in research studies. In recent years, structural equation modeling (SEM) has become more popular. To distinguish itself from the measurement model of the SEM (i.e., confirmatory factor analysis), factor analysis is always referred to as EFA. However, a review of published articles using EFA demonstrates that some of the researchers, and even the reviewers, are bewildered with its usage and applications. For example, EFA (also known as common factor analysis) is always confused with principal component analysis (PCA). Henson and Roberts commented that PCA was often misused as a substitute or variant of EFA. Though both PCA and EFA are exploratory techniques that can be used to summarize the data and to test hypotheses (Haig, 2006), their usage and application are quite different in nature. The central idea in PCA is summarization. It is a data reduction procedure (i.e., to simply reduce a large number of items to a smaller number of underlying latent dimensions). Strictly speaking, PCA should be considered as “component analysis”, but it is frequently mistaken as a form of factor analysis. In contrast, EFA is used to examine the factor structure or the pattern of relationships among

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This chapter was previously published in Advances in Mathematics Research. Volume 19, edited by Albert R. Baswell, New York: Nova Publishers Inc., 2015. * Corresponding Author: Eddie T. C. Lam, Ph.D., Dept. of Health & Human Performance, Cleveland State University, 2121 Euclid Avenue, JH 143, Cleveland, OH 44115-2214. Tel: (216)687-5051, Fax: (216)6875410, E-mail: [email protected].

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Eddie T. C. Lam and Anita N. Lee

variables. The main purpose of current article is to provide an overview of these two analytic methods and their applications along with some recommended practices.

In: Mathematical Research Summaries. Volume 1 Editor: Matthew A. Rowe

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Chapter 95

EXPLORATORY STRUCTURAL EQUATION MODELING: A NEW TREND OF FACTOR ANALYSIS

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Anita N. Lee1, DPE and Eddie T. C. Lam2, PhD 1

Department of Health and Physical Education Eastern Connecticut State University, CT, US 2 Department of Health and Human Performance Cleveland State University, Ohio, US

RESEARCH SUMMARY Structural equation modeling (SEM) is a multivariate statistical method to estimate the causal relationship among latent variables commonly employed in education and social sciences. Traditionally, confirmatory factor analysis (CFA) measurement models are used prior to the SEM analysis. Marsh as well as Marsh, Hau, and Grayson indicated that many psychology measuring instruments cannot even meet the minimum goodness-of-fit criteria. Asparouhov and Muthén indicated that SEM using CFA measurement model cannot achieve satisfactory model fit frequently, and yet extensive model modifications are required. Misspecification of zero loadings would lead factor distortion with overestimated factor correlations. Therefore, Asparouhov and Muthén suggested that SEM with exploratory factor analysis (EFA) measurement model is a better technique to avoid these issues. Instead of confirming the relationships among observed variables and latent variables prior to performing SEM, the EFA-SEM (ESEM) approach with rotation is incorporated within the SEM. This commentary discusses the benefits and restriction of SEM using confirmatory approach and the benefits of SEM by exploratory approach.

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This chapter was previously published in Advances in Mathematics Research. Volume 19, edited by Albert R. Baswell, New York: Nova Publishers Inc., 2015.  Correspondence should be sent to Anita N. Lee, Eastern Connecticut State University, Department of Health and Physical Education, 83 Windham Street, Willimantic, CT 06226. E-mail: [email protected].

In: Mathematical Research Summaries. Volume 1 Editor: Matthew A. Rowe

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Chapter 96

QUANTUM INFORMATION MEASURES AND MOLECULAR PHASE EQUILIBRIA

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Roman F. Nalewajski Department of Theoretical Chemistry, Jagiellonian University, Cracow, Poland

RESEARCH SUMMARY Information Theory is applied to explore molecular equilibrium states. Non-classical (phase/current related) complements of the classical (probability based) measures of the resultant information content in electronic states are introduced and the information principles for determining molecular equilibria are examined. The “vertical” (probability-constrained) entropic rules are explored within the familiar Levy and Harriman-Zumbach-Maschke constructions of Density Functional Theory. A close parallelism between the vertical maximum-entropy and minimum-energy principles in quantum mechanics and their thermodynamic analogs is emphasized. A relation between the probability and phase distributions in the “horizontal” (probability-unconstrained) phase-equilibria is explored. These solutions are shown to involve the spatial phase contribution related to the system electron density. Selected properties of such molecular equilibrium states are examined. The complete specification of the equilibrium states of molecular/promolecular fragments, including the subsystem density and the equilibrium phase of the system as a whole, is advocated and illustrated for bonded hydrogens in H2. Elements of the non-equilibrium thermodynamic description of molecular systems are formulated. They recognize the independent probability and phase densities, the associated currents, and their contributions to the quantum entropy density and its current. The phase and entropy continuity equations are explored and the local rates of production (sources) of these quantities are identified.

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This chapter was previously published in Advances in Mathematics Research. Volume 19, edited by Albert R. Baswell, New York: Nova Publishers Inc., 2015.

In: Mathematical Research Summaries. Volume 1 Editor: Matthew A. Rowe

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Chapter 97

A MATHEMATICAL MODEL AND OPTIMIZATION OF RECTANGULAR MUFFLERS HYBRIDIZED WITH ONE-CHANNEL SPLITTERS BY SA METHOD

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Min-Chie Chiu* Department of Mechanical and Automation Engineering, Chung Chou University of Science and Technology, Taiwan, R.O.C.

RESEARCH SUMMARY The application of rectangular mufflers internally hybridized with splitters is a leading technology in industrial noise abatement, today. However, there has been a palpable lack of academic work in exploring the acoustical performance of space-constrained mufflers with splitters. Therefore, an assessment of the Sound Transmission Loss (STL) of rectangular mufflers internally hybridized with a one-channel splitter within a limited space will be considered, here. Based on the plane wave theory, an acoustical lumped method is adopted and transformed to a four-pole system matrix. The simulated annealing (SA) method, a robust scheme utilized to search for the global optimum by imitating a physical annealing process, is used during this optimization process. Before dealing with a broadband noise, the STL’s maximization relative to a one-tone noise (500Hz) is offered to confirm the SA method’s reliability. Consequently, the research presented in this paper can provide an efficient way in maximizing the acoustical performance of rectangular mufflers that are internally hybridized with a one-channel splitter within a limited space.

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This chapter was previously published in Advances in Mathematics Research. Volume 19, edited by Albert R. Baswell, New York: Nova Publishers Inc., 2015. * Corresponding author: Min-Chie Chiu. Phone: (886)-4-8359000#2544; Fax No.: (886)-4-8394076; E-mail: [email protected]. Mailing address: Department of Mechanical and Automation Engineering, Chung Chou University of Science and Technology, 6, Lane 2, Sec.3, Shanchiao Rd., Yuanlin, Changhua 51003, Taiwan, R.O.C.

In: Mathematical Research Summaries. Volume 1 Editor: Matthew A. Rowe

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Chapter 98

WORST-CASE ANALYSIS VERSUS AVERAGE-CASE ANALYSIS FOR COMBINATORIAL OPTIMIZATION PROBLEMS #

Nodari Vakhania* Facultad de Ciencias, UAEMor, Mexico

RESEARCH SUMMARY Two basic computational complexity measures are the worst-case and the average-case complexities. The worst-case estimation is useful since it guarantees a certain worst-case behavior of the given algorithm for a worst possible, for that algorithm, problem instance. At the same time, the worst-case estimation might be quite unpractical as the latter worst possible problem instance may never occur in practice. The probabilistic average-case analysis tries to capture the most commonly expected problem instances for a given application and estimate the behavior of the algorithm for these problem instances. Time and also space complexities (in the worst or average cases) estimate the expected amount of computer time and memory, respectively, required for a given exact or approximation algorithm. For an approximate algorithm it is also reasonable to think about the average-case quality estimation of that algorithm; i.e., estimation of the quality of the solutions that the algorithm would deliver for the most common (for a given application) problem instances. The authors consider a well-known strongly NP-hard job-shop scheduling problem and a combinatorial enumeration algorithm that reduces the solution space of this problem. The authors estimate this reduction on the basis of the proposed probabilistic model, that shows an exponential reduction of the whole set of the feasible solutions.

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This chapter was previously published in Advances in Mathematics Research. Volume 19, edited by Albert R. Baswell, New York: Nova Publishers Inc., 2015. * E-mail address: [email protected]

In: Mathematical Research Summaries. Volume 1 Editor: Matthew A. Rowe

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Chapter 99

MATHEMATICAL AND STATISTICAL APPLIED METHODS: STUDYING THE RELATIONSHIP BETWEEN CLIMATIC VARIABLES AND COTTON PRODUCTION #

Zakaria M. Sawan Cotton Research Institute, Agricultural Research Center, Ministry of Agriculture & Land Reclamation, Giza, Egypt

RESEARCH SUMMARY This study investigates the predicted effects of climatic factors during convenient intervals (in days) on cotton (G. barbadense) flower and boll production compared with daily observations. Also, covers the statistical relationship between climatic variables and aspects of cotton production and the effects of climatic factors prevailing prior to flowering or subsequent to boll setting on flower and boll production and retention in cotton. Further, cotton flower and boll production as affected by climatic factors and soil moisture status has been considered. Evaporation, sunshine duration, relative humidity, surface soil temperature at 1800 h, and maximum air temperature, are the important climatic factors that significantly affect flower and boll production. The least important variables were found to be surface soil temperature at 0600 h and minimum temperature. The five-day interval was found to be more adequately and sensibly related to yield parameters. Evaporation; minimum humidity and sunshine duration were the most effective climatic factors during preceding and succeeding periods on boll production and retention. There was a negative correlation between flower and boll production and either evaporation or sunshine duration, while that correlation with minimum relative humidity was positive. The soil moisture status showed low and insignificant correlation with flower and boll production. Higher minimum relative humidity, short period of sunshine duration, and low temperatures enhanced flower and boll formation.

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This chapter was previously published in Advances in Mathematics Research. Volume 19, edited by Albert R. Baswell, New York: Nova Publishers Inc., 2015.  Email: [email protected]

In: Mathematical Research Summaries. Volume 1 Editor: Matthew A. Rowe

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Chapter 100

QUANTUM CRYPTOGRAPHY WITHIN SEVERAL SEQUENTIAL ATTACKS IN BB84 PROTOCOL #

Mustapha Dehmani, Hamid Ez-Zahraouy and Abdelilah Benyoussef Laboratory of Magnetism and High Energy Physics (URAC 12) Physics Department, Faculty of Sciences, University Mohammed V Rabat, Morocco

RESEARCH SUMMARY The work of this chapter focuses on the study of information security with the BB84 quantum cryptography protocol in several sequential cloning and interception-resend attacks in both perfect and depolarizing quantum channels. We have shown that quantum error, mutual information and information security depend strongly on the number of spies, their angles of attack, their probability of interception and channel noise. However, the transition "non-secure information to secure information" can take place by increasing the number of sequential attacks. We also studied the safety information in the case where the states of the quantum protocol BB84 bases are not all orthogonal. It turns out that the protocol is optimal in terms of specific non orthogonally. Besides, the effect of the anisotropy of the transmission channel on the basis of signal states of entangled photons was also studied. For highly entangled signals, we have shown that the amount of transmitted information is maximal, in the case of a channel depolarizer sufficiently anisotropic, unlike the case of weakly entangled signals wherein the amount of transmitted information is maximal in the case where the channel is perfectly isotropic.

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This chapter was previously published in Advances in Mathematics Research. Volume 19, edited by Albert R. Baswell, New York: Nova Publishers Inc., 2015.

In: Mathematical Research Summaries. Volume 1 Editor: Matthew A. Rowe

ISBN: 978-1-53612-021-9 © 2017 Nova Science Publishers, Inc.

Chapter 101

FOUNDATIONS OF ISO-DIFFERENTIAL CALCULUS. VOLUME 5: ISO-STOCHASTIC DIFFERENTIAL EQUATIONS #

Svetlin Georgiev* Faculty of Mathematics and Informatics, Department of Differential Equations, Sofia University, Sofia, Bulgaria

RESEARCH SUMMARY This book is intended for readers who have had a course in iso-differential calculus and theory of probability. It can be used for a senior undergraduate course. Chapter 1 represents a short introduction to the theory of iso-probability theory. They are defined iso-probability measure, iso-probability space, random iso-variable of the first, second, third, fourth and fifth kind, iso-expected values, iso-martingales, iso-Brownian motion, iso-Wiener processes, Paley-Wiener-Zygmund integral, It ˆo’s iso-integral, and they are deducted some of their properties. Chapter 2 is devoted on the iso-stochastic differential equations of the first, second and third kind, and for them they are proved the general existence and uniqueness theorems. They are given some methods for solving of some classes iso-stochastic differential equations. Chapter 3 deals with the linear iso-stochastic differential equations. The dependence on parameters and initial data is considered in Chapter 4. In Chapter 5 is investigated the stability of the main classes iso-stochastic differential equations. Iso-Stratonovich iso-integral and its properties are considered in Chapter 6.

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This chapter was previously published as a book: Foundations of Iso-Differential Calculus. Volume 5: Iso-Stochastic Differential Equations, by Svetlin Georgiev, New York: Nova Publishers Inc., 2015. * Email: [email protected] or [email protected]

In: Mathematical Research Summaries. Volume 1 Editor: Matthew A. Rowe

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Chapter 102

COMPUTATIONAL RECIPES OF LINEAR AND NONLINEAR SINGULAR INTEGRAL EQUATIONS AND RELATIVISTIC MECHANICS IN ENGINEERING AND APPLIED SCIENCE. VOLUME I #

Evangelos G. Ladopoulos* Civil Engineer, Mechanical Engineer Interpaper Research Organization, Athens, Greece

RESEARCH SUMMARY The present book deals with the computational recipes of the finite-part singular integral equations, the multidimensional singular integral equations and the non-linear singular integral equations, which are widely used in many fields of engineering mechanics and mathematical physics with an applied character, like elasticity, plasticity, thermoelastoplasticity, viscoelasticity, viscoplasticity, fracture mechanics, structural analysis, elastodynamics, fluid mechanics, hydraulics, potential flows and aerodynamics. Such types of linear and non-linear singular integral equations form the latest high technology on the solution of very important problems of solid and fluid mechanics and therefore special attention should be given by the reader of the present book, who is interested for the new computational technology of the twentieth-one century. Chapter 1 deals with a historical report and an extended outline of References, for the numerical evaluation methods for the finite-part singular integral equations, the multidimensional singular integral equations and the non-linear singular integral equations. Chapter 2 is devoted with the computational recipes for the solution of the finite-part singular integral equations defined in Banach spaces and in general Hilbert spaces. In the same

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This chapter was previously published as a book: Computational Recipes of Linear and Non-Linear Singular Integral Equations and Relativistic Mechanics in Engineering and Applied Science. Volume I, by Evangelos G. Ladopoulos, New York: Nova Publishers Inc., 2015. * E-mail: [email protected]

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Chapter are proposed and investigated all possible approximation methods for the numerical evaluation of the finite-part singular integral equations, as closed form solutions for the above types of integral equations are available only in simple cases. Also, Chapter 2 provides further several computational integration rules for the solution of the finite-part singular integral equations. Furthermore, Chapter 3 deals with the application of the finite-part singular integral equations in fracture mechanics and elasticity, by calculating the stress intensity factors in several crack problems which are reduced to the solution of such a type (or systems) of integral equations. Chapter 4 provides further the application of singular integral equations in aerodynamics, by studying planar airfoils in two-dimensional aerodynamics. In Chapter 5 the Singular Integral Operators Method (S.I.O.M.) is introduced and investigated for the numerical evaluation of the multidimensional singular integral equations. This approximation method in many cases offers important advantages over “domain” type solutions, like finite elements and finite difference, as well as analytical methods such as complex variable methods. Chapter 6 is devoted with the application of the multidimensional singular integral equations in elasticity, viscoelasticity and fracture mechanics of isotropic solids, by considering several two- and three-dimensional elastic stress analysis methods and crack problems. On the other hand, in Chapter 7 is being investigated a special field of applied mechanics, named as Relativistic Mechanics, which is a combination of the classical theory of elasticity and general relativity. Relativistic Mechanics has two main branches Relativistic Elasticity and Relativistic Thermo-Elasticity and according to the above theory, the relative stress tensor for moving structures has been formulated and a formula has been given between the relative stress tensor and the absolute stress tensor of the stationary frame. This leads to the Universal Equation of Elasticity and the Universal Equation of Thermo-Elasticity. Beyond the above, Chapter 8 deals with the application of the multidimensional singular integral equations in elasticity and fracture mechanics of anisotropic solids, by considering two- and three-dimensional elastic stress analysis. In this case the fundamental solutions of anisotropic stress field analysis are being investigated. Also, Chapter 9 provides further the application of the multidimensional singular integral equations in plasticity of isotropic solids by proposing and studying several applications of two- and three-dimensional plasticity and thermoelastoplasticity.

