Podstawy mnogościowe wielomianów symetrycznych wielu zmiennych w notacji spektralnej : zarys teorii

• Autorzy: Piwowarczyk T.

Warianty tytułu

EN

Set bases of symmetrical multinominals of numerous variables in spectral notation (theoretical outline)

• Języki publikacji: PL

Abstrakty

EN

All symmetric polynomials of multiple variables, with the variables belonging to the fixed, final set, are denoted by means of some abstract symbols. They are known as spectral, or multipower symbols. This set is analysed from a point of view of a set theory. The article contains the definitions of those relations which are used for computing elements in numerous subsets, such as equivalence relation, ordering relation, quotient sets, combinatorics formulas. In other words, some set theory model is proposed for symmetric polynomials of multiple variables. Such a model provides a solid basis for the further study of symmetric polynomials, and first of all, for the study of their numerous vector subspaces. This study will be developed in a theoretically unlimited set of algebraic identities which are particularly useful when it comes to engineering applications

Słowa kluczowe

PL

analiza matematyczna wielomianów; przestrzeń wektorowa; wielomiany symetryczne

EN

mathematical analysis of polynomials; vector space; symmetric polynomials

• Wydawca: Wydawnictwo Politechniki Krakowskiej im. Tadeusza Kościuszki
• Czasopismo: Czasopismo Techniczne. Elektrotechnika
• Rocznik: 2000
• Tom: R. 97, z. 4-E
• Strony: 38--60
• Opis fizyczny: Bibliogr. 24 poz., wz., wykr.

Twórcy

autor

Piwowarczyk T.

Bibliografia

• [1] G.Birkhoff, S. Mc Lane, A survey of Modern Algebra, New York 1954.
• [2] A. CayIey, The Collected Mathematical Papers, Vol. XII, Cambridge 1897.
• [3] D. Cox, J. Little, D. O'Shea, Ideals, Varieties and Algorithms, An Introduction to Computational Algebraic Geometry and Commutative Algebra, Springer New York 1998.
• [4] J. Flachsmezer, Kombinatorik, Eine Einfuerung in die mengentheoretische Denkweise, VEB Deutscher Verlag der Wissenschaften, Berlin 1969.
• [5] P.A. Fuhrmann, A Polynomial Approach to Linear Algebra, Springer Verlag, New York 1996.
• [6] N. Juringius, Recherche sur les Fonction Symetriques, Lund 1932.
• [7] T. Kaczorek, Wektory i macierze w automatyce i elektrotechnice, WNT, Warszawa 1998.
• [8] J. Komorowski, Od liczb zespolonych do tensorów, spinorów, algebr liego i kwadryk, PWN, Warszawa 1978.
• [9] A. Kurosh, Higher Algebra, Mir Publishers, Moscow 1972.
• [10] S. Lang, Algebra, Addison-Wesley, Reading, Mass., 1970.
• [11] E. Layer, T. Piwowarczyk, Quality of Approximation of a Non Linear Simplified Model by a Simplified One, The Fifth International Symposium on Methods and Models in Automation and Robotics, Międzyzdroje 25-29 August 1998.
• [12] E. Layer, T. Piwowarczyk, Application of Generalized Fibonacci Sequence to Simplification of Mathematical Models of Linear Dynamic Systems, Archives of Electrical Engineering, Vol. XLVIII, NO. 1-2, pp. 19-30, Warsow 1999.
• [13] E. Layer, T. Piwowarczyk, Generalized Fibonacci Series, Journal Systems - Analysis - Modelling - Simulation, Gordon & Breach Science Publisher, USA 1999.
• [14] A. Mostowski, M. Stark, Elementy algebry wyższej, PWN, Warszawa 1965.
• [15] B. Noble, J.W. Daniel, Applied Linear Algebra, Prentice-Hall, Inc. Englewood Cliffs, New Jersey 07632, 1977.
• [16] T. Piwowarczyk, Multipower Notation of Symmetrical Polynomials in Engineering Calculus, PAN, Cracow 2000.
• [17] T. Piwowarczyk, Coefficients of Power Expansion of Original as Functions of Transform Coefficients, „Czasopismo Techniczne", Wydawnictwo Politechniki Krakowskiej, Cracow 1996.
• [18] T. Piwowarczyk, Symmetrical Polynomials of Multiple Variables in Electrical Circuits, „Czasopismo Techniczne", Wydawnictwo Politechniki Krakowskiej, Cracow 1999.
• [19] T. Piwowarczyk, Multipower Notation of Symmetrical Polynomials in Engineering Calculus, WIGSMiE PAN, Kraków 2000.
• [20] M.R. Spiegel, Laplace Transforms, Schaum's Outline Series, McGraw-Hill, United State of America 1965.
• [21] A. Turowicz, Geometria zer wielomianów, PWN, Warszawa 1967.
• [22] N.J. Wilenkin, Kombinatoryka, PWN, Warszawa 1972.
• [23] F. Winkler, Polynomial Algorithms in Computer Algebra, Springer Wien New York 1996.
• [24] R.E. Zippel, Computer Algebra and Parallelism, Second International Workshop Ithaca, USA, May 9-11, 1990 Proceedings, Springer-Verlag 1990.