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Romanian Journal of Information Technology and Automatic Control / Vol. 18, No. 4, 2008


TEOREMA NOETHER ȘI FUNDAMENTELE MODELĂRII MATEMATICE

Neculai Andrei

Abstract:

The mathematical models of physical sysytems are expressed as systems of partial differential equations. All these equations are comming from the conservation laws, thus obtaining a well posed model satisfaying the completeness, minimality and non-contradiction principles. Besides, using the mathematical language in mathematical models all the words are rectified. Expressed into a minimal and non-contradictory manner, the mathematical models do not face the circularity. By Noether theorem we see that the conservation laws are comming from the symmetries of the Lagrange function associated to the physical system we analyse. Therefore, our known and predictible Universe is based on the concept of symmetry. If there is a conservation law in a system, then the Lagrange function associated to that system must be invariant to some infinitesimal, continuous transformations. Noether theorem is the fundamentals for mathematical modeling.

Keywords:
Noether theorem, symmetry, conservation laws.

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CITE THIS PAPER AS:
Neculai Andrei, "TEOREMA NOETHER ȘI FUNDAMENTELE MODELĂRII MATEMATICE", Romanian Journal of Information Technology and Automatic Control, ISSN 1220-1758, vol. 18(4), pp. 11-22, 2008.