In: Mathematical Research Summaries. Volume 1 Editor: Matthew A. Rowe

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Chapter 103

COMPUTATIONAL RECIPES OF LINEAR AND NONLINEAR SINGULAR INTEGRAL EQUATIONS AND RELATIVISTIC MECHANICS IN ENGINEERING AND APPLIED SCIENCE. VOLUME II #

Evangelos G. Ladopoulos* Civil Engineer, Mechanical Engineer Interpaper Research Organization, Athens, Greece

RESEARCH SUMMARY The present book deals with the computational recipes of the finite-part singular integral equations, the multidimensional singular integral equations and the non-linear singular integral equations, which are widely used in many fields of engineering mechanics and mathematical physics with an applied character, like elasticity, plasticity, thermoelastoplasticity, viscoelasticity, viscoplasticity, fracture mechanics, structural analysis, elastodynamics, fluid mechanics, hydraulics, potential flows and aerodynamics. Such types of linear and non-linear singular integral equations form the latest high technology on the solution of very important problems of solid and fluid mechanics and therefore special attention should be given by the reader of the present book, who is interested for the new computational technology of the twentieth-one century. Chapter 10 deals with the coupling method of singular integral equations and finite elements in elasticity. This combined method is especially used in cases of unbounded domains or regions of high stress concentration. Furthermore, Chapter 11 presents a plate bending analysis by using multidimensional singular integral equations. Also, in the same Chapter the coupling method of singular integral equations and finite elements is applied to

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This chapter was previously published as a book: Computational Recipes of Linear and Non-Linear Singular Integral Equations and Relativistic Mechanics in Engineering and Applied Science. Volume II, by Evangelos G. Ladopoulos, New York: Nova Publishers Inc., 2015. * E-mail: [email protected]

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the solution of plate bending problems. On the other hand, in Chapter 12 the multidimensional singular integral equations are applied to the solution of potential flows problems and in hydraulics. Applications are given to the solution of potential flows over spillways and in open-channel transitions. Also, in Chapter 13 are introduced and investigated the hypersingular integral equations, which are a special kind of finite-part singular integral equations. Computational recipes are used for the numerical evaluation of the hypersingular integral equations. In Chapter 14 some general computer program codes for elastostatics and potential flow problems are outlined. Thus, the Fortran code of these programs is given, together with an analytical description of the subroutines which are used. Special attention should be given by the reader of this book to the above computer programs which provide the solution of the generalized problems of elastostatics and potential problems. Furthermore, Chapter 15 is devoted with the investigation of several approximation methods (like the collocation and the quadrature methods) for the numerical evaluation of the non-linear singular integral equations, as closed form solutions of such type of non-linear integral equations are very difficult to be determined. In the same Chapter the non-linear programming method is extensively outlined and investigated. Chapter 16 provides further the application of the non-linear singular integral equations in fluid mechanics, fluid dynamics and aerodynamics, for the solution of generalized problems of turbomachines and aircrafts. Furthermore in the same Chapter the non-linear singular integral equations are applied to the determination of the velocity and pressure coefficient field around a NACA airfoil in 2-D inviscid and unsteady flow. Finally, Chapter 17 is devoted with the application of the non-linear integro-differential equations in structural analysis, by considering two non-linear problems of an orthotropic shallow spherical shell analysis and a sandwich plates stress analysis. Also, Chapter 18 deals with the application of the non-linear singular integral equations in the theory of elastodynamics, for the solution of the seismic wave equation.

In: Mathematical Research Summaries. Volume 1 Editor: Matthew A. Rowe

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Chapter 104

THE LAX-MILGRAM THEOREM AND SOME APPLICATIONS TO PARTIAL DIFFERENTIAL EQUATIONS #

Paul Bracken Department of Mathematics, University of Texas, Edinburg, TX, US

RESEARCH SUMMARY The Lax-Milgram theorem can be used to prove existence and uniqueness of weak solutions to partial differential equations, in particular, elliptic boundary value problems. After introducing some pertinent information required for the development of the theorem, it is stated and two proofs are given in detail. Several examples of its application to relevant boundary value problems are presented. Some consequences of these results and their relevance to computational aspects of the subject are summarized at the end.

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This chapter was previously published in Partial Differential Equations: Classification, Properties and Applications, edited by Deborah E. Richards, New York: Nova Publishers Inc., 2015.

In: Mathematical Research Summaries. Volume 1 Editor: Matthew A. Rowe

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Chapter 105

COUPLED PDES AND CONTROL SYSTEMS ARISING IN CLIMATE DYNAMICS: OCEAN-ATMOSPHERE INTERACTIONS AND TROPICAL INSTABILITY WAVES

#

Aziz Belmiloudi* Institut de Recherche Mathématique de Rennes (IRMAR), Rennes, France

RESEARCH SUMMARY This chapter investigates nonlinear control problems for coupled partial differential equations arising from climate and circulation dynamics in equatorial zone. The phenomenon and processes that we want to modelize, by coupled and time-dependent PDEs, occur in tropical Atlantic and Pacific regions: the circulation is there characterized by steady zonal currents varying monthly or seasonally and by long waves propagating westward along the equator known as "equatorial waves", driven by the variability of atmospheric currents and superimposed to the steady mean currents. The equatorial waves can be connected with strong vertical velocities and then induce "upwellings" or "downwellings". This study corresponds to the modeling of tropical instability waves (taking into account the complex interaction between the atmosphere and the ocean circulation) which are illustrated by the "El Ni ˜ no" phenomena and tropical cyclones. After the introduction in which we give background, motivation and fundamental principles governing circulation dynamics, we present a mathematical model of circulation mechanisms, operating in the equatorial zone, in a global climate system, and give some assumptions and notations. The equations are non-linear, timedependent and coupled, and are of Navier-Stokes type for the velocity and pressure, and of transport-diffusion type for the temperature, with non linear boundary and interface conditions. Afterword, we investigate the well-posedness of governing nonlinear systems. For #

This chapter was previously published in Partial Differential Equations: Classification, Properties and Applications, edited by Deborah E. Richards, New York: Nova Publishers Inc., 2015. * IRMAR-INSA de Rennes, 20 avenue des Buttes de Coësmes, CS 14315,35043 Rennes Cédex, France; E-mail address: [email protected]; [email protected]

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provide the uniqueness, we prove some regularity results. Next, sensitivity and control problems are presented and analyzed. The problem is controlled by the variability of the heat interface-stress between the ocean and atmosphere. The observation is the vorticity of the ocean and (or) of the atmosphere. Finally, we conclude this work with some comments and possible future developments.

In: Mathematical Research Summaries. Volume 1 Editor: Matthew A. Rowe

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Chapter 106

INTEGRATION OF PDE WITH THE HELP OF ANALYSIS OVER OCTONIONS AND CAYLEY-DICKSON ALGEBRAS #

Sergey V. Ludkovsky* Department of Applied Mathematics, Moscow State Technical University MIREA, Moscow, Russia

RESEARCH SUMMARY The chapter is devoted to the integration of partial differential equations (PDE) with the help of non-commutative analysis over octonions and Cayley-Dickson algebras. For this purpose a non-commutative line integration of functions and generalized functions is studied. First, second and higher order PDE with continuous, piecewise continuous and generalized variable coefficients over Cayley-Dickson algebras are investigated. Then solutions of some types of non-linear PDE over Cayley-Dickson algebras are studied. This technique is based on decompositions of partial differential operators (PDO) into products of lower order PDO over octonions and Cayley-Dickson algebras. Moreover, PDE of higher order with real and complex coefficients and with variable coefficients with or without boundary conditions are considered. Applications to Sobolev’s mixed type PDE are investigated as well. Local, global solutions and problems with boundary conditions are described.

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This chapter was previously published in Partial Differential Equations: Classification, Properties and Applications, edited by Deborah E. Richards, New York: Nova Publishers Inc., 2015. * E-mail address: [email protected]

In: Mathematical Research Summaries. Volume 1 Editor: Matthew A. Rowe

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Chapter 107

MIXED BOUNDARY-VALUE PROBLEM FOR DIVERGENT HYPERBOLIC PDE: EXISTENCE AND PROPERTIES OF SOLUTIONS, APPLICATIONS IN SEQUENTIAL OPTIMAL CONTROL WITH POINTWISE IN TIME STATE CONSTRAINTS , * #

V. S. Gavrilov† and M. I. Sumin‡ Mechanics and Mathematics Faculty, Nizhnii Novgorod State University, Nizhnii Novgorod, Russia

RESEARCH SUMMARY The chapter is devoted to the study of a sequential optimization problem for a semilinear hyperbolic divergent equation with pointwise state inequality constraint and with mixed boundary conditions. The chapter consists of two main parts. The first part is devoted to the study of the existence and uniqueness of solutions to semilinear hyperbolic divergent equations. Also in this part we study a linear hyperbolic divergent equation with a Radon measure in the right part. We study the following questions: existence, uniqueness and stability of solutions to such equations with mixed boundary condition; special integral representations of solutions to such equations; and the stability of solutions of linear hyperbolic divergent equations.

*

This work was supported by the Russian Foundation for Basic Research (project no. 13-02-12155-ofi−m), by the Ministry of Education and Science of the Russian Federation within the framework of project part of state tasks in the field of scientific activity in 2014-2016 (code no. 1727), and by the grant within the agreement of August 27, 2013 No. 02.B.49.21.0003 between the Ministry of Education and Science of the Russian Federation and Lobachevskii State University of Nizhnii Novgorod. # This chapter was previously published in Partial Differential Equations: Classification, Properties and Applications, edited by Deborah E. Richards, New York: Nova Publishers Inc., 2015. † E-mail address: [email protected] ‡ E-mail address: [email protected]

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In the second part of the paper, using the results of its first part, we have studied in detail the optimal control problem with pointwise in time state constraints. The state constraint contains a functional parameter that belongs to the class of continuous functions and occurs as an additive term. We compute the first variations of functionals on the basis of a so-called two-parameter needle variation of controls. We consider necessary conditions for minimizing sequences in an optimal control problem with a pointwise in time state constraint of inequality type and with dynamics described by a semilinear hyperbolic equation in divergence form with mixed boundary condition. For the parametric optimization problem, we also consider regularity and normality conditions stipulated by the differential properties of its value function.

In: Mathematical Research Summaries. Volume 1 Editor: Matthew A. Rowe

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Chapter 108

USING MATHEMATICAL TESSELLATION TO MODEL SPHERICAL PARTICLE PACKING STRUCTURES #

Larysa Burtseva1,* and Frank Werner2,† 1

Engineering Institute of the Autonomous University of Baja California, Mexicali, Mexico 2 Faculty of Mathematics, Otto-von-Guericke University, Magdeburg, Germany

RESEARCH SUMMARY In recent years, the literature shows an increasing interest to tessellation methods based on Voronoi diagrams to model different structures as packing of spheres. Voronoi diagrams have found numerous practical and theoretical applications in a large number of fields in science and technology as well as in computer graphics. A useful property of Voronoi diagrams is that they represent cellular structures found in the nature and technology in a natural manner, easily to understand and to design. Although this approach is really not new, meanwhile its intensive use and, consecutively, a systematical study started around 2000 with advances in nanoscience and nanotechnology. In this chapter, two basic tessellation methods are considered in more detail: the Voronoi-Delaunay tessellation and the Voronoi diagram in Laguerre geometry, as well as some of their generalizations. The principal concepts of both tessellation methods are briefly explained for a better understanding of this approach. A review of the related literature is given, focusing mainly on new mathematical tools and several particularities of the applications considered.

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This chapter was previously published in Advances in Mathematics Research. Volume 20, edited by Albert R. Baswell, New York: Nova Publishers Inc., 2015. * E-mail address: [email protected] † E-mail address: [email protected]

In: Mathematical Research Summaries. Volume 1 Editor: Matthew A. Rowe

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Chapter 109

FURTHER RESULTS ON FRACTIONAL CALCULUS FOR NON-DIFFERENTIABLE FUNCTIONS APPLICATIONS TO Z-TRANSFORM AND GENERALIZED FUNCTIONS #

Jumarie Guy* Department of Mathematics, University of Québec at Montréal, Downtown Station, Montréal, Qc, Canada

RESEARCH SUMMARY Purpose. It is shown that fractional difference could be useful to study sampled data anticipatory systems with long-range memory, either they are non-random (deterministic) or stochastic. And to this end, one uses the Z-transform. One takes this opportunity to clarify the derivation and the practical meaning of our local Leibniz fractional derivative chain rule for non-differentiable functions on the one hand, and to begin with some prospects of applications to the fractional derivative of generalized functions on the other hand. Design/methodology/approach. One first bears in mind the essential of the fractional difference which we are dealing with, and then we calculate its Z-transform. Then one combines the results so obtained with the Z-transform of fractional Gaussian white noise as we defined it using the Maruyama’s notation. Results. One can express the Z-transform of the fractional difference in terms of the modified Z-transform, therefore new prospects for possible generalizations and for the applications. The Z-transform of the white noise is investigated, and using the central limit theorem, one can consider it as a Gaussian random variable with known mean and variance. The fractional derivative of the Dirac’s delta function is derived, as well as the fractional derivative of the Heaviside step function.

