| 1. |
- Babich, M. V., et al.
(författare)
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Quasi periodic vortex structures in two-dimensional flows in an inviscid incompressible fluid
- 2005
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Ingår i: Russian journal of mathematical physics. - New York : John Wiley & Sons. - 1061-9208 .- 1555-6638. ; 12:2, s. 121-156
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Tidskriftsartikel (refereegranskat)abstract
- We consider a two-dimensional steady motion of an inviscid incompressible fluid described by the equation &UDelta; u(x,y) = F(u(x,y)), where u(x,y) is the streamfunction, &UDelta; is the Laplace operator, and F((.)) an arbitrary function measuring the flow vorticity. Apparently, until now, the only way to treat an equation of the above type with nontrivial function F analytically is to use the algebro-geometric method for integrable equations. In particular, we investigate the Cosh-Laplace equation (ChL) &UDelta; u(x,y) = ± 4cosh(u(x,y)) by means of the special technique of finite-gap integration, which allows us to obtain real solutions of the ChL equation by using a Riemann surface with appropriate symmetry. We study the first nontrivial case corresponding to a Riemann surface of genus g = 3. The hydrodynamical interpretation of finite-gap solutions is meaningful, and we try to understand the fluid processes described by these solutions. To this end, we take a Riemann surface with additional symmetry properties. We present four five-parameter families of exact solutions. These solutions are given in terms of Jacobi elliptic functions, which enables us to directly investigate the relevant properties. We also find explicit formulas for the lines of singularity. It is of interest from the point of view of algebraic geometry that the structure of the theta divisor can be described.
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| 2. |
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| 3. |
- Kamotski, I., et al.
(författare)
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Estimate for a solution to the water wave problem in the presence of a submerged body
- 2013
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Ingår i: Russian journal of mathematical physics. - : MAIK Nauka/Interperiodica. - 1061-9208 .- 1555-6638. ; 20:4, s. 453-467
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Tidskriftsartikel (refereegranskat)abstract
- We study the two-dimensional problem of propagation of linear water waves in deep water in the presence of a submerged body. Under some geometrical requirements, we derive an explicit bound for the solution depending on the domain and the functions on the right-hand side.
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| 4. |
- Khrennikov, Andrei, 1958-, et al.
(författare)
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Measures on the Hilbert space of a quantum system
- 2017
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Ingår i: Russian journal of mathematical physics. - : Springer. - 1061-9208 .- 1555-6638. ; 24:2, s. 234-240
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Tidskriftsartikel (refereegranskat)abstract
- The paper is the first in a series of papers on the use of measures and generalized measures in quantum theory. In particular, a survey of the proofs of equivalence of various definitions of the density operator is presented. The exposition is of algebraic nature, and analytic assumptions are usually omitted.
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| 5. |
- Kozlov, Vladimir
(författare)
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Traction boundary value problem for anisotropic elasticity in polyhedral domains
- 2001
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Ingår i: Russian journal of mathematical physics. - 1061-9208 .- 1555-6638. ; 8:3, s. 275-286
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Tidskriftsartikel (refereegranskat)abstract
- The traction boundary value problem for anisotropic elasticity is considered. For polyhedral domains in R-3, it is proved that the displacements are Holder continuous. In the n-dimensional case, n > 3, the Holder continuity is proved for domains with conic points on the boundary. The proof is based on the study of spectrum of operator pencils associated with singularities of the boundary, which is of independent interest.
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| 6. |
- Oleschko, K., et al.
(författare)
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Transport through a network of capillaries from ultrametric diffusion equation with quadratic nonlinearity
- 2017
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Ingår i: Russian journal of mathematical physics. - : MAIK NAUKA/INTERPERIODICA/SPRINGER. - 1061-9208 .- 1555-6638. ; 24:4, s. 505-516
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Tidskriftsartikel (refereegranskat)abstract
- This paper is about a novel mathematical framework to model transport (of, e.g., fluid or gas) through networks of capillaries. This framework takes into account the tree structure of the networks of capillaries. (Roughly speaking, we use the tree-like system of coordinates.) As is well known, tree-geometry can be topologically described as the geometry of an ultrametric space, i.e., a metric space in which the metric satisfies the strong triangle inequality: in each triangle, the third side is less than or equal to the maximum of two other sides. Thus transport (e.g., of oil or emulsion of oil and water in porous media, or blood and air in biological organisms) through networks of capillaries can be mathematically modelled as ultrametric diffusion. Such modelling was performed in a series of recently published papers of the authors. However, the process of transport through capillaries can be only approximately described by the linear diffusion, because the concentration of, e.g., oil droplets, in a capillary can essentially modify the dynamics. Therefore nonlinear dynamical equations provide a more adequate model of transport in a network of capillaries. We consider a nonlinear ultrametric diffusion equation with quadratic nonlinearity - to model transport in such a network. Here, as in the linear case, we apply the theory of ultrametric wavelets. The paper also contains a simple introduction to theory of ultrametric spaces and analysis on them.
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| 7. |
- Khrennikov, Andrei
(författare)
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Generalized probabilities taking values in non-Archimedean fields and in topological groups.
- 2007
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Ingår i: Russian Journal of Mathematical Physics. - : MAIK Nauka Interperiodica, Moscow. - 1061-9208. ; 14:2, s. 142-159
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Tidskriftsartikel (refereegranskat)abstract
- We develop an analog of probability theory for probabilities taking values in topological groups. We generalize Kolmogorov's method of axiomatization of probability theory, and the main distinguishing features of frequency probabilities are taken as axioms in the measure-theoretic approach. We also present a survey of non-Kolmogorovian probabilistic models, including models with negative-, complex-, and p-adic-valued probabilities. The last model is discussed in detail. The introduction of probabilities with p-adic values (as well as with more general non-Archimedean values) is one of the main motivations to consider generalized probabilities with values in more general topological groups than the additive group of real numbers. We also discuss applications of non-Kolmogorovian models in physics and cognitive sciences. A part of the paper is devoted to statistical interpretation of probabilities with values in topological groups (in particular, in non-Archimedean fields).
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| 8. |
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