Výsledky vyhledávání - "D. V. Tunitskii"

On one extremal problem of adaptive machine learning for detection of anomalies

Publikováno v: Automation and Remote Control. 69:942-952

An adaptive algorithm to solve a wide range of problems of unsupervised learning by constructing a sequence of interrelated extremal principles was proposed. The least squares method with a priori defined weights used as a starting point enabled dete

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_________::75ae7e9a7f3ced43e1796da518f2956b
https://doi.org/10.1134/s0005117908060052

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Hyperbolic Monge-Ampère systems

Autor: D V Tunitskii

Publikováno v: Sbornik: Mathematics. 197:1223-1258

The subject of the paper is the solubility of the Cauchy problem for strictly hyperbolic systems of Monge-Ampere equations and, in particu- lar, for quasilinear systems of equations with two independent variables. It is proved that this problem has a

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_________::d4dc6c5e2fd3189ae53efd09139bbbac
https://doi.org/10.1070/sm2006v197n08abeh003796

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Monge-Ampére equations and characteristic connection functors

Autor: D V Tunitskii

Publikováno v: Izvestiya: Mathematics. 65:1243-1290

We investigate contact equivalence of Monge-Ampere equations. We define a category of Monge-Ampere equations and introduce the notion of a characteristic connection functor. This functor maps the category of Monge-Ampere equations to the category of

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_________::5d83d03d571e337f0527c2e37875be7a
https://doi.org/10.1070/im2001v065n06abeh000368

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On the global solubility of the Monge-Ampere hyperbolic equations

Autor: D V Tunitskii

Publikováno v: Izvestiya: Mathematics. 61:1069-1111

This paper is devoted to the solubility of the Cauchy problem for the Monge-Ampere hyperbolic equations, in particular, for quasi-linear equations with two independent variables. It is proved that this problem has a unique maximal solution in the cla

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_________::d168614ee89244032309ac9e0339aab0
https://doi.org/10.1070/im1997v061n05abeh000163

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Equivalence and characteristic connections of the Monge-Ampere equations

Autor: D V Tunitskii

Publikováno v: Sbornik: Mathematics. 188:771-797

The present paper is devoted to the problem of contact equivalence of the Monge-Ampere equations with two independent variables. When the Monge-Ampere equation is in general position an affine connection can be associated with it in a natural manner.

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_________::2dfa478a55aa111b6544e25cdab85558
https://doi.org/10.1070/sm1997v188n05abeh000235

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On the contact linearization of Monge-Ampere equations

Autor: D V Tunitskii

Publikováno v: Izvestiya: Mathematics. 60:425-451

This paper is devoted to the solution of a number of problems related to the contact classification of Monge-Ampere equations with two independent variables. In the 1870s Sophus Lie formulated the problem of finding whether a local reduction of a giv

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_________::d396ed4600f12289f40ce7896397c32c
https://doi.org/10.1070/im1996v060n02abeh000076

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