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This chapter was previously published in Advances in Mathematics Research. Volume 20, edited by Albert R. Baswell, New York: Nova Publishers Inc., 2015. * E-mail address: jumarie.guy @ uqam.ca

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Research limitations/implications. The framework of this investigation is applied mathematics directed towards applications physics and engineering. Practical implications. It appears that, at first glance, it could be interesting to analyze many real systems by using the Z-transform of fractional derivative instead of modified Ztransform. Originality/value. The paper inserts fractional calculus in the framework of sampled data systems, and provides an approach to handle Z-transform of fractional white noise by using the central limit theorem. In addition it contributes some support to the use of complex-valued variables in the modelling of physical natural systems.

In: Mathematical Research Summaries. Volume 1 Editor: Matthew A. Rowe

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Chapter 110

LOW EARTH ORBIT SATELLITE CONSTELLATIONS FOR LOCAL TELECOMMUNICATION AND MONITORING SERVICES #

Mauro Pontani* University “La Sapienza”, Rome, Italy

RESEARCH SUMMARY Low Earth orbit satellite constellations deserve several advantages with respect to geostationary platforms, i.e. lower costs for satellite development and launch, increased imaging resolution, as well as reduced power requirements and signal time delays. This research is concerned with low Earth orbit constellation design, based on an original method that uses a correlation function. All the satellites are placed in repeating ground track orbits, and two conflicting requirements are considered: the maximization of the maximum continuous coverage and the minimization of the maximum revisit time of a target area located on the Earth surface. A suitable way of determining the related optimal constellation configurations is based on avoiding overlapping between visible passes of distinct satellites. With this intent, an analytic expression can be derived for the correlation function, which is employed to evaluate the overlapping between visible passes. Then, an algorithmic search for the zeros of this function allows determining several constellation configurations with the desired characteristics. This heuristic method turns out to be a successful approach for constellation design, and several results are reported with reference to distinct repeating orbits and different regions all over the world.

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This chapter was previously published in Advances in Mathematics Research. Volume 20, edited by Albert R. Baswell, New York: Nova Publishers Inc., 2015. * E-mail address: [email protected].

In: Mathematical Research Summaries. Volume 1 Editor: Matthew A. Rowe

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Chapter 111

ALGORITHM FOR AUTONOMOUSLY CALIBRATING REFERENCE FLAT OF INTERFEROMETER AND RESIDUAL INFLUENCE OF LINEAR SHIFT WITH TWO-FLAT METHOD #

Ikumatsu Fujimoto Okuwa Technical Research Center, Yamaguchi, Japan

RESEARCH SUMMARY A two-flat method for autonomously calibrating the reference flat of an interferometer is proposed with mathematical analysis. The calibration method is comprised of two steps. The first step is multiple rotations of a specimen, and the second is multiple linear shifts of it. In this study, the usual assumptions regarding the rotation are unnecessary, but the pitching error caused by a linear shift is assumed to be continuous with respect to the linear shift and approximated by zero for any sufficiently small linear shift. The flatness of a reference flat is determined based on the fact that the flatness derived mainly by rotation equals that derived mainly by linear shifts. Based on the above assumptions, the proposed algorithm, which is realized by mainly utilizing basic knowledge of linear algebra in functional space, can be used to determine the rotating tilt errors and linear shift errors, allowing the reference flat to be calibrated accurately. In this paper, the mathematical algorithm for autonomously calibrating the reference flat is explained in detail.

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This chapter was previously published in Advances in Mathematics Research. Volume 20, edited by Albert R. Baswell, New York: Nova Publishers Inc., 2015.

In: Mathematical Research Summaries. Volume 1 Editor: Matthew A. Rowe

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Chapter 112

DEALING WITH NON-SIGNIFICANT INTERACTIONS STATUSES BETWEEN TREATMENTS BY A SUGGESTED STATISTICAL APPROACH #

Zakaria M. Sawan* Cotton Research Institute, Agricultural Research Center, Ministry of Agriculture and Land Reclamation, Giza, Egypt

RESEARCH SUMMARY Because it is possible that experimental error could mask the pronounced effects of the interactions a statistical approach for dealing with the non-significant interactions between treatments is suggested. This approach depends on the least significant difference (LSD) values to verify the significant differences between treatment combinations regardless of the non-significance of the interaction effects from the ANOVA.   

#

A field experiment on cotton yield resulted in a non-statistically significant interaction. An approach for follow-up examination between treatments based on least significant difference values was suggested to identify the effect regardless of insignificance. It was found that the classical formula used in calculating the significance of interactions suffers a possible shortage that can be eliminated by applying a suggested revision.

This chapter was previously published in Advances in Mathematics Research. Volume 20, edited by Albert R. Baswell, New York: Nova Publishers Inc., 2015. * E-mail address: [email protected]; Address: 9 Gamaa Street, 12619, Giza, Egypt

In: Mathematical Research Summaries. Volume 1 Editor: Matthew A. Rowe

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Chapter 113

STOCHASTIC SIMULTANEOUS PERTURBATION AS POWERFUL METHOD FOR STATE AND PARAMETER ESTIMATION IN HIGH DIMENSIONAL SYSTEMS #

Hong Son Hoang* and Remy Baraille† SHOM/HOM/REC, Toulouse, France

RESEARCH SUMMARY This chapter is devoted to the question on how different state and parameter estimation problems in high dimensional systems can be solved efficiently in a simple and low-cost way using a stochastic simultaneous perturbation (SSP) approach. The basic feature of the SSP method is to approximate the gradient vector (and Hessian matrix) by integrating two or three times the numerical model subject to the control vector whose components are perturbed simultaneously by specific independent random variables. The SSP method allows to solve the optimization and estimation problems, regardless of the size of a control vector and without the need to construct a linear tangent system and adjoint code as required in traditional optimization approaches. Simple demonstration on convergence of gradient and Hessian approximation will be given. Simulations and experiments on different practical problems like parameter identification, estimating transition matrix of the linear system ... have been carried out. In particular, application to the important problems on estimation of the prediction error covariance matrix (ECM) in the filter design as well as optimization of the filter performance for data assimilation in very high dimensional ocean models will be presented in detail.

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This chapter was previously published in Advances in Mathematics Research. Volume 20, edited by Albert R. Baswell, New York: Nova Publishers Inc., 2015. * E-mail address: [email protected] † E-mail address: [email protected]

In: Mathematical Research Summaries. Volume 1 Editor: Matthew A. Rowe

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Chapter 114

BOUNDED TRAJECTORIES OF UNSTABLE PIECEWISE LINEAR SYSTEMS AND ITS APPLICATIONS #

L. J. Ontañón–García1,* and E. Campos–Cantón2,† 1

Coordinacíon Académica Región Altiplano Oeste, Universidad Autónoma de San Luis Potosí, Salinas de Hidalgo, SLP, México 2 División de Matemáticas Aplicadas, Instituto Potosino de Investigación Científica y Tecnológica A.C., San Luis Potosí, SLP, México

RESEARCH SUMMARY The dynamics of a linear system can result in unbounded trajectories depending on the stability of its equilibrium point. However, to restrain the resulting trajectories of the system and in order to generate self-sustained oscillations, unstable dissipative systems can be designed along with the location of two or more new piecewise linear subsystems to trap the trajectories. To do so one must consider the intrinsic dynamic which is determined by the stability of each equilibrium point added to the overall system. A mechanism to generate bounded trajectories of unstable linear systems is based on a switching control law changing the equilibrium point of an unstable dissipative system. The dynamical systems resulting from this method can be implemented electronically and have applications in areas such as communications and encryption, due to phenomena involving their dynamics, like multistability and multi-scrolls attractors.

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This chapter was previously published in Advances in Mathematics Research. Volume 20, edited by Albert R. Baswell, New York: Nova Publishers Inc., 2015. * E-mail address: [email protected] † E-mail address: [email protected]

In: Mathematical Research Summaries. Volume 1 Editor: Matthew A. Rowe

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Chapter 115

MATHEMATICAL MODELING FOR PREDICTING BATTERY LIFETIME THROUGH ELECTRICAL MODELS #

Cleber M. D. Porciuncula*, Airam Sausen† and Paulo Sérgio Sausen‡ Master’s Program in Mathematical Modeling, Regional University of Northwestern, Rio Grande do Sul State (UNIJUÍ), Ijuí – RS – Brazil

RESEARCH SUMMARY This chapter performs the modeling mathematical of the batteries lifetime from electric models, aiming to get an accurate model that be easy to implement and simple to use by the user. Two electrical models are utilized, the first is denominated Battery electric model, inserted in computational tool Matlab, and the second is called electric model for Predicting Runtime and IV Performance, that is considered a model highly accurate of the technical literature. The evaluation of the models occurs following the methodology: firstly a comparative analysis is realized between the simulations results of the Battery electric model with experimental data obtained from testbed for Lithium-Ion batteries, BL5F model, used in cell phones Nokia; second a comparative analysis is realized between the electric models Battery and for Predicting Runtime and IV Performance, from data experimental obtained of the testbed, for Lithium-Ion polymer batteries, PL-383562 model. Simulations results show that both models are accurate. On the other hand the Battery electric model is easy to implement and simple to use by user because there isn’t need tests experimental for obtaining

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This chapter was previously published in Advances in Mathematics Research. Volume 20, edited by Albert R. Baswell, New York: Nova Publishers Inc., 2015. * E-mail address: [email protected] † E-mail address: [email protected] ‡ E-mail address: [email protected]

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the parameters of the simulated battery. It is noteworthy that this represents a significant advantage of the model as regards the simplicity of the calibration process.

In: Mathematical Research Summaries. Volume 1 Editor: Matthew A. Rowe

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Chapter 116

MATHEMATICAL MODELING OF THE LITHIUM-ION BATTERY LIFETIME USING SYSTEM IDENTIFICATION THEORY #

Leugim Corteze Romio*, Airam Sausen†, Paulo Sérgio Sausen‡ and Manuel Reimbold§ Master’s Program in Mathematical Modeling, Regional University of Northwestern Rio Grande do Sul State (UNIJUÍ), Ijuí – RS – Brazil

RESEARCH SUMMARY This chapter presents the development of a mathematical model that may be used to predict the mobile devices battery lifetime, through the System Identification theory. Data collected from a test platform are used for realization of the mathematical modeling of a Lithium-Ion battery, BL5F model, used in cell phones Nokia N95. The identified model belongs to structure of linear parametric models and it is AutoRegressive with eXogenous input (ARX). This model is also compared with the Rakhmatov and Vrudhula model, which is regarded a physical model highly accurate of the technical literature. From simulations results it is found that the ARX model presents good accuracy with average error of 3.39%.

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This chapter was previously published in Advances in Mathematics Research. Volume 20, edited by Albert R. Baswell, New York: Nova Publishers Inc., 2015. * E-mail address: [email protected] † E-mail address: [email protected] ‡ E-mail address: [email protected] § E-mail address: [email protected]

In: Mathematical Research Summaries. Volume 1 Editor: Matthew A. Rowe

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Chapter 117

NONLINEAR EVOLUTION EQUATIONS AND SOLITON SOLUTIONS #

Yucui Guo1,* and Anjan Biswas2,† 1

Beijing University of Posts and Telecommunications, Beijing, China 2 Delaware State University, Dover, DE, US

RESEARCH SUMMARY This book focuses on the study of the theories and solving methods of nonlinear partial differential equations or called nonlinear evolution equations or nonlinear mathematical physics equations, especially on an interesting kind of solutions of these equations, so called solitary wave solutions or soliton solutions and their applications. It can be used as textbook and reference book for graduate students and teachers whose research fields are applied mathematics, applied physics and nonlinear science, etc. It is also available for researchers engaging in research on nonlinear science as a reference book. This book emphasizes particularly on clear concepts, rigorous derivation, reasoning through measuring, and logical reasoning. Due to the research boom on nonlinear partial differential equations beginning in 1960, it has been developing only for half a century up to now, and it is still a young discipline corresponding to other classical branches of mathematics. Although there are already some good books published globally, some of them are at the high starting point so that beginners are not easy to understand. At the same time, since the research of nonlinear partial differential equations is interdisciplinary, physicists, mathematicians, and scientists in engineering areas have been studying and paying attention to this field, and their ways must be different. Some works have very strong professional orientation, and are difficult to be understood for persons who don’t have too much professional knowledge. The goal of this book is to make it understandable for persons who have only the basic knowledge of college #

This chapter was previously published as a book: Nonlinear Evolution Equations and Soliton Solutions, by Yucui Guo and Anjan Biswas, New York: Nova Publishers Inc., 2016. * E-mail: [email protected] † E-mail: [email protected], [email protected]

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mathematics and physics, and to help readers understand well the content of the text, some contents helpful are concisely described in the appendixes. In the process of writing this book, the authors’ goal is to make a systematical and complete theory and help beginners in this field entry as soon as possible through reading this book. The book also includes some work of the authors as well as graduate students. Here the authors gives credit and thanks to all the authors of references. Most of contents of the manuscript have been taught in a degree course of graduated students in Beijing University of Posts and Telecommunications, the course named as “Nonlinear Partial Differential Equations and Their Applications.” Thanks to the graduate students who had learned the course, it is their enthusiasm and curiosity to motivate the authors to continuously explore in this field, and practice hard, and aspire to write a book for the new students. The purpose and desire is good, and time and effort also spent, but because our academic level is limited, shortcomings and mistakes may still exist. We sincerely hope that readers put forward valuable opinions and suggestions, so that the book will be improved. The research objects of this book are nonlinear partial differential equations or called nonlinear evolution equations. Due to they are derived from physics and some engineering disciplines and have distinct physical meaning, and they often describe the development of phenomenon with time, so they are also called nonlinear evolution equations or nonlinear mathematical physics equations. As we all know, mathematical physics equations are just mathematical equations with background of physics, including algebraic equations, function equations, ordinary differential equations, partial differential equations, integral equations and differential integral equations, difference equation, and so on. The course named “mathematical physics equations” or “the method of mathematical physics” usually given at the undergraduate level studies linear partial differential equations and their solutions. This book focuses on the research of nonlinear partial differential equations with physical background and related theory. The mathematical form of a nonlinear partial differential equation containing of time and space variables can usually be expressed as

P(t , x; u, ux , ut , uxx , uxt , utt , where

)0

u  u( x, t ) is the target quantity, that is the unknown function; x is spatial

coordinate, and sometimes may be 2-dimension,

 x, y  , or 3-dimension,  x, y, z  , or even

, xn ); t is the time coordinate and sometimes may be multidimensional ( x1 , x2 , generalized time coordinate, because of it may be a variable gone through the coordinate transformation in process for establishing mathematical model.

ux , ut , uxx , utt denote

respectively the first and second order partial derivatives for coordinates x and t . So called nonlinear partial differential equations refer to there are higher power terms of unknown function and (or) derivatives of unknown function contained in them, so they cannot be written as the following linear form. The second-order linear partial differential equation with two independent variables as an example expresses as

