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2009 | Vol. 35, no 1 | 7-13
Tytuł artykułu

Mathematical modeling of dynamical systems by generalized functions

Autorzy
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
The distributions or generalized functions are linear and continuous functionals defined by the class of functions which become null outside of a compact set and have derivatives of any order. The calculus with distributions was used to the modeling of linear systems. Generalized functions are also useful in the study of non-linear systems. In this paper, it is proved that the distributions with compact support represent a first approximation in the mathematical modeling of a system with infinite fading memory. The demonstration of this statement is the main part of the paper. The mathematical tool used is the differential calculus in the locally-convex topological space of the histories of inputs in system. The last part refers to the ε-distribution, R. Vallée's recent concept, and enumerates some applications.
Słowa kluczowe
Wydawca

Czasopismo
Rocznik
Strony
7-13
Opis fizyczny
Bibliogr. 13 poz.
Twórcy
autor
  • Romanian Academy, Romanian Comittee for History and Philosophy of Science and Technology (CRIFST), Calea Victoriei 125, 061581 Bucharest, Romania, eufrosinaotl@gmail.com
Bibliografia
  • [1] Balakrishnan A.V., State Space Theory of Linear Time-Varying Systems, [in:] System Theory, L.A. Zadeh, E. Polak (eds.), McGraw-Hill, 1969, pp. 95-125,
  • [2] Friedlander F.G., Joshi M., Introduction to the Theory of Distributions, Cambridge University Press, 2nd ed., 2008.
  • [3] Guelfand I.M., Chilov G.E., Théorie des distributions, Vol. 2, Dunod, Paris, 1964.
  • [4] Kanvvall R.P., Generalized Functions: Theory and Technique, 2nd ed., Birkhauser, Springer Verlag, Basel-Boston-Berlin, 1998.
  • [5] Mânzatu E., The second principle of thermodynamics as a consequence of the Riesz representation theorem for continuous and linear functional, Tensor, N.S., Japan, Vol. 39, 1982.
  • [6] Marinescu G., Espaces vectoriels pseudotopologiques et théorie des distributions, Veb Deutche Verlag der Wissenshaften, Berlin, Germany, 1963.
  • [7] Otlacan E., The Synergy and the Chaos Identified in the Constitutive Equation of a Dynamic System, Computing Anticipatory Systems, AIP Conference Proceedings 718, CASYS’03, Edited by Daniel Dubois, Melville, New York, 2004, pp. 328-337.
  • [8] Kecs W., Teodorescu P.P., Theory of Distributions with Applications in Technics, (Introducere în teoria distribuţtilor cu aplicaţii in tehnică) Editura Tehnică, Bucureşti, 1975.
  • [9] Schwartz L., Théorie des distributions, I, II, Hermann, Paris, 1950, 1951.
  • [10] Stanasila O., Mathematical Analysis (Analiză matematică), Editura Didactică şi Pedagogică, Bucureşti, 1981.
  • [11] Teodorescu P.P., Dynamics of linear elastic bodies, Editura Academiei; Abacus Press, Tunbridge Wells, Kent, 1975.
  • [12] Vallée R., About Wiener’s Generalized Harmonic Analysis, Kybernetes, Vol. 23, No. 6/7, 1994.
  • [13] Vallée R., On certain distributions met in signal theory and other domains of systems science, Systems Science, Vol. 30, No. 2, 2004.
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.baztech-article-BAT5-0042-0020
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