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Abstra t. úÁÉÓËÉ ÌÅË ÉÊ Ï ÁÌÇÅÂÒÅ ÄÌÑ ×ÔÏÒÏÇÏ ËÕÒÓÁ ÆÁËÕÌØÔÅÔÁ ÍÁÔÅÍÁÔÉËÉ ÷ûü, ÏÓÅÎØ 2012/13 ÕÞÅÂÎÏÇÏ ÇÏÄÁ

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1.1. óÉÍÍÅÔÒÉÞÅÓËÉÅ ÍÎÏÇÏÞÌÅÎÙ. òÁÓÓÍÏÔÒÉÍ ËÏÌØ Ï ÍÎÏÇÏÞÌÅÎÏ× ÏÔ n ÅÒÅÍÅÎÎÙÈ K [x ; : : : ; xn ℄. üÔÏ ÍÎÏÖÅÓÔ×Ï ËÏÎÅÞÎÙÈ ÌÉÎÅÊÎÙÈ ËÏÍÂÉÎÁ ÉÊ ÍÏÎÏÍÏ× ×ÉÄÁ ak1 :::kn xk1 : : : xknn , ÇÄÅ ak1 :::kn ∈ K , ËÏÔÏÒÙÅ ÍÏÖÎÏ ÓËÌÁÄÙ×ÁÔØ É ÕÍÎÏÖÁÔØ Ï ÏÂÙÞÎÙÍ ÒÁ×ÉÌÁÍ. þÉÓÌÏ k = k + · · · + kn ÎÁÚÙ×ÁÅÔÓÑ ÓÔÅÅÎØÀ ÍÏÎÏÍÁ. óÔÅÅÎØ ÍÎÏÇÏÞÌÅÎÁ | ÜÔÏ ÍÁËÓÉÍÕÍ Ï ÓÔÅÅÎÑÍ ×ÈÏÄÑÝÉÈ × ÎÅÇÏ ÍÏÎÏÍÏ×. îÁ ËÏÌØ Å K [x ; : : : ; xn ℄ ÄÅÊÓÔ×ÕÅÔ ÓÉÍÍÅÔÒÉÞÅÓËÁÑ ÇÒÕÁ Sn. å£ ÄÅÊÓÔ×ÉÅ ÎÁ ÏÂÒÁÚÕÀÝÉÈ x ; : : : ; xn ÚÁÄÁ£ÔÓÑ ÅÒÅÓÔÁÎÏ×ËÁÍÉ ÅÒÅÍÅÎÎÙÈ: (xi) = x i , É ÒÏÄÏÌÖÁÅÔÓÑ ÎÁ ÍÏÎÏÍÙ Ï ÍÕÌØÔÉÌÉËÁÔÉ×ÎÏÓÔÉ: (axk1 : : : xknn ) = xk1 : : : xknn , É ÄÁÌÅÅ ÎÁ ×ÓÅ ÍÎÏÇÏÞÌÅÎÙ Ï ÌÉÎÅÊÎÏÓÔÉ. íÎÏÇÏÞÌÅÎÙ, ÉÎ×ÁÒÉÁÎÔÎÙÅ ÒÉ ÜÔÏÍ ÄÅÊÓÔ×ÉÉ, ÎÁÚÙ×ÁÀÔÓÑ ÓÉÍÍÅÔÒÉÞÅÓËÉÍÉ. ïÒÅÄÅÌÅÎÉÅ 1.1. íÎÏÇÏÞÌÅÎ ÏÔ n ÅÒÅÍÅÎÎÙÈ ÎÁÚÙ×ÁÅÔÓÑ ÓÉÍÍÅÔÒÉÞÅÓËÉÍ, ÅÓÌÉ ÏÎ ÅÒÅÈÏÄÉÔ × ÓÅÂÑ ÒÉ ÌÀÂÙÈ ÅÒÅÓÔÁÎÏ×ËÁÈ ÅÒÅÍÅÎÎÙÈ. çÒÕÁ ÅÒÅÓÔÁÎÏ×ÏË ÏÒÏÖÄÁÅÔÓÑ ÔÒÁÎÓÏÚÉ ÉÑÍÉ. ðÏÜÔÏÍÕ ÍÏÖÎÏ ÄÁÔØ ÓÌÅÄÕÀÝÅÅ ÏÒÅÄÅÌÅÎÉÅ, ÜË×É×ÁÌÅÎÔÎÏÅ ÒÅÄÙÄÕÝÅÍÕ: ïÒÅÄÅÌÅÎÉÅ 1.2. íÎÏÇÏÞÌÅÎ ÏÔ n ÅÒÅÍÅÎÎÙÈ ÎÁÚÙ×ÁÅÔÓÑ ÓÉÍÍÅÔÒÉÞÅÓËÉÍ, ÅÓÌÉ ÏÎ ÅÒÅÈÏÄÉÔ × ÓÅÂÑ ÒÉ ÅÒÅÓÔÁÎÏ×ËÅ ÌÀÂÙÈ Ä×ÕÈ ÅÒÅÍÅÎÎÙÈ. ðÒÉ×ÅÄÅÍ ÒÉÍÅÒÙ ÓÉÍÍÅÔÒÉÞÅÓËÉÈ ÍÎÏÇÏÞÌÅÎÏ×. k k k ðÒÉÍÅÒ 1.3 (ÍÎÏÇÏÞÌÅÎÙ îØÀÔÏÎÁ). sk = x + x + · · · + xn , ÇÄÅ k ≥ 1. 1

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÷Ù ÉÓÏÌØÚÕÅÔÅ ÜÔÉ ÚÁÉÓËÉ ÎÁ Ó×ÏÊ ÓÔÒÁÈ É ÒÉÓË. îÉËÔÏ ÎÅ ÇÁÒÁÎÔÉÒÕÅÔ, ÞÔÏ ÉÈ ÔÅËÓÔ ÏÌÎÏÓÔØÀ ÓÏÏÔ×ÅÔÓÔ×ÕÅÔ ÓÏÄÅÒÖÁÎÉÀ ÌÅË ÉÊ. ÅÍ ÂÏÌÅÅ ÎÅ ÇÁÒÁÎÔÉÒÕÅÔÓÑ ÏÔÓÕÔÓÔ×ÉÅ × ÜÔÏÍ ÔÅËÓÔÅ ÏÛÉÂÏË. ÷ÒÏÞÅÍ, Ï ÎÁÊÄÅÎÎÙÈ ÏÛÉÂËÁÈ ÌÕÞÛÅ ÓÏÏÂÝÁÔØ Á×ÔÏÒÕ. 1

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(ÜÌÅÍÅÎÔÁÒÎÙÅ ÓÉÍÍÅÔÒÉÞÅÓËÉÅ ÍÎÏÇÏÞÌÅÎÙ).  = P P x + · · · + xn ,  = i

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