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247

A( x, y)uxx  2B( x, y)uxy  C ( x, y)u yy  D( x, y)ux  E ( x, y)u y  F ( x, y)u  f ( x, y) There are a hundred kinds of nonlinear partial differential equations having physical meaning by now. Typical and representative equations are KdV equation

ut  uux  uxxx  0

(0.1)

uxx  utt  sin u

(0.2)

iut  uxx   u u  0

(0.3)

Sine - Gordon equation

and nonlinear Schrodinger equation 2

and so on. Although these differential equations have simple forms, the essences of them are very different with that of linear differential equations. For example, the uniqueness, single value, boundedness, and the superposition principle of the solutions, etc. of linear differential equations, are likely not to exist to nonlinear ones. Therefore, for nonlinear partial differential equations, there are no general theory and methods to solve them. But it is interesting that many nonlinear partial differential equations have a kind of special solutions, so called solitary waves or solitons which are very meaningful. Due to the physical background and meaning of nonlinear partial differential equations and special properties of solitary waves, the methods for solving them and solitary wave theory become a new and vivid branch of nonlinear science and one of the frontier and hot issues of scientific development. A system is nonlinear if the output is not proportional to the input. The first example is mechanical spring, which generates elongation or displacement under the action of force. When the displacement is small, the force is proportional to the displacement, the relationship between force and displacement is linear relationship, which obeying the Hooke's law F  kx . However when displacement goes larger Hooke's law fails and the spring becomes a nonlinear oscillator. The second example is mathematical pendulum, only when the angular displacement of the pendulum is very small, its behavior is linear. And for a dielectric crystal, when the light intensity input is no longer proportional to the output one, it becomes nonlinear dielectric crystals. In fact, almost all of the known systems in natural science or social science are nonlinear, when the input is large enough. Therefore, the numbers of nonlinear systems are much larger than that of linear systems. It can be said that the objective world is nonlinear and linear is only an approximation, and the equations describing these nonlinear behaviors are likely to be nonlinear partial differential equations. Thus, understanding, researching, and applying nonlinear partial differential equations are inevitable in the development of science. With the development of computer science, many

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nonlinear problems can be solved with computers, which were impossible to solve manually. So, in a sense, nonlinear science is developing with the progression of computer science. This book mainly studies the solutions of nonlinear evolution equations, soliton theory and its application. In mathematics, the solutions of nonlinear evolution equations which have the following properties are called the solitary waves or solitons: 1. They are a kind of traveling waves which spread to the single direction, namely in the form of  ( x  at ) or  ( x  at ) ; 2. They distribute in a small area of the space, namely lim u  0 , sometimes also x 

having lim ux  0 and lim uxx  0 , etc. x 

x 

3. Wave shapes keep unchanged with the evolution of time; 4. Interactions between solitary waves have elastic properties as similar as the particles do. The solitary wave which has property of elastic collision is called soliton.

(a)

(c)

(b)

(d)

Figure 1.1. Four types of solitary waves.

There are four kinds of solitons commonly: (1) the bell shaped soliton (Figure 1.1 (a)), (2) the ante- bell shaped soliton (Figure 1.1 (b)), (3) the kink soliton (Figure 1.1 (c)) and (4) the ante - kink soliton (Figure 1.1 (d)). The basic steps of solving practical problems using mathematical method are shown as follows. First step is to simplify the actual problem and form a physical model; Then to quantify the physical model, namely, to establish the mathematical model--the nonlinear partial differential equations; The third step is to solve the partial differential equation, that is

Nonlinear Evolution Equations and Soliton Solutions

249

to find out the solutions of them, sometimes with certain boundary conditions; The final procedure is to analyze the results obtained, which is used to explain phenomena in nature and guide practice, namely to solve actual problem. It is generally to go through several processes from the physical model to the mathematical model: (1) To set up time and space coordinates, different problems need to choose different coordinate systems; (2) To determine the target variables and their coordinates of physical process studied, which is a very important. Choosing characterization parameters correctly is sometimes the beginning to establish a new discipline; (3) To find out law of physical process by supposing, guessing, and using the existing laws, namely to establish the physics axiom, which is the hard task. The mathematical models established in the course of mathematical physics equations only involve some simple physical processes. Through which the general methods to quantify physical models have been shown. In this book, more attention is paid to the derivation of mathematical models from the physical processes, for to research the mathematical physics problems, it is impossible to consider only mathematical problems with not thinking the physical pictures. The physical image and geometry image often play a simple and clear key role to understand fully the mathematical problems. Once the mathematical model has been established from the physical process, the following task is to seek the right method to solve the models, which are nonlinear partial differential equations in this book. With the continuous development of science, it is paid more and more attention to solve nonlinear partial differential equations. A large number of nonlinear partial differential equations are deduced from astronomy, physics, mechanics, earth science and life science and all kinds of engineering sciences, especially in different branches of physics, such as fluid mechanics, nonlinear optics, plasma theory and quantum field theory, etc. Majority of these equations have solutions in the form of a solitary wave which was first noticed by J. S. Russell, a British scientist, in 1830. The nonlinear science has been getting rapid development since the 1960 s. Many achievements have been also obtained in the aspect of solving nonlinear partial differential equations. Some of the important and typical methods will be discussed in detail in this book. Due to the complexity of nonlinear mathematical physics equations themselves, there is no general method for solving them, the basic thoughts of various methods are to use some transformations or decompositions to simplify the complex equations into simple ones to be dealt with. The forms of transformation and decomposition are also varied, which sometimes need to try and guess mathematically and physically. These conjecture or assumption themselves may not be universal, but the thought supporting them has universal significance. Math skills and physical intuition will get perfect embodiment here as far as possible. It is to point out once again that the book is accomplished on the basis of the lecture notes of the course, named for nonlinear partial differential equations and their applications, for graduate students in Beijing University of Posts and Telecommunications. Authors wish to thank all of the students who had learned over the course. It is that their constantly thinking and insightful questions that make the book more profound and perfect. Special thanks to the students who participated in the course the first time it was taught, Wang Xin, Xu Shujiang, Ye Peng, Li Huaying and Li Juan, etc. who input the manuscript into computer. Chapters 1 through 6 of this book and all the appendixes were written by Prof. Yucui Guo, and Chapter 7 was written by Dr. Anjan Biswas.

In: Mathematical Research Summaries. Volume 1 Editor: Matthew A. Rowe

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Chapter 118

THE DETERMINANTS OF CAPITAL STRUCTURE CHOICE FOR CHINESE LISTED COMPANIES BASED ON STRUCTURAL EQUATION MODELING APPROACH

#

Xin-Dan Li1, Xiang-Nan Feng2, Bin Lu3 and Xin-Yuan Song2, 1

School of Management and Engineering, Nanjing University, China Department of Statistics, the Chinese University of Hong Kong, China 3 School of Finance, Nanjing University of Finance and Economics, China 2

RESEARCH SUMMARY This chapter proposes a Bayesian approach based on structural equation modeling (SEM) to empirically test the determinants of capital structure choice for the Chinese listed companies. The chapter investigates major unobservable theoretical attributes identified by capital structure theories and constructs proxies for these attributes considering specific institutional settings in China. The findings suggest that some firm-specific factors relevant to explaining capital structure in developed economies are also related to the Chinese economy. Unique determinants of capital structure choice for Chinese listed companies are also identified, which are closely related to the special micro and macroeconomic situations in China.

#

This chapter was previously published in Structural Equation Modeling (SEM): Concepts, Applications, and Misconceptions, edited by Larry Rivera, New York: Nova Publishers Inc., 2015.  Corresponding author: Xin-Yuan Song is Associate Professor, Department of Statistics, the Chinese University of Hong Kong, Hong Kong, China, [email protected].

In: Mathematical Research Summaries. Volume 1 Editor: Matthew A. Rowe

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Chapter 119

AN EXAMINATION OF PREDICTORS AND OUTCOMES RELATED TO SCHOOL CLIMATE USING LATENT CLASS ANALYSIS #

Christine DiStefano, Elizabeth Leighton, Mihaela Ene and Diane M. Monrad University of South Carolina, US

RESEARCH SUMMARY A favorable school climate provides the structure within which students, teachers, administrators, and parents function cooperatively and constructively. Measures of school climate, however, have received only passing interest from policy makers as critical elements in accountability reporting. This study used a state-wide dataset of climate ratings from 610 elementary schools and considered multidimensional information from both teachers and students to produce latent classes of school climate. Two variables, school size and a school’s poverty index, were used as covariates when creating latent classes. In addition, two measures of school performance were examined as distal outcomes. The study identified four classes, where classes were distinguished based upon school climate scores. Differences in outcome variables and covariates were observed across the classes. The information may be used by school personnel in examinations of malleable factors related to school performance.

#

This chapter was previously published in Structural Equation Modeling (SEM): Concepts, Applications, and Misconceptions, edited by Larry Rivera, New York: Nova Publishers Inc., 2015.  Correspondence: 138 Wardlaw Hall, Columbia, SC 29208, [email protected], 803-777-4362

In: Mathematical Research Summaries. Volume 1 Editor: Matthew A. Rowe

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Chapter 120

ASSESSING MEDIATION IN SIMPLE AND COMPLEX MODELS #

Thomas Ledermann1,* and Siegfried Macho2 1

2

University of Basel, Switzerland University of Fribourg, Switzerland

RESEARCH SUMMARY This chapter addresses the testing of specific effects and contrasts in three types of mediation models: models with up to four simultaneous (parallel) mediators, models with two sequential mediators, and single-mediator models with two initial variables. We use the delta method and provide equations to calculate standard errors for simple and total indirect effects, total effects, and specific contrasts in each type of model. We also demonstrate how bootstrap interval estimates of specific effects and contrasts can be obtained using phantom models and how indirect effects involving different initial variables can be compared in a scale-free fashion. Testing contrasts, we show how common requirements for complete mediation can be made stronger. Limitations of both, statistics using standard errors based on normal theory and bootstrapping to test mediation, along with new methods are discussed. The methods are illustrated using publicly available datasets. Supplementary material available online includes Amos, OpenMx, and Mplus files to estimate the models and an Excel spreadsheet to calculate the effects.

#

This chapter was previously published in Structural Equation Modeling (SEM): Concepts, Applications, and Misconceptions, edited by Larry Rivera, New York: Nova Publishers Inc., 2015. * Corresponding author: Thomas Ledermann, [email protected].

In: Mathematical Research Summaries. Volume 1 Editor: Matthew A. Rowe

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Chapter 121

SYMMETRIC BOOLEAN FUNCTIONS

#

Peter M. Maurer Dept. of Computer Science, Baylor University, Waco, Texas, US

RESEARCH SUMMARY The purpose of this chapter is to summarize what is known about symmetric Boolean functions, but will concentrate primarily on my own work. I will discuss several new types of symmetry, along with tools and analytical techniques for detecting and studying such symmetries. First, I will provide a comprehensive introduction to the mathematics of group theory, and show how this serves as a basis for the study of symmetric Boolean functions. I will extend these ideas to matrix-based symmetry, and show how matrix-based symmetry greatly expands the concept of permutation-based symmetry. The new types of symmetry discussed in this chapter will include conjugate symmetry, super-symmetry, exotic symmetry, and hyper-symmetry. The names “super-symmetry,” “exotic symmetry,” and “hyper symmetry” have not appeared in print and will be defined in the chapter. These are all matrix-based symmetries. In addition I will discuss the existing symmetry types: anti-symmetry, hierarchical symmetry, and Kronecker symmetry and potential extensions to such.

#

This chapter was previously published in Boolean Functions: Theory, Fundamentals and Engineering Applications, edited by Allen Hines, New York: Nova Publishers Inc., 2015.

In: Mathematical Research Summaries. Volume 1 Editor: Matthew A. Rowe

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Chapter 122

BOOLEAN FUNCTIONS: ALL-OPTICAL IMPLEMENTATION USING QUANTUM-DOT SEMICONDUCTOR OPTICAL AMPLIFIERS IN MACH-ZEHNDER INTERFEROMETER #

K. E. Zoiros*, E. Dimitriadou and T. Houbavlis Democritus University of Thrace, Department of Electrical and Computer Engineering, Lightwave Communications Research Group, Xanthi, Greece

RESEARCH SUMMARY Boolean functions provide the necessary framework for expressing the operation of logic gates, which are the key building units for the accomplishment of signal processing tasks in fundamental and system-oriented level. With the unceasing increase of digital information volume, the capability of executing these functions has been progressively evolved from electronics to photonics so as to avoid the severe constraints imposed in the former domain. This book chapter reviews how this can be done exclusively by means of light by exploring the novel technology of quantum-dot semiconductor optical amplifiers (QD-SOAs), which are incorporated in a switching structure formed by the Mach-Zehnder interferometer (MZI). For this purpose we initially present some state-of-the-art technologies that are available for realizing all-optically logic operations, with particular emphasis on the well-established option of SOAs. We underline the limitations in handling ultrafast information when using conventional-type SOAs and we comment on the various solutions that have been proposed for overcoming them. We highlight the need for adopting the novel approach of QD-SOAs in order to successfully confront the challenge of keeping pace with the rapid increase of single channel data rates. We justify this choice by referring to the attractive inherent properties of #

This chapter was previously published in Boolean Functions: Theory, Fundamentals and Engineering Applications, edited by Allen Hines, New York: Nova Publishers Inc., 2015. * Corresponding author: Tel: +30 25410 79 975, Fax: +30 25410 79 595, Email: [email protected].

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K. E. Zoiros, E. Dimitriadou and T. Houbavlis

these devices and how they are combined with those of the MZI to achieve ultra high speed switching. We physically and theoretically describe the operation of QD-SOAs, first as standalone entities and then when they are incorporated in the MZI. We demonstrate how the basic configuration of the latter can be modified and driven so as to produce different Boolean functions at its two output ports in a versatile and reconfigurable manner. We identify a set of such functions and explain the reasons for their selection according to their role and significance. We define performance criteria and adapt them to the special nature of the logical outcome of each target function. We provide simulation results concerning the impact of critical operating parameters on these metrics and based on their concise interpretation we give guidelines for the execution of each Boolean function both with logical correctness and high quality. We also address several practical issues regarding the real implementation of these functions. Finally, we report on characteristic lightwave digital applications of enhanced functionality enabled through complex circuits, which are synthesized and formulated by combinations of the considered QD-SOA-based MZI Boolean functions.

