Showing papers in "Journal of Mathematical Sciences in 2015"
TL;DR: In this article, the boundary behavior of ring Q-homeomorphisms in terms of Caratheodory's prime ends is studied and criteria for the Dirichlet problem for the degenerate Beltrami equation are given.
Abstract: We first study the boundary behavior of ring Q-homeomorphisms in terms of Caratheodory’s prime ends and then give criteria to the solvability of the Dirichlet problem for the degenerate Beltrami equation \( \overline{\partial} \)f = μ∂f in arbitrary bounded finitely connected domains D of the complex plane ℂ.
66 citations
TL;DR: In this article, the dynamics of generalized Forchheimer equations for slightly compressible fluids are tudied by means of initial boundary value problem for the pressure, and it is shown that the solutions continuously depend on the boundary data and the forchheimer polynomials.
Abstract: The dynamics of generalized Forchheimer equations for slightly compressible fluids are tudied by means of initial boundary value problem for the pressure. We prove that the solutions continuously depend on the boundary data and the Forchheimer polynomials. New bounds for the solutions are established in the Lα-norm for all α ≥ 1, and then are used to improve estimates for their spatial and time derivatives. New Poincare–Sobolev inequalities and nonlinear Gronwall type estimates for nonlinear differential inequalities are utilized to achieve better asymptotic bounds. The methods developed can be applied to other degenerate parabolic equations. Bibliography: 25 titles.
38 citations
TL;DR: For a bounded and convex domain Ω ⊂ ℝ3, the Maxwell constants are bounded from below and above by the Friedrichs and Poincare constants of Ω, respectively as discussