Here we address two optimization problems: the search for Nash equilibria in polymatrix games and the quadratic-linear bilevel programming problem. It can be shown that each of the problems possesses a hidden nonconve...
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(纸本)9789616165457
Here we address two optimization problems: the search for Nash equilibria in polymatrix games and the quadratic-linear bilevel programming problem. It can be shown that each of the problems possesses a hidden nonconvexity and, as a consequence, a rather large number of local solutions which are different from global ones. Further, the principal elements of Global Search theory are sketched. Finally, we present the results of computational solutions.
In the article we develop an approach to the study of nonlinear problems of mathematical physics, proposed in A. F. Sidorov’s school of thought, and apply it to solving boundary value problems with degeneracy for the...
In the article we develop an approach to the study of nonlinear problems of mathematical physics, proposed in A. F. Sidorov’s school of thought, and apply it to solving boundary value problems with degeneracy for the nonlinear heat (porous medium) equation. The essence of the approach is that the solution of problems is constructed in the form of multiple power series. The convergence of the constructed series is proved by the majorant method. It allows us to propose the existence and uniqueness theorem, which is analogous to the Cauchy-Kovalevskaya theorem for the considered problem. A constructive scheme for finding the coefficients of the series is proposed. A special feature of the study is that the boundary condition is given on a moving closed manifold.
A degenerate nonlinear parabolic-type equation with a specified source function is solved. Boundary value problems for various kinds of boundary conditions are considered. Solution algorithms based on the boundary ele...
A degenerate nonlinear parabolic-type equation with a specified source function is solved. Boundary value problems for various kinds of boundary conditions are considered. Solution algorithms based on the boundary element method are constructed. Some examples are discussed. The comparison of the obtained BEM solutions with known exact solutions gives good results.
A nonlinear second-order parabolic equation with two variables is considered. Under additional conditions, this equation can be interpreted as the porous medium equation in case of dependence of the unknown function o...
A nonlinear second-order parabolic equation with two variables is considered. Under additional conditions, this equation can be interpreted as the porous medium equation in case of dependence of the unknown function on two variables: time and distance from the origin. The equation has a wide variety of applications in continuum mechanics, for example, it is applicable for mathematical modeling of filtration of ideal polytropic gas in porous media or heat conduction. The authors deal with a special solutions which are usually called heat waves. A special feature of such solution is that it consists of two continuously joined solutions. The first of them is trivial and the second one is nonnegative. The heat wave solution can have discontinuous derivatives on the line of joint which is called the front of heat wave, i.e. smoothness of the solution, generally speaking, is broken. The most natural problem which has such solutions is the so-called 'the Sakharov problem of the initiation of a heat wave'. New solutions of the problem in the form of multiple power series for physical variables are constructed. The coefficients of the series are obtained from tridiagonal systems of linear algebraic equations. Herewith, the elements of matrices of this systems depend on the matrix order and the condition of the diagonal dominance is not fulfilled. The recurrent formulas for the coefficients are suggested.
In this paper we present the Transalg system, designed to produce SAT encodings for discrete functions, written as programs in a specific language. Translation of such programs to SAT is based on propositional encodin...
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In this paper we present the Transalg system, designed to produce SAT encodings for discrete functions, written as programs in a specific language. Translation of such programs to SAT is based on propositional encoding methods for formal computing models and on the concept of symbolic execution. We used the Transalg system to make SAT encodings for a number of cryptographic functions.
In this paper we consider the approach to solving the problem of search for systems of diagonal orthogonal Latin squares in the form of the Boolean Satisfiability problem. We describe two different propositional encod...
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In this paper we consider the approach to solving the problem of search for systems of diagonal orthogonal Latin squares in the form of the Boolean Satisfiability problem. We describe two different propositional encodings that we use. The first encoding is constructed for finding pairs of orthogonal diagonal Latin squares of order 10. Using this encoding we managed to find 17 previously unknown pairs of such squares using the volunteer computing project SAT@home. The second encoding is constructed for finding pseudotriples of orthogonal diagonal Latin squares of order 10. Using the pairs found with the help of SAT@home and the second encoding we successfully constructed several new pseudotriples of diagonal Latin squares of order 10.
In this paper, a cryptanalysis of the Bivium keystream generator in the SAT form is considered. For encoding the initial cryptanalysis problem into SAT a special program system Transalg was used. For an obtained SAT i...
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In this paper, a cryptanalysis of the Bivium keystream generator in the SAT form is considered. For encoding the initial cryptanalysis problem into SAT a special program system Transalg was used. For an obtained SAT instance we use Monte Carlo method to search for a partitioning with good time estimation. Several weakened cryptanalysis instances of the Bivium generator were successfully solved in the volunteer computing project SAT@home using corresponding partitionings found on a computing cluster.
In the framework of the quasipotential method in quantum electrodynamics we calculate the contribution of light pseudoscalar (PS) and axial-vector (AV) mesons to the interaction operator of a muon and a proton in muon...
In the framework of the quasipotential method in quantum electrodynamics we calculate the contribution of light pseudoscalar (PS) and axial-vector (AV) mesons to the interaction operator of a muon and a proton in muonic hydrogen atom. The coupling of mesons with the muon is via two-photon intermediate state. The parametrization of the transition form factor of two photons into PS and AV mesons, based on the experimental data on the transition form factors and QCD asymptotics, is used. Numerical estimates of the contributions to the hyperfine structure of the spectrum of the S and P levels are presented. It is shown that such contribution to the hyperfine splitting in muonic hydrogen is rather important for a comparison with precise experimental data.
Under consideration is some model of magnetic insulation of a vacuum diode. It is represented by a system of two nonlinear ordinary differential equations of the second order. The integrability of the system under stu...
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In this paper, we develop a global search method for finding a Nash equilibrium in a hexamatrix game (polymatrix game of three players). The method, on the one hand, is based on the equivalence theorem of the problem ...
In this paper, we develop a global search method for finding a Nash equilibrium in a hexamatrix game (polymatrix game of three players). The method, on the one hand, is based on the equivalence theorem of the problem of finding a Nash equilibrium in the game and a special mathematical optimization problem, and, on the other hand, on the usage of Global Search theory for solving the latter problem. The efficiency of this approach is demonstrated by the results of computational testing.
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