In: Mathematical Research Summaries. Volume 1 Editor: Matthew A. Rowe

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Chapter 123

SELECTIVE HARVESTING AND TIME DELAY IN A PREDATOR-PREY MODEL WITH INFECTIOUS PREYS

#

A. Tchuinté Tamen1,4,* , A. Laohombe1,4, J. J. Tewa2,4,† and S. Bowong3,4,‡ 1

Faculty of Science, University of Yaoundé I, Cameroon 2 National Advanced School of Engineering, University of Yaoundé I, Cameroon 3 Department of Mathematics and Computer Science, Faculty of Science, University of Douala, Cameroon 4 LIRIMA, GRIMCAPE team project, CETIC project, University of Yaoundé I, Cameroon

RESEARCH SUMMARY Disease in the prey population increases the risk of prey outcomes in predation or to be harvested. In this paper, an eco-epidemiological model consisting of predator-prey model with SIS disease in the prey population is proposed and analyzed. Selective harvesting and time delay are taken into account. In our model, we also consider two generalized Holling response functions of type III both in the predator and the prey equations. Qualitative mathematical analysis of our model is performed. We investigate the positivity and the boundedness of solutions of the model. Important thresholds are identified and their implications are explained. Existence and stability analysis of equilibria are carried out: monostabilities and bistability. A Hopf bifurcation exists both in the presence of zero and non-zero time lag. A dynamically consistent nonstandard finite difference scheme is designed and numerical simulations that illustrate the theory are provided. #

This chapter was previously published in Ordinary and Partial Differential Equations, edited by Raymond Brewer, New York: Nova Publishers Inc., 2015. * E-mail address: [email protected] † E-mail address: [email protected] ‡ E-mail address: [email protected]

In: Mathematical Research Summaries. Volume 1 Editor: Matthew A. Rowe

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Chapter 124

ANALYSIS OF AN AGE-STRUCTURED SEIL MODEL WITH DEMOGRAPHICS PROCESS AND LOST OF SIGHT INDIVIDUALS #

Demasse Djidjou1,4,*, A. Mendy2,4,†, Lam Mountaga2,4, ‡ and J. J. Tewa3,4,‡§ 1

University of Yaoundé I, Faculty of Science, Department of Mathematics, Yaoundé, Cameroun, 2 University Cheikh Anta Diop, Dakar Faculty of Science and Technic, Department of mathematics, 3 National Advanced School of Engineering University of Yaoundé I, Department of Mathematics and Physics, Yaoundé, Cameroon 4 LIRIMA, GRIMCAPE team project, CETIC project, University of Yaoundé I, Cameroon

RESEARCH SUMMARY In this paper, we consider a mathematical S-E-I-L (Susceptible- Latently infectedInfected-Lost of sight) model for the spread of a directly transmitted infectious disease in an age-structured population; taking into account the demographic process. First we establish the mathematical well-posedness of the time evolution problem by using the integrated semigroup approach. Next we prove that the basic reproduction ratio R0 is given as the #

This chapter was previously published in Ordinary and Partial Differential Equations, edited by Raymond Brewer, New York: Nova Publishers Inc., 2015. * E-mail address: [email protected] † E-mail address: [email protected] ‡ E-mail address: [email protected] § Email address: [email protected]

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Demasse Djidjou, A. Mendy, Lam Mountaga et al.

spectral radius of a positive operator, and an endemic state exist if and only if the basic reproduction ratio R0 is greater than unity, while the disease-free equilibrium is locally asymptotically stable if R0 < 1. We also show that the endemic steady states are forwardly bifurcated from the disease-free steady state when R0 cross the unity. Finally we examine the conditions for the local stability of the endemic steady states.

In: Mathematical Research Summaries. Volume 1 Editor: Matthew A. Rowe

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Chapter 125

REALIZATIONS OF sl(3, ) IN TERMS OF CHEBYSHEV POLYNOMIALS AND ORTHOGONAL SYSTEMS OF FUNCTIONS. SYMMETRY BREAKING AND VARIATIONAL SYMMETRIES #

R. Campoamor-Stursberg1,* and E. Fernández Saiz2,† 1

Instituto de Matemática Interdisciplinar and Depto. de Geometría y Topología, Universidad Complutense, Madrid, Spain 2 Depto. de Geometría y Topología, Universidad Complutense, Madrid, Spain

RESEARCH SUMMARY Starting from the classical Chebyshev ordinary differential equation (ODE), a generic realization of its Lie algebra of point symmetries sl(3, ) is obtained in terms of the Chebyshev polynomials of first and second kind. It is shown that the corresponding structure tensor of the symmetry algebra does not depend on the parameter n of the Chebyshev equation. A slight modification of the ansatz enables us to obtain a generic realization of the point symmetries of linear homogeneous second-order ODEs admitting fundamental solutions of trigonometric and hyperbolic type. The problem of constructing orthogonal systems of functions in terms of point symmetries is considered. Finally, the variational symmetries of homogeneous ODEs with maximal symmetry are analyzed. It is shown that non-linear deformations of an ODE preserving a certain subalgebra of Noether symmetries are deeply related to the symmetry breaking problem.

#

This chapter was previously published in Ordinary and Partial Differential Equations, edited by Raymond Brewer, New York: Nova Publishers Inc., 2015. * E-mail address: [email protected] † E-mail address: [email protected]

In: Mathematical Research Summaries. Volume 1 Editor: Matthew A. Rowe

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Chapter 126

SOLITARY WAVES IN THE NONLINEAR DIRAC EQUATION AT THE CONTINUUM LIMIT: STABILITY AND DYNAMICS #

Jesús Cuevas-Maraver1,2,* , Panayotis G. Kevrekidis3,4, Avadh Saxena4, Fred Cooper4,5 and Franz Mertens6 1

Grupo de Física No Lineal, Departamento de Física Aplicada I, Universidad de Sevilla, Escuela Politécnica Superior, Sevilla, Spain 2 Instituto de Matemáticas de la Universidad de Sevilla (IMUS), Sevilla, Spain 3 Department of Mathematics and Statistics, University of Massachusetts, Amherst, MA, US 4 Center for Nonlinear Studies and Theoretical Division, Los Alamos National Laboratory, Los Alamos, New Mexico, US 5 Santa Fe Institute, Santa Fe, NM, US 6 Physikalisches Institut, Universität Bayreuth, Bayreuth, Germany

RESEARCH SUMMARY In the present work, we give a comparative summary of different recent contributions to the theme of the linear stability and nonlinear dynamics of solitary waves in the nonlinear Dirac equation in the form of the Gross-Neveu model. We indicate some of the key controversial statements in publications within the past few years and we attempt to address them to the best of our current understanding. The conclusion that we reach is that the solitary wave solution of the model is spectrally stable in the cubic nonlinearity case, however, it may become unstable through an instability amounting to the violation of the Vakhitov-Kolokolov criterion for higher exponents. We find that for the Dirac model, the interval of instability is narrower. Furthermore, contrary to what is the case in the nonlinear Schrðdinger analogue of #

This chapter was previously published in Ordinary and Partial Differential Equations, edited by Raymond Brewer, New York: Nova Publishers Inc., 2015. * E-mail address: [email protected]

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Jesús Cuevas-Maraver, Panayotis G. Kevrekidis, Avadh Saxena et al.

the model, the unstable dynamical evolution, does not lead to collapse (blowup) and hence it appears that the relativistic nature of the model mitigates the collapse instability. Various issues associated with different numerical schemes are highlighted and some possibilities for future alleviation of these is suggested.

In: Mathematical Research Summaries. Volume 1 Editor: Matthew A. Rowe

ISBN: 978-1-53612-021-9 © 2017 Nova Science Publishers, Inc.

Chapter 127

MODELING OF CORRUPTION IN HIERARCHICAL ORGANIZATIONS #

Olga I. Gorbaneva*, Guennady A. Ougolnitsky† and Anatoly B. Usov‡ Department of Applied Mathematics and Computer Science Southern Federal University, Russian Federation

RESEARCH SUMMARY This book focuses on hierarchical organizational structures. Secondly, the authors perform modeling in the context of solving control problems. Next, the conditions of corrupting a major task of control consisting of ensuring sustainable development of modeled hierarchical organizations are reviewed. Here, the authors proceed from the original concept of sustainable management. In contrast to the classical approach of G. Becker and S. RoseAckerman (which states that the efficiency of anti-corruption struggle is defined via comparing losses due to corruption and the costs of such measures), the above concept applies certain requirements of sustainable development of a modeled system with proper consideration of economic restrictions. Finally, the empirical base and identification of mathematical models is examined.

#

This chapter was previously published as a book: Modeling of Corruption in Hierarchical Organizations, by Olga I. Gorbaneva, Guennady A. Ougolnitsky and Anatoly B. Usov, New York: Nova Publishers Inc., 2015. * [email protected] † [email protected] ‡ [email protected]

In: Mathematical Research Summaries. Volume 1 Editor: Matthew A. Rowe

ISBN: 978-1-53612-021-9 © 2017 Nova Science Publishers, Inc.

Chapter 128

BINARY PERIODIC SIGNALS AND FLOWS

#

Serban E. Vlad* The Romanian Society of Applied and Industrial Mathematics, Oradea, Romania

RESEARCH SUMMARY The signals from digital electrical engineering are modeled by discrete time and real time functions, whose values are binary n-tuples and which are also called signals. The asynchronous circuits, representing the devices that work with such signals, are modeled by Boolean autonomous deterministic regular asynchronous systems, shortly by asynchronous flows. The attribute ‘Boolean’ vaguely refers to the binary Boole algebra; ‘autonomous’ means that there is no input; ‘deterministic’ means the existence of a unique state function; and ‘regular’ indicates the existence of a Boolean function that iterates its coordinates independently on each other (i.e. asynchronously). Strong analogies exist with the real, usual dynamical systems. The purpose of this research monograph is to study the periodicity of the signals and of their values, as well as the periodicity of the asynchronous flows. The monograph addresses systems theory and computer science that apply to researchers, but it is also interesting to those that study periodicity itself. From this last perspective, the signals may be thought of as functions with finitely many values. At the same time, the asynchronous flows may be considered as special cases of variable structure systems. The bibliography consists of works of real, dynamical systems that produce analogies.

#

This chapter was previously published as a book: Binary Periodic Signals and Flows, by Serban E. Vlad, New York: Nova Publishers Inc., 2016. * E-mail address: [email protected]

In: Mathematical Research Summaries. Volume 1 Editor: Matthew A. Rowe

ISBN: 978-1-53612-021-9 © 2017 Nova Science Publishers, Inc.

Chapter 129

PSEUDO-MATROIDS AND CUTS OF MATROIDS

#

Sergey A. Gizunov* and V. N. Lyamin† Scientific Research Institute "KVANT", Moscow, Russia

RESEARCH SUMMARY This book is dedicated to the study of algebraic characteristics of some structures of matroid type. The notions of pseudo-matroids generated by mappings of matroids, Gmappings of binary matroids and semi-matroids are introduced. Some results on general matroid theory and an algorithmic solution for exponential complexity of problems with enumeration of all non-isomorphic binary matroids are found. The theoretical results are applied to the solution of some practical problems. This monograph is beneficial to specialists in discrete mathematics and matroids, information transmission technologies, as well as students and post-graduates.

#

This chapter was previously published as a book: Pseudo-Matroids and Cuts of Matroids, by Sergey A. Gizunov and V. N. Lyamin, New York: Nova Publishers Inc., 2016. * Email: [email protected] † Email: [email protected]

In: Mathematical Research Summaries. Volume 1 Editor: Matthew A. Rowe

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Chapter 130

FOUNDATIONS OF ISO-DIFFERENTIAL CALCULUS. VOLUME 6: THEORY OF ISO-FUNCTIONS OF A REAL ISO-VARIABLE #

Svetlin Georgiev* Faculty of Mathematics and Informatics, Department of Differential Equations, Sofia University, Sofia, Bulgaria

RESEARCH SUMMARY This book is intended for readers who have had a course in theory of functions, isodifferential calculus and it can be used for a senior undergraduate course. Chapter 1 deals with the infinite sets. We introduce the main operations on the sets. They are considered the one-to-one correspondences, the denumerable sets and the nondenumerable sets, and their properties. In Chapter 2 are introduced the point sets. They are defined the limit points, the interior points, the open sets, the closed sets. They are considered the structure of the bounded open and the closed sets. Also, they are given some of their main properties. In Chapter 3 are studied the measurable sets. They are defined and deducted the main properties of the measure of a bounded open set, a bounded closed set, the outer and the inner measures of a bounded set. Chapter 4 is devoted to the theory of the measurable iso-functions. They are considered the main classes of the measurable iso-functions and they are deducted their properties. In Chapter 5 is defined the Lebesgue iso-integral of a bounded iso-function. They are given its main properties. In Chapter 6 are studied the square iso-summable iso-functions, the iso-orthogonal systems, the iso-spaces 𝐿̂𝑝 and 𝑙̂𝑝 , p > 1. The Stieltjes iso-integral and its properties are investigated in Chapter 7. #

This chapter was previously published as a book: Foundations of Iso-Differential Calculus. Volume 6: Theory of Iso-Functions of a Real Iso-Variable, by Svetlin Georgiev, New York: Nova Publishers Inc., 2016. * Email: [email protected] or [email protected]

In: Mathematical Research Summaries. Volume 1 Editor: Matthew A. Rowe

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Chapter 131

CALCULATING CHARACTERIZATION OF MONOPSONIC DEGREE IN THE RECYCLED SOLID WASTE MARKET IN METROPOLITAN REGIONS OF BRAZIL #

Rilton Gonçalo Bonfim Primo1, and José Félix García Rodríguez2,† 1

Centro de Estudios por la Amistad de Latinoamérica, Asia y África, Brazil 2 Departamento de Ciencias Económicas y Administrativas, Universidad Juárez Autónoma de Tabasco, Villahermosa, TAB, Mexico

RESEARCH SUMMARY The goal of this essay is to encourage and make an aport to calculate the characterization of monopsony in the market of recycled solid waste in metropolitan regions of Brazil. This was done by estimating the corresponding deviation between price and added value, circumstantially and structurally privileging the links in the chain of reverse logistics of residue, from the lone scavenger to the industry. We will make a theoretical approach of the social significance of concentrated markets. This work presents a tool to calculate the degree of monopsonization, which is a first step towards Fair Trade. It also refers to an efficient experimentation in the Northeast of Brazil.

#

This chapter was previously published in Models and Methods for Supporting Decision-Making in Human Health and Environment Protection, edited by Carlos N. Bouza, Flávio L. de Mello and Marcos Negreiros, New York: Nova Publishers Inc., 2016.  Rilton Gonçalo Bonfim Primo: Rua Areal de Baixo, nº 136, apto. 414, Largo 2 de Julho, Salvador, Bahia, Brasil. CEP 40060-210. E-mail: [email protected]. † José Félix García Rodríguez: Carrillo Puerto, nº 272, Colonia Carrizal, CP 86108, Vilhermosa, Tabasco, México. E-mail: [email protected].

In: Mathematical Research Summaries. Volume 1 Editor: Matthew A. Rowe

ISBN: 978-1-53612-021-9 © 2017 Nova Science Publishers, Inc.

