OLEG GRABAR (1923–2011)

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REGULAR ARTI CLE Oleg

The paper describes the quantized Hamilton dynamics (QHD) approach that extends classical Hamiltonian dynamics and captures quantum effects, such as zero point energy, tunneling, decoherence, branching, and statespecific dynamics. The approximations are made by closures of the hierarchy of Heisenberg equations for quantum observables with the higher order observables decomposed into products of...

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Research Statement Oleg N. Smirnov

1.1 Graded associative algebras. A nite Z-grading of an algebra A is a decomposition A = L n i=?n A i such that A i A j A i+j , where A i = 0 for jij > n. From now on a grading means a nite Z-grading. I am interested in associative graded algebras because they arise naturally in study of Lie algebras, although the subject is certainly interesting in its own right. A classiication of gradings of...

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Stochastic aggregation of point particles revisited . Oleg

In the present letter we employ the method of the dynamical renormalisation group to compute the average mass distribution of aggregating point particles in 2 dimensions in the regime when the effects of local mass distribution fluctuations are essential. PACS numbers: 05.10.Cc, 82.20.Mj.

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List of Results Oleg N. Smirnov

This list is a short overview of some of my results. One can nd a more detailed description in my Research Statement or at 1. Simple associative algebras with nite Z-grading. Here, R is a simple algebra with a nite Z-grading over a commutative ring. A description of all such algebras was given 18]. As a corollary, it was proved that every (not necessarily nite dimensional) simple Lie algebra of...

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Linear determining equations , differential constraints and invariant solutions . Oleg

A construction of differential constraints compatible with partial differential equations is considered. Certain linear determining equations with parameters are used to find such differential constraints. They generalize the classical determining equations used in the search for admissible Lie operators. As applications of this approach non-linear heat equations and Gibbons-Tsarev's equation a...

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ژورنال

عنوان ژورنال: International Journal of Middle East Studies

سال: 2011

ISSN: 0020-7438,1471-6380

DOI: 10.1017/s0020743811001140