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Warianty tytułu
Konferencja
Modelowanie w mechanice/Sympozjum (XLIV; 2005; Gliwice; Polska)
Języki publikacji
Abstrakty
The aim of the paper is to present a new algebraic system with specifically defined addition and multiplication operations. The new numbers called perturbation numbers are introduced. It's proved that the new algebraic system (Re,+s,8E) is imbedded into the system of real numbers. Some additional properties as subtraction, inversion and division are presented too. Some elementary formulations of matrices and vectors of new numbers are introduced, as well as some basic properties of perturbation matrices, inverse matrices and solution properties of linear equations and eigenvalue problems in the new algebraic system of perturbation elements. Classical perturbation problems can be solved in the new algebraic system as easy as usual problems of applied mathematics, theoretical physics and techniques. Additional analytical transformations are not required.
Słowa kluczowe
Rocznik
Tom
Strony
413--418
Opis fizyczny
Bibliogr. 16 poz.
Twórcy
autor
- Zakład Mechaniki Teoretycznej Politechnika Śląska, 44-100 Gliwice , ul. Krzywoustego 7 tel. 32 237-18-14
Bibliografia
- [1] Bellman R.: Introduction to Matrix Analysis, Mc-Graw-Hill Book Company, Inc.L, New York Toronto London, 1976.
- [2] Bialynicki-Birula A.: Algebra, PWN, Warszawa, 1971.
- [3] Gelfand I. М.: Wykłady z algebry liniowej, PWN, Warszawa, 1971.
- [4] Gomuliński A., Witkowski М.: Mechanika budowli, kurs dla zaawansowanych, Oficyna Wyd. Pol. Warszawskiej, Warszawa, 1993.
- [5] Kaczorek Т.: Wektory i macierze w automatyce i elektrotechnice, WN-T, Warszawa, 1998.
- [6] Kato Т.: Perturbation Theory for Linear Operators, Springer-Verlag, Berlin Heidelberg New York, 1966.
- [7] Kiełbasiński A., Schwetlick H.: Numerische lineare Algebra, VEB Deutcher Verlag der Wissenschaften, Berlin, 1988.
- [8] Korn G. A., Korn Т. М.: Matematyka dla pracowników naukowych i inżynierów cz.I, PWN, Warszawa, 1983.
- [9] Lankaster P.: Theory of Matrices, Academic Press, New York London, 1978.
- [10] Rayleigh L.: The Theory of Sound, vol.I. London, 1927.
- [11] Rellich F.: Stórumgstheory der Spektralzerlegung, I, Math. Ann., 113, 600-619, 1936.
- [12] Schródinger E.: Quantisierung als Eigenwertproblem, Ann. Physik, 80,437-490, 1926.
- [13] Skrzypczyk J.: Perturbation methods - New arithmetic. Zeszyty naukowe Pol. Śl., ser. Budownictwo, Gliwice, 2003.
- [14] Skrzypczyk J.: Metody perturbacyjne - Nowa arytmetyka, Zeszyty Naukowe Katedry Mechaniki Stosowanej Politechniki Śląskiej 23, Gliwice 2004, str. 363-368.
- [15] Skrzypczyk J.: Perturbation methods I- Algebra, Functions, Linear Equations, Eigenvalue Problems: New Algebraic Methodology, Proc. of International Conference NEW TRENDS IN STATICS AND DYNAMICS OF BUILDINGS, October 2003, Faculty of Civil Engineering SUT Bratislava, Slovakia, pp. 55-58.
- [16] Skrzypczyk J., Winkler A.: Perturbation methods II- Differentiation, Integration and Elements of Functional Analysis with Applications to Perturbed Wave Equation, Proc. of International Conference NEW TRENDS IN STATICS AND DYNAMICS OF BUILDINGS, October 2003, Faculty of Civil Engineering SUT Bratislava, Slovakia, pp. 147-150
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-article-BSL9-0044-0005