On Chebyshev polynomials and torus knots

In this work we demonstrate that the q-numbers and their two-parameter generalization, the q,p-numbers, can be used to obtain some polynomial invariants for torus knots and links. First, we show that the q-numbers, which are closely connected with the Chebyshev polynomials, can also be related with the Alexander polynomials for the class T(s,2) of torus knots, s being an odd integer, and used for finding the corresponding skein relation. Then, we develop this procedure in order to obtain, with the help of q,p-numbers, the generalized two-variable Alexander polynomials, and prove their direct connection with the HOMFLY polynomials and the skein relation of the latter.Comment: 6 pages (two-column UJP style

Analysis of the Efficiency PETSc and PETIGA Libraries in Solving the Problem of Crystal Growth

We present an analysis of high performance computational method for solving the problem of crystal grows. The method uses PETSc and PETIGA C-language based libraries and supports parallel computing. The evolution of calculation process was studied in series of special computations are obtained on innovative mobile cluster platform, which provides exclusive system tuning abilities. The results of research confirm the high efficiency of the proposed algorithm on multi-core computer systems and allow us to recommend the use of PETSc and PETIGA for solving high order differential equations

Особенности эмоционально-ценностного компонента профессиональной идентичности учителя основной школы

У статті представлено результати експериментального дослідження емоційно-ціннісного компонента професійної ідентичності вчителя основної школи. Виявлено його особливості у вчителів різних типів навчальних закладів: гімназій та звичайних загальноосвітніх навчальних закладів.The results of experimental research of emotionally-valued компонента of professional identity of teacher of basic school are presented in the article. Found out his features for the teachers of different types of educational establishments: high schools and ordinary general educational establishments.В статье представлены результаты экспериментального исследования эмоционально-ценностного компонента профессиональной идентичности учителя основной школы. Обнаружены его особенности у учителей разных типов учебных заведений: гимназий и обычных общеобразовательных учебных заведений