Chapter 132

ESTIMATION OF DERIVATIVES, FROM ECONOMY TO ENVIRONMENT: A STUDY OF THE MANAGEMENT OF EUTROPHICATION OF A FRESH WATER BASIN’S DATA #

Sira M. Allende-Alonso1,*, Dan C. Chen2, Carlos N. Bouza1, José M. Sautto-Vallejo3 and Agustín Santiago-Moreno3 1

Mathematics and Computation Faculty, University of Havana, Cuba 2 Smith and King College, Calcutta, India 3 Universidad Autónoma de Guerrero, Guerrero, México

RESEARCH SUMMARY The use of derivatives is common in Economic studies. Econometricians have developed alternative procedures to estimate derivatives of conditional expectations. They use non parametric approaches. The management of different environment problems are similar to the financial ones. Hence, we tackle the use of them in the environmental issues associated with the contamination of a basin by Eutrophication. This paper is concerned with a comparissone of the influence of derivatives estimators for studying the contamination due to chlorophyll in a basin. The use of direct and indirect methods is discussed. The conclusions are based on the results of a large simulation study developed using collected data on contamination of a basin. A main result is that Bootstrap performs fairly better than the other procedures based on kernels inclusive under asymptotic considerations.

#

This chapter was previously published in Models and Methods for Supporting Decision-Making in Human Health and Environment Protection, edited by Carlos N. Bouza, Flávio L. de Mello and Marcos Negreiros, New York: Nova Publishers Inc., 2016. * Corresponding Author address: Mathematics and Computation Faculty, University of Havana, Cuba, C.P. 10400, Vedado. Email: [email protected].

In: Mathematical Research Summaries. Volume 1 Editor: Matthew A. Rowe

ISBN: 978-1-53612-021-9 © 2017 Nova Science Publishers, Inc.

Chapter 133

MODELING ENVIRONMENTAL PHENOMENA AND MEDICAL CLASSIFICATION OF PATIENTS: CASE STUDIES #

Carlos N. Bouza * Departamento de Matemática Aplicada, Facultad de Matemática y Computación, Universidad de la Habana, Cuba

RESEARCH SUMMARY The use of quantitative methods for implementing the management of environmental and medical problems is common. However, many environmental and medical applications needs using, sophisticated modeling, for implementing adequate decision procedures. In this chapter we present a study of biodiversity and of patient classification. Both problems use indexes and statistical studies about them are developed. They lead to an evaluation of their behavior. The studies are concerned with the construction of strata, for studying biodiversity issues, and with the classification of patients visiting hospitasl with pneumonia.

#

This chapter was previously published in Models and Methods for Supporting Decision-Making in Human Health and Environment Protection, edited by Carlos N. Bouza, Flávio L. de Mello and Marcos Negreiros, New York: Nova Publishers Inc., 2016. * Corresponding author: [email protected].

In: Mathematical Research Summaries. Volume 1 Editor: Matthew A. Rowe

ISBN: 978-1-53612-021-9 © 2017 Nova Science Publishers, Inc.

Chapter 134

ANALYSIS OF EFFECT OF ENVIRONMENTAL DISCHARGE AND AWARENESS PROGRAMS ON JAPANESE ENCEPHALITIS SPREAD USING MATHEMATICAL MODELING AND SIMULATION

#

Nita H. Shah1,*, Urmila Chaudhari2, Jyoti Gupta1 and Bijal Yeolekar1 1

Department of Mathematics, Gujarat University, Ahmedabad, Gujarat, India 2 Department of Applied Sciences, Faculty of Engineering and Technology, Parul University, Vadodara, Gujarat, India

RESEARCH SUMMARY In this chapter, the transmission of Japanese Encephalitis (JE) is studied through the system of non-linear differential equation. The effect of environment discharge and awareness program is incorporated to study the spread of the infectious disease. It is assumed that JE spreads when one comes in contact with susceptible and infected mosquitoes only. The awareness program is proportional to the number of infectious. It is assumed that due to awareness programs, susceptible individual form a separate class and avoid contact with infectious. The stability analysis is worked out. Numerical simulation in each compartment is carried out to investigate the spread of the disease.

#

This chapter was previously published in Models and Methods for Supporting Decision-Making in Human Health and Environment Protection, edited by Carlos N. Bouza, Flávio L. de Mello and Marcos Negreiros, New York: Nova Publishers Inc., 2016. * Corresponding Author address: Email: [email protected].

In: Mathematical Research Summaries. Volume 1 Editor: Matthew A. Rowe

ISBN: 978-1-53612-021-9 © 2017 Nova Science Publishers, Inc.

Chapter 135

ESTIMATION AND COMPARISON OF THE LIKELIHOOD RATIOS OF BINARY DIAGNOSTIC TESTS #

José Antonio Roldán-Nofuentes1,* and Raid M. Amro2,† 1

Department of Statistics (Biostatistics), Faculty of Medicine, University of Granada, Granada, Spain 2 Department of Mathematics, Faculty of Education, Alquds Open University, Palestine

RESEARCH SUMMARY Positive and negative likelihood ratios are parameters that are used to assess and compare the accuracy of binary diagnostic tests. Likelihood ratios only depend on the sensitivity and specificity of the diagnostic test and quantify the increase in the knowledge about the presence of the disease through the application of the diagnostic test. This study is a review of likelihood ratios, their estimation for a single diagnostic test and the comparison of the likelihood ratios of two diagnostic tests in a paired design. Two programmes written in R are presented to solve the problems studied. The results are applied to the diagnosis of prostate cancer.

#

This chapter was previously published in Models and Methods for Supporting Decision-Making in Human Health and Environment Protection, edited by Carlos N. Bouza, Flávio L. de Mello and Marcos Negreiros, New York: Nova Publishers Inc., 2016. * E-mail: [email protected]. † E-mail: [email protected].

In: Mathematical Research Summaries. Volume 1 Editor: Matthew A. Rowe

ISBN: 978-1-53612-021-9 © 2017 Nova Science Publishers, Inc.

Chapter 136

HEALTH PLANNING INFORMATION ACQUIRED FROM UNSTRUCTURED DATA ABOUT DIABETES MELLITUS #

Rodrigo Santos Souza1, Edilberto Strauss2 and Flávio Luis de Mello2,* 1

State University of Ceará and Federal Institute of Ceará, CE, Brazil 2 Electronic and Computer Engineering Department, Federal University of Rio de Janeiro, Rio de Janeiro, Brazil

RESEARCH SUMMARY This chapter presents a work on the usage of the crowd’s knowledge, the application of semantics in the context of the Internet, and the social networking phenomenon in order to provide a collaborative information platform applied to health planning. A proof of concept was developed based on diabetes disease, providing a description of the methodology employed and the fundamentals aspect that support this study. The exponential growth of Internet content suggests that there is an opportunity for developing a more selective and qualitative knowledge consume. It might be adapted to population’ health improvement and disease prevention. On the Internet, and more specifically on social networks, blogs and other forms of expression, such health knowledge is spread into the crowd, where information is provided in a collaborative way. Therefore, this work aims to investigate the current situation of dispersed knowledge over the Internet and use it to support strategic planning within the Brazilian public health.

#

This chapter was previously published in Models and Methods for Supporting Decision-Making in Human Health and Environment Protection, edited by Carlos N. Bouza, Flávio L. de Mello and Marcos Negreiros, New York: Nova Publishers Inc., 2016. * E-mail: [email protected].

In: Mathematical Research Summaries. Volume 1 Editor: Matthew A. Rowe

ISBN: 978-1-53612-021-9 © 2017 Nova Science Publishers, Inc.

Chapter 137

APPLYING FUZZY MODEL TO MAP VULNERABILITY AREAS OF TRYPANOSOMA CRUZI TRANSMISSION

#

Samanta Cristina das Chagas Xavier1, Marcello Goulart Teixeira2, André Luiz Rodrigues Roque1, Ana Maria Jansen1 and Luiz Felipe Coutinho Ferreira da Silva3, 1

Laboratory of Tripanosomatid Biology, Oswaldo Cruz Foundation (IOC/FIOCRUZ), Rio de Janeiro, Brazil 2 Departament of Computation Science, Mathematics Institute, Federal University of Rio de Janeiro (UFRJ), Brazil 3 Laboratory of Cartography, Military Institute of Engineering (IME), Rio de Janeiro, Brazil

RESEARCH SUMMARY We have developed a novel approach for Chagas disease prediction. We tested the method of spatial fuzzy inference approach as a diagnostic tool of the environmental variables which regulate the Trypanosoma cruzi transmission in nature. The set of primary and secondary variables were treated by the fuzzy method of spatial inference in order to build an integrated model. This model demonstrated the possibility to use this novel approach in order to identify areas with different degrees of risk, thus allowing a continuous and integrated representation of the variables involved in the T. cruzi transmission in nature. The output data obtained can be used to support decision making in epidemiological surveillance of Chagas disease and are certainly an example that can be applied to several other parasite infections in distinct areas. #

This chapter was previously published in Models and Methods for Supporting Decision-Making in Human Health and Environment Protection, edited by Carlos N. Bouza, Flávio L. de Mello and Marcos Negreiros, New York: Nova Publishers Inc., 2016.  Corresponding author: Luiz Felipe Coutinho Ferreira da Silva. Email: [email protected].

In: Mathematical Research Summaries. Volume 1 Editor: Matthew A. Rowe

ISBN: 978-1-53612-021-9 © 2017 Nova Science Publishers, Inc.

Chapter 138

USAGE OF AUTOMATIC THEOREM PROVING IN THE RECOGNITION OF BRAIN EMOTIONS ACTIVATIONS #

Flávio Luis de Mello* and Edilberto Strauss Electronic and Computer Engineering Department, Federal University of Rio de Janeiro, Rio de Janeiro, Brazil

RESEARCH SUMMARY The mental operations associated with emotion are different neural mechanisms that correspond to each emotion degrees. It is notorious that science lacks knowledge on the operation of such mechanisms, despite being known that some regions are related to particular emotions. It is usual to enumerate the relationship , while it would be much more interesting if they explain the brain engine aspects. This chapter presents a technique for modeling human brain as a computable object by using theorem proving and digital image processing. A pattern cerebral activation recognizer knowledge base was created from functional magnetic resonance images in order to systemize the cerebral activation human process for a limited set of emotional stimulations.

#

This chapter was previously published in Models and Methods for Supporting Decision-Making in Human Health and Environment Protection, edited by Carlos N. Bouza, Flávio L. de Mello and Marcos Negreiros, New York: Nova Publishers Inc., 2016. * Computer and Electronics Engineering Department DEL/Poli/UFRJ, Federal University of Rio de Janeiro, Centro de Tecnologia, sl.H212B, Ilha do Fundão, Rio de Janeiro, RJ, Brazil, CEP 21949-900. Email: [email protected].

In: Mathematical Research Summaries. Volume 1 Editor: Matthew A. Rowe

ISBN: 978-1-53612-021-9 © 2017 Nova Science Publishers, Inc.

Chapter 139

RADIOLOGY INFORMATION SYSTEM WITH KNOWLEDGE REASONING #

Sérgio Ricardo Pereira Soares1,*, Edilberto Strauss2 and Flávio Luis de Mello2 1

State University of Ceará and Federal Institute of Ceará, CE, Brazil 2 Electronic and Computer Engineering Department, Federal University of Rio de Janeiro, Rio de Janeiro, Brazil

RESEARCH SUMMARY The purpose of this article is to define an Information System which uses medical radiologic cases in DICOM format in order to create a knowledge repository and an approach to retrieval of the correct cases using keywords. This repository aims to improve the medical radiologists’ capacity to provide more accurate and faster diagnoses by using case based reasoning techniques. Besides, it also helps teaching radiological techniques to newly radiologists. The construction of such repository demands to join together various radiologic cases of Magnetic Resonance Image and Computer Tomography equipments, and allows pointing out semantic problems associated to the filling information by the time exams are made. It also suggests that is necessary to create a fulfillment policy of form fields so that later searches can be executed easily and interactively.

#

*

This chapter was previously published in Models and Methods for Supporting Decision-Making in Human Health and Environment Protection, edited by Carlos N. Bouza, Flávio L. de Mello and Marcos Negreiros, New York: Nova Publishers Inc., 2016. State University of Ceará, Av. Dr. Silas Munguba, 1700 - Campus do Itaperi, Fortaleza, CE, Brazil. Email: [email protected].

In: Mathematical Research Summaries. Volume 1 Editor: Matthew A. Rowe

ISBN: 978-1-53612-021-9 © 2017 Nova Science Publishers, Inc.

Chapter 140

DESIGN OF ROUTES FOR WASTE COLLECTION: CENTRO HABANA’S CASE STUDY #

Joanna Campbell Amos and Sira Allende Alonso Mathematics and Computation Faculty, University of Havana, Cuba

RESEARCH SUMMARY Waste management deals with the collection, transport and disposal of the solid waste. In recent years waste management has become a problem worldwide due to population growth (especially in urban areas), the environmental effects of residues accumulation and the progressive increment of the costs in waste management. Hence, municipalities need to improve solid waste management. In particular, it is important to reduce the distance travelled by the collection vehicles. Routes design for collecting domiciliary residues can be modeled as arc-edge routing problem on a mixed graph, the Mixed Chinese Postman's Problem (MCPP). MCPP is a NP-Hard problem in contrast with the –Chinese Postman´s Problem on directed and undirected graphs (CPP). This work deals with the routes design of domiciliary residues using the implementation of a new heuristic for MCCP. The use of the system for designing the collection routes in a municipality of Havana, Cuba is described.

#

This chapter was previously published in Models and Methods for Supporting Decision-Making in Human Health and Environment Protection, edited by Carlos N. Bouza, Flávio L. de Mello and Marcos Negreiros, New York: Nova Publishers Inc., 2016.  Corresponding Author address: Email:[email protected], Email:[email protected].

In: Mathematical Research Summaries. Volume 1 Editor: Matthew A. Rowe

ISBN: 978-1-53612-021-9 © 2017 Nova Science Publishers, Inc.

Chapter 141

COMPARISON METHODS OF DIGITAL ELEVATION MODEL CORRECTION, IN THE SUBWATERSHED V ANIVERSARIO, CUYAGUATEJE BASIN CUBA #

Yeleine Almoza Hernández1,*, Abdiel Fernández Alvarez1, Yasser Vázquez1 and Andrea Petroseli2 1

Departamento Física-Matemática, Facultad Ciencias Técnicas, Universidad Agraria de la Habana, Cuba 2DAFNE Department, Tuscia University, Italy

RESEARCH SUMMARY For several decades, the terrain topography has been studied in depth due to its importance and influence in other disciplines, like vegetation sciences, territorial planning, hydrology and others. Digital Elevation Model (DEM) data as the others raster data, is a matrix of cells regularly spaced, where the attribute is the elevation datum, usually measured at particular ground positions and later interpolated in order to reconstruct the whole matrix of cells. Digital Elevation Models are useful because, from them, we can obtain other interesting data. Consequently, we consider helpful the continuous efforts to gain a better understanding of the preprocessing techniques aiming to correct Digital Elevation Models. For these reasons, the aim of the present research work is to analyze the geomorphological transformations produced by three DEMs correction methods in the particular scenario of V Aniversario subwatershed, Cuyaguateje River. For this analysis, the following correction methods have been selected: Fill method because is the most widely used in literature; TOPAZ method, which combines fills and cut; and finally, the physically based method PEM4PIT. The results shows the capabilities of mathematical methods (TOPAZ and Fill) over physically based method PEM4PIT, to correct depression getting the best final #

This chapter was previously published in Models and Methods for Supporting Decision-Making in Human Health and Environment Protection, edited by Carlos N. Bouza, Flávio L. de Mello and Marcos Negreiros, New York: Nova Publishers Inc., 2016. * Email: [email protected].

298

Yeleine Almoza Hernández, Abdiel Fernández Alvarez, Yasser Vázquez et al.

correlation with the original DEM, in doing so creating less errors introduction for further works based on DEMs. TOPAZ seems preferable to correct basins with high particular geomorphic characteristics like the research study area.

In: Mathematical Research Summaries. Volume 1 Editor: Matthew A. Rowe

ISBN: 978-1-53612-021-9 © 2017 Nova Science Publishers, Inc.

Chapter 142

AN INTEGER OPTIMIZATION MODEL FOR WASTE COLLECTION FREQUENCY PROBLEM #

Joanna Campbell Amos1, Sira Allende Alonso1 and Marcos José Negreiros Gomes2,* 1

2

University of Havana, Havana, Cuba State University of Ceará, Ceará, Brazil

RESEARCH SUMMARY A systematic collection service is fundamental to human health and premise for the waste recycling processes. Constraints in the availability of resources cause deficiencies in the service of solid waste collection and their accumulation in streets. In this paper an integer programming model is proposed for fixing a time table of waste collection in sectors of a given area. It is assumed known the capacity of the available collection fleet and the amount of wastes generated daily in each sector. The goal is to minimize the accumulation of waste residues in the area.

#

This chapter was previously published in Models and Methods for Supporting Decision-Making in Human Health and Environment Protection, edited by Carlos N. Bouza, Flávio L. de Mello and Marcos Negreiros, New York: Nova Publishers Inc., 2016. * Email: [email protected] , [email protected], [email protected].

In: Mathematical Research Summaries. Volume 1 Editor: Matthew A. Rowe

ISBN: 978-1-53612-021-9 © 2017 Nova Science Publishers, Inc.

Chapter 143

EVOLVING AN INTELLIGENT FRAMEWORK FOR DECISION-MAKING PROCESS IN E-HEALTH SYSTEMS #

Leonardo M. Gardini1, Carina Oliveira2, Reinaldo Braga2, Ronaldo Ramos2, Luiz O. M. Andrade3 and Mauro Oliveira2,* 1

State University of Ceará, Fortaleza, Brazil Federal Institute of Ceará, Fortaleza, Brazil 3 Federal University of Ceará, Fortaleza, Brazil 2

RESEARCH SUMMARY This paper presents improvements of LARIISA, a framework that makes use of contextaware information to support decision-making and governance in the public health area. More specifically, two relevant e-health applications are presented to illustrate the LARIISA system. The first one uses Bayesian networks in dengue scenarios. The second application uses ontology to manage home care scenarios. In both cases, the contributions related to the LARIISA framework include patient health diagnosis provided remotely, support for decision-making health systems, and context information for context-aware health systems.

#

This chapter was previously published in Models and Methods for Supporting Decision-Making in Human Health and Environment Protection, edited by Carlos N. Bouza, Flávio L. de Mello and Marcos Negreiros, New York: Nova Publishers Inc., 2016. * Corresponding Author address. Email: [email protected].

In: Mathematical Research Summaries. Volume 1 Editor: Matthew A. Rowe

ISBN: 978-1-53612-021-9 © 2017 Nova Science Publishers, Inc.

Chapter 144

HEART DISEASES PREDICTION USING DATA FROM HEALTH ASSURANCE SYSTEMS #

Ronaldo Ramos1,*, César Mattos2, Amauri Júnior1, Ajalmar Neto1, Guilherme Barreto2, Helio Mazza3 and Márcio Mota4 1

Federal Institute of Ceará, Brazil Federal University of Ceará, Brazil 3 DYAD e Associados, Brazil 4 State University of Ceará, Brazil

2

RESEARCH SUMMARY Health insurance companies usually keep huge databases containing the service usage records done by their clients. In this article, we present an experimental comparison that has been made among several kinds of classifiers in order to find an optimal model to predict the development of heart diseases based on this type of data. To construct the prediction model we developed a method for pattern labeling called TWINF (Time Window into Near Future), which is used for building the test and training sets to be submitted to the classifiers. Then, over a period of four years, we conducted experiments using dozens of classifiers in order to see which one would be most suitable to forecast the occurrence of heart diseases six months earlier. Later on we will see the results of the experiments. Note that the labeled patterns used to have thousands of attributes, which lead us to a course of dimensionality problem.

#

This chapter was previously published in Models and Methods for Supporting Decision-Making in Human Health and Environment Protection, edited by Carlos N. Bouza, Flávio L. de Mello and Marcos Negreiros, New York: Nova Publishers Inc., 2016. * Corresponding Author address email: [email protected].

In: Mathematical Research Summaries. Volume 1 Editor: Matthew A. Rowe

ISBN: 978-1-53612-021-9 © 2017 Nova Science Publishers, Inc.

Chapter 145

ITERATIVE ALGORITHMS I

#

Ioannis K. Argyros,*,1 and Á. Alberto Magreñán2,† 1

Department of Mathematical Sciences, Cameron University, Lawton, OK, US 2 Departmento de Matematicas, Universidad Internacional de La Rioja Logroño, La Rioja, Spain

RESEARCH SUMMARY It is a well-known fact that iterative methods have been studied since problems where we cannot find a solution in a closed form. There exist methods with different behaviors when they are applied to different functions, methods with higher order of convergence, methods with great zones of convergence, methods which do not require the evaluation of any derivative, etc. and researchers are developing new iterative methods frequently. Once these iterative methods appeared, several researchers have studied them in different terms: convergence conditions, real dynamics, complex dynamics, optimal order of convergence, etc. This phenomena motivated the authors to study the most used and classical ones as for example Newton’s method or its derivative-free alternative the Secant method. Related to the convergence of iterative methods, the most well known conditions are the Kantorovich ones, who developed a theory which has allow many researchers to continue and experiment with these conditions. Many authors in the recent years have studied modifications of these conditions related, for example, to centered conditions, w-conditions or even convergence in Hilbert spaces. In this monograph, we present the complete recent work of the past decade of the authors on Convergence and Dynamics of iterative methods. It is the natural outgrowth of their related publications in these areas. The chapters are self-contained and can be read independently. Moreover, an extensive list of references is given in each chapter, in order to

#

This chapter was previously published as a book: Iterative Algorithms I, by Ioannis K. Argyros and Á. Alberto Magreñán, New York: Nova Publishers Inc., 2017. * Email: [email protected] † [email protected]

306

Ioannis K. Argyros and Á. Alberto Magreñán

allow reader to use the previous ideas. For these reasons, we think that several advanced courses can be taught using this book. The list of presented topic of our related studies follows.                       

Secant-type methods; Efficient Steffensen-type algorithms for solving nonlinear equations; On the semilocal convergence of Halley’s method under a center-Lipschitz condition on the second Fréchet derivative; An improved convergence analysis of Newton’s method for twice Fréchet differentiable operators; Expanding the applicability of Newton’s method using Smale’s a-theory; Newton-type methods on Riemannian Manifolds under Kantorovich-type conditions; Improved local convergence analysis of inexact Gauss-Newton like methods; Expanding the Applicability of Lavrentiev Regularization Methods for Ill-posed Problems; A semilocal convergence for a uniparametric family of efficient secant-like methods; On the semilocal convergence of a two-step Newton-like projection method for illposed equations; New Approach to Relaxed Proximal Point Algorithms Based on A−maximal; Newton-type Iterative Methods for Nonlinear Ill-posed Hammerstein-type Equations; Enlarging the convergence domain of secant-like methods for equations; Solving nonlinear equations system via an efficient genetic algorithm with symmetric and harmonious individuals; On the Semilocal Convergence of Modified Newton-Tikhonov Regularization Method for Nonlinear Ill-posed Problems; Local convergence analysis of proximal Gauss-Newton method for penalized nonlinear least squares problems; On the convergence of a Damped Newton method with modified right-hand side vector; Local convergence of inexact Newton-like method Under weak Lipschitz conditions; Expanding the applicability of Secant method with applications; Expanding the convergence domain for Chun-Stanica-Neta family of third order methods in Banach spaces; Local convergence of modified Halley-like methods with less computation of inversion; Local convergence for an improved Jarratt-type method in Banach space; Enlarging the convergence domain of secant-like methods for equations.

The book’s results are expected to find applications in many areas of applied mathematics, engineering, computer science and real problems. As such this monograph is suitable to researchers, graduate students and seminars in the above subjects, also to be in all science and engineering libraries. The preparation of this book took place during 2015-2016 in Lawton, Oklahoma, USA and Logroño, La Rioja, Spain.

In: Mathematical Research Summaries. Volume 1 Editor: Matthew A. Rowe

ISBN: 978-1-53612-021-9 © 2017 Nova Science Publishers, Inc.

Chapter 146

ITERATIVE ALGORITHMS II

#

Ioannis K. Argyros,*,1 and Á. Alberto Magreñán2,† 1

Department of Mathematical Sciences, Cameron University, Lawton, OK, US 2 Departmento de Matematicas, Universidad Internacional de La Rioja, Logroño, La Rioja, Spain

RESEARCH SUMMARY In this monograph, we present the complete recent work of the past decade of the authors on convergence and applications of iterative methods. It is the natural outgrowth of their related publications in these areas. The chapters are self-contained and can be read independently. Moreover, an extensive list of references is given in each chapter, in order to allow reader to use the previous ideas. For these reasons, we think that several advanced courses can be taught using this book. The list of presented topic of our related studies follows:          #

Convergence of Halley’s method under centered Lipschitz condition on the second Fréchet derivative; Semilocal convergence of Steffensen-type algorithms; Some weaker extensions of the Kantorovich theorem for solving equations; Improved convergence analysis of Newton’s method; Extending the applicability of Newton’s method; Extending the applicability of Newton’s method for sections on Riemannian manifolds; Two-step Newton methods; Discretized Newton-Tikhonov Method;

This chapter was previously published as a book: Iterative Algorithms II, by Ioannis K. Argyros and Á. Alberto Magreñán, New York: Nova Publishers Inc., 2017. * Email: [email protected] † [email protected]

308

Ioannis K. Argyros and Á. Alberto Magreñán          

Relaxed secant-type methods; Newton-Kantorovich method for analytic operators; Iterative Regularization methods for ill-posed Hammerstein type Operator Equations; Local convergence of a fifth order Method in Banach space; Local convergence of the Gauss-Newton method; Expanding the applicability of the Gauss-Newton method for convex optimization under a majorant condition; An Analysis of Lavrentiev Regularization Methods and Newton-type Iterative methods for Nonlinear Ill-posed Hammerstein-type Equations; Local Convergence of a multi-point-parameter Newton-like methods in Banach space; On an iterative method for unconstrained optimization; Inexact two-point Newton-like methods under general conditions.

The book’s results are expected to find applications in many areas of applied mathematics, engineering, computer science and real problems. As such this monograph is suitable to researchers, graduate students and seminars in the above subjects, also to be in all science and engineering libraries. The preparation of this book took place during 2015-2016 in Lawton, Oklahoma, USA and Logroño, La Rioja, Spain.

In: Mathematical Research Summaries. Volume 1 Editor: Matthew A. Rowe

ISBN: 978-1-53612-021-9 © 2017 Nova Science Publishers, Inc.

Chapter 147

CHAOS THEORY AND FINANCIAL STATEMENTS

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Fernando Juárez School of Business, Universidad del Rosario, Bogotá, Colombia

RESEARCH SUMMARY The purpose of this chapter is to show some applications of chaos theory to financial statements. Although chaos theory has been used in several financial topics, it is not usually involved with financial statements, which seem to remain impervious to it. To describe the analytical possibilities that chaos theory has in financial statements, a description of some features of chaos theory and their interest with regard to financial statements is made. Next, the application of chaos theory in a specific topic, such as the analysis of the accounting equation is presented. In addition, explanations of the possibilities of chaos theory in analyzing financial statements accounts and ratios, using several models of chaos theory, are provided. Finally the use of recurrence analysis is described to provide different perspectives on financial statements information. The intention is to create an interest in viewing financial statements as a complex information system.

#

This chapter was previously published in Chaos Theory: Origins, Applications and Limitations, edited by Anthony Reed, New York: Nova Publishers Inc., 2017  Corresponding author: Fernando Juárez. School of Business, Universidad del Rosario, Bogotá, Colombia. E-mail: [email protected].

In: Mathematical Research Summaries. Volume 1 Editor: Matthew A. Rowe

ISBN: 978-1-53612-021-9 © 2017 Nova Science Publishers, Inc.

Chapter 148

APPLYING CHAOS THEORY TO WORK: THE CHAOS THEORY OF CAREERS #

Robert Pryor* School of Education, Australian Catholic University (National), Sydney, Australia

RESEARCH SUMMARY The changing nature of career development and working itself in the twenty-first century called into question traditional theories of employment and vocational decision making. A new perspective was required which, while not jettisoning the advances of the previous century of theorizing, research and assessment, addressed the new challenges of complexity, change, chance and connection in employment and education. Also what was sought was a theoretical approach which linked the psychology of career development with the broader currents of contemporary scientific thinking in general. Chaos theory was viewed as an approach which met these criteria. This chapter describes how the Chaos Theory of Careers (Pryor and Bright, 2011) developed out of discontent with previous career development theories and how fundamental concepts such as non-linearity, emergence, systems thinking, attraction, unplanned change, chance and aperiodicity, could be applied to work and career development to produce new insights for theory, research, assessment and counseling in the field. Some illustrations of this ongoing work are presented along with an agenda for further development of the application of chaos theory to career development.

# *

This chapter was previously published in Chaos Theory: Origins, Applications and Limitations, edited by Anthony Reed, New York: Nova Publishers Inc., 2017 Corresponding author: Prof. Robert Pryor, 8 Kennedy Place, Bayview, N.S.W. 2104, Australia Email: [email protected].

In: Mathematical Research Summaries. Volume 1 Editor: Matthew A. Rowe

ISBN: 978-1-53612-021-9 © 2017 Nova Science Publishers, Inc.

Chapter 149

APPLICATION OF CHAOS THEORY TO VENTRICULAR WALL BIOMECHANICS #

Walter E. Legnani1*, PhD, Leandro J. Cymberknop1,2, PhD and Ricardo L. Armentano1,2, PhD 1

Signals and Image Processing Center (CPSI), Universidad Tecnológica Nacional, Buenos Aires, Argentina Faculty of Engineering and Natural Sciences, Universidad Favaloro, Buenos Aires, Argentina

RESEARCH SUMMARY The concept of chaos in science is mainly associated with the field of nonlinear dynamics, which is characterized essentially by a disproportionately respond to stimuli. In this way of reasoning, physiology constitutes one of the more abundant sources of case studies in the research community. Consequently, the presence of nonlinearities in physiological interactions imposes a limitation to linear analysis in providing a wide description of the underlying dynamics. This complex nature arises from the interaction of multiscale (time and space) structural units, jointly with regulatory feedback loops. In this chapter, nonlinear time series analysis has been applied to ventricular wall thickness (VWT) variations, in order to identify the presence of complex behaviors under different conditions. One important advantage of applying chaos theory relays in the opportunity to avoid assumptions related to the condition of the system, pre-existing models or its relation to any specific physical variable. Observed chaoticity (based on the results of determinism tests and values of positive largest Lyapunov exponents) would imply the presence of an underlying ‘multiscale structure’ in VWT waveform composition. A specific situation is accused in the absence of flow supply to cardiac tissues, denoting a phenomenon known as ‘ischemia.’ Under this condition, myocardial cells may die (infarction) as a consequence of the absence #

This chapter was previously published in Chaos Theory: Origins, Applications and Limitations, edited by Anthony Reed, New York: Nova Publishers Inc., 2017 * Corresponding Author Email: [email protected].

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of oxygen. Concerning physiological processes, it is known that the loss of high frequency components of the signals involved denotes the presence of age or disease. For instance, submission of VWT variation to an ischemic process (by means of left circumflex coronary artery flow obstruction) would derive in a ‘waveform loss of complexity’ which could be associated to a decrease in fractal dimension or wavelet entropy values. Moreover, nonlinear system characterization of VWT pulsatility suggests that evaluated time series belong to a chaotic process and the obtained parameters might constitute a measure of the ventricular wall capacity to adapt to different biological situations. Nevertheless, it is noteworthy that required data were obtained using invasive acquisition techniques, which are expensive and complicated to implement. Besides, time series demand a representative number of samples in order to properly differentiate a basal state from the development of an ischemic process. Examples showed here constitute a new holistic approach, which can help to develop a better characterization VWT mechanics in health and disease. Significant changes observed in nonlinear indicators such as entropy, largest Lyapunov exponents, embedding dimension as well as fractal measures could be associated to the different pathological conditions manifested by the cardiac muscle, in terms of its own structure. As a result, particular intrinsic states related to ventricular wall mechanics could be better understood, complementing in this way information provided by traditional (clinical) indexes.

In: Mathematical Research Summaries. Volume 1 Editor: Matthew A. Rowe

ISBN: 978-1-53612-021-9 © 2017 Nova Science Publishers, Inc.

Chapter 150

COMPLEXITY AND SYNCHRONIZATION IN THE PROCESS OF BIOCHEMICAL SUBSTANCE EXCHANGE IN A DIFFUSIVELY COUPLED RING OF CELLS #

D. T. Mihailović*, G. Mimić and I. Arsenić University of Novi Sad, Faculty of Agriculture, Novi Sad, Serbia

RESEARCH SUMMARY In this chapter we numerically investigate a model of a diffusively coupled ring of cells. To model the dynamics of individual cells we consider a map with cell affinity, which is a generalization of the logistic map. First, we study the basic features of a one-cell system in terms of the Lyapunov exponent, Sample entropy and Kolmogorov complexity. Second, we test the complexity of this generalized logistic map via an information measure based on Kolmogorov complexity using the Lempel-Ziv algorithm. We compute a complexity counter indicating the number of distinct patterns in the generalized logistic map time series. The number of patterns in the measured time series is shown to increase with time series length but has a saturation value within the logistic time series. Third, the notion of observational heterarchy, which is a perpetual negotiation process between the different levels of the description of a phenomenon, is reviewed. We also study how the active coupling induced by observational heterarchy modifies the synchronization property of a model with N c = 80 cells. We observe that heterarchy has a dynamic structure that emerges from the existence of internal observers that can perform reinterpretation when we define heterarchy as observational heterarchy. We show numerically that active coupling enhances the synchronization of biochemical substance exchange under several conditions of cell affinity.

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This chapter was previously published in Chaos Theory: Origins, Applications and Limitations, edited by Anthony Reed, New York: Nova Publishers Inc., 2017 * Corresponding author: Dositej Obradovic, Sq. 8, 21000 Novi Sad, Serbia, [email protected].

In: Mathematical Research Summaries. Volume 1 Editor: Matthew A. Rowe

ISBN: 978-1-53612-021-9 © 2017 Nova Science Publishers, Inc.

Chapter 151

UNVEILING THE ESCAPE MECHANISM OF ORBITS IN HAMILTONIAN SYSTEMS WITH MULTIPLE EXIT CHANNELS #

Euaggelos E. Zotos* Department of Physics, School of Sciences, Aristotle University of Thessaloniki, Thessaloniki, Greece

RESEARCH SUMMARY The aim of this chapter is to numerically reveal the escape properties of orbits in a dynamical system of a two-dimensional perturbed harmonic oscillator, which is a characteristic example of open Hamiltonian systems. In the system of the perturbed harmonic oscillator and for energies above the critical energy of escape several channels of escape are present thus making the escape process a very intriguing problem. We conduct a thorough numerical investigation classifying orbits as escaping and non-escaping (regular or chaotic), considering only un-bounded motion for several levels of energy. The smaller alignment index (SALI) is calculated by numerically integrating the variational equations in an attempt to safely distinguish and with certainty between ordered and chaotic non-escaping motion. Our exploration takes place in different types of two-dimensional planes thus allowing us to form a general overview of the escape process. It is of particular interest, to locate the basins of escape toward the different escape channels and also to relate them with the corresponding escape time of the orbits. It was found that in all examined cases regions of non-escaping motion coexist with several basins of escape. The larger escape periods have been measured for orbits with initial conditions in the vicinity of the fractal structures, while the lowest escape rates belong to orbits with initial conditions inside the basins of escape.

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This chapter was previously published in Chaos Theory: Origins, Applications and Limitations, edited by Anthony Reed, New York: Nova Publishers Inc., 2017 * E-mail address: [email protected]

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We hope our numerical analysis to be useful for a further understanding of the escape mechanism of orbits in open Hamiltonian systems with two degrees of freedom.

In: Mathematical Research Summaries. Volume 1 Editor: Matthew A. Rowe

ISBN: 978-1-53612-021-9 © 2017 Nova Science Publishers, Inc.

Chapter 152

MATHEMATICAL MODELING OF INTRACELLULAR PROCESSES

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P. M. Gotovtsev, Ya. E. Sergeeva, A. V. Komova, I. A. Konova, K. V. Gorin, G. U. Badranova, V. M. Pojidaev and R. G. Vasilov National Research Centre “Kurchatov Institute”, NBICS-Centre, Biotechnology and Bioenergy Laboratory, Moscow, Russia

RESEARCH SUMMARY Mathematical modeling of intracellular processes is an actively developing field of study. Different scientific groups use various approaches and principles for the modeling of all range of processes, from single biochemical reactions to cellular metabolism. Each of the approaches used has its advantages and disadvantages and requires different input. This article includes the review and analysis of the modern works in the field. The main approaches to the modeling of intracellular processes are discussed, including flux balance analysis, Petri nets, thermodynamics approaches for systems far from equilibrium, “blackbox” modeling etc. Also the article involves the analysis of approaches to the structures of mathematical models, organization of links between sub-models and the possibilities of use of various methods while modeling a single metabolic process or a metabolism of a certain microorganism.

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This chapter was previously published in Advances in Mathematics Research. Volume 21, edited by Albert R. Baswell, New York: Nova Publishers Inc., 2017.  E-mail address: [email protected] (Corresponding author).

In: Mathematical Research Summaries. Volume 1 Editor: Matthew A. Rowe

ISBN: 978-1-53612-021-9 © 2017 Nova Science Publishers, Inc.

Chapter 153

IMPROVING THE EFFICIENCY OF BEZIER BASIS FUNCTION IN OBJECT SURFACE MODELING

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J. A. Muñoz-Rodríguez* Centro de Investigaciones en Optica, A. C. Leon, Gto, Mexico

RESEARCH SUMMARY We present a review of our computational algorithms to achieve an efficient cubic Bezier basis functions to provide interpolation with continuity for object shape modeling. In this technique, the surface model is performed by means of Bezier networks based on object surface points.This modeling technique expands the Bezier basis functions to preserve continuity G1 and interpolation.From these surface properties, model accuracy and object representation are improved. Also, this cubic network reduces memory size to represent the object surface.It is because the model is implemented with few mathematical terms. The surface model is defined by means of the network weights and the control points, which are retrieved from the object surface. This computational model represents the object surface with high accuracy. It is because the network interpolates all object surface points. The contribution of the proposed technique is elucidated by an evaluation based on interpolation, continuity, model accuracy, and memory size of the traditional models.

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This chapter was previously published in Advances in Mathematics Research. Volume 21, edited by Albert R. Baswell, New York: Nova Publishers Inc., 2017. * E-mail address: [email protected]; Tel.: (477) 441 42 00.

In: Mathematical Research Summaries. Volume 1 Editor: Matthew A. Rowe

ISBN: 978-1-53612-021-9 © 2017 Nova Science Publishers, Inc.

Chapter 154

PERFORMANCE EVALUATION OF TWODIMENSIONAL LINEAR DISCRIMINANT ANALYSIS FOR IMAGES #

Tetsuya Yoshida1,* and Yuu Yamada2 1

Graduate School of Humanities and Science, Nara Women’s University, Nara, Japan 2 Graduate School of Information Science and Technology, Hokkaido University, Sapporo, Japan

RESEARCH SUMMARY Inexpensive high resolution digital cameras makes it easy to take a lot of photos in daily life, and the photos are often uploaded into social networks to share with friends. Folksonomy or social tagging have been widely used for effective sharing of resources. Since tags or meta information may be available on images, exploitation of the available label information is useful to improve the performance of image categorization. Chapter 3 presents performance evaluation of simultaneous coding of scatter matrices in Two-Dimensional Linear Discriminant Analysis (2DLDA). 2DLDA is an extension of Linear Discriminant Analysis (LDA) for 2-dimensional objects such as images. In 2DLDA, matrices which are used for linear mapping are iteratively calculated based on the eigenvectors of asymmetric matrices. The authors report performance evaluation of simultaneous coding of scatter matrices with which eigenvectors can be stably calculated. Furthermore, for faster calculation, they also report the evaluation of approximate decomposition of scatter matrices based on its several leading eigenvectors. The authors regard that two-dimensional methods for image analysis conduct learning of linear mapping from the original image to its compressed image, and evaluated performance in terms of supervised clustering. Results are encouraging, and

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This chapter was previously published in Advances in Mathematics Research. Volume 21, edited by Albert R. Baswell, New York: Nova Publishers Inc., 2017. * E-mail address: [email protected]

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indicate that the authors approach can achieve comparative performance with the original 2DLDA with reduced computation time.

In: Mathematical Research Summaries. Volume 1 Editor: Matthew A. Rowe

ISBN: 978-1-53612-021-9 © 2017 Nova Science Publishers, Inc.

Chapter 155

FROM PSEUDOHOLOMORPHIC FUNCTIONS TO THE ASSOCIATED REAL MANIFOLD #

Giampiero Esposito1,* and Raju Roychowdhury2 1

INFN, Sezione di Napoli, Complesso Universitario di Monte S. Angelo, Napoli, Italy 2 Instituto de Fisica, Universidade de Sao Paulo, Sao Paulo, Brazil

RESEARCH SUMMARY This paper studies first the differential inequalities that make it possible to build a global theory of pseudoholomorphic functions in the case of one or several complex variables. In the case of one complex dimension, we prove that the differential inequalities describing pseudoholomorphicity can be used to define a one-real-dimensional manifold (by the vanishing of a function with nonzero gradient), which is here a 1-parameter family of plane curves. On studying the associated envelopes, such a parameter can be eliminated by solving two nonlinear partial differential equations. The classical differential geometry of curves can be therefore exploited to get a novel perspective on the equations describing the global theory of pseudoholomorphic functions.

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This chapter was previously published in Advances in Mathematics Research. Volume 21, edited by Albert R. Baswell, New York: Nova Publishers Inc., 2017. * E-mail address: [email protected]

In: Mathematical Research Summaries. Volume 1 Editor: Matthew A. Rowe

ISBN: 978-1-53612-021-9 © 2017 Nova Science Publishers, Inc.

Chapter 156

NUMERICAL AND ANALYTICAL METHODS FOR BOND PRICING IN SHORT RATE CONVERGENCE MODELS OF INTEREST RATES , * #

Zuzana Bučková, Beáta Stehlíková and Daniel Ševčovič† Department of Applied Mathematics and Statistics, Comenius University in Bratislava, Slovakia

RESEARCH SUMMARY We discuss recent advances on short interest rate models which can be formulated in terms of a stochastic differential equation for the instantaneous interest rate (also called short rate) or a system of such equations in case the short rate is assumed to depend on other stochastic factors. Our focus is on convergence models which explain the evolution of interest rate in connection with the adoption of the Euro currency. The domestic short rate depends on a stochastic European short rate. In short rate models, the bond prices determining the term structure of interest rate, are obtained as solutions to partial differential equations. Analytical solutions are available in special cases only. Therefore the authors are concerned with a question how to obtain their approximations. We use both analytical and numerical methods to obtain an approximate solution to the partial differential equation for bond prices.

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The research has been supported by VEGA 1/0251/16 project and FP7-PEOPLE-2012-ITN project #304617 STRIKE. # This chapter was previously published in Advances in Mathematics Research. Volume 21, edited by Albert R. Baswell, New York: Nova Publishers Inc., 2017. † E-mail address: [email protected] (Corresponding author).

In: Mathematical Research Summaries. Volume 1 Editor: Matthew A. Rowe

ISBN: 978-1-53612-021-9 © 2017 Nova Science Publishers, Inc.

Chapter 157

STRUCTURAL TRANSFORMATIONS IN THE RELATIONSHIPS BETWEEN MATHEMATICS AND MUSIC UP TO THE RENAISSANCE AND THE EMERGENCE OF THE IDEA OF NUMBER AS A CONTINUOUS QUANTITY #

Oscar João Abdounur* University of São Paulo, Max Planck Institute for the History of Science, Berlin, Germany

RESEARCH SUMMARY This chapter aims at evincing a conceptual change in the relationships between mathematics and theoretical western music throughout its history from Antiquity to Renaissance, in which structural changes in the conception of ratio associated with the relationships between theoretical music and practical problems played a special role. It identifies situations in the historical development of such a relationship, which show signs of changes on the understanding of music, in which music comes from a arithmetical speculative subject to a sonorous one, associated respectively to music without sounds and with it. In the context of resistance of the Platonic-Pythagorean tradition to changes in theories of ratio and proportion; this chapter will look preliminarily at the evidence of singular transformations in treatises of mathematics and theoretical music of the early modern period. As a result, it is possible to analyse, on the one hand, the emergence of the idea of number in the context of changes on theory of ratios, which borrows semantically distinct but structurally similar attributes from arithmetic analogous structures, as well as, on the other hand, the role of structural problems of theoretical music on the intensification of such a process. #

This chapter was previously published in Advances in Mathematics Research. Volume 21, edited by Albert R. Baswell, New York: Nova Publishers Inc., 2017. * E-mail address: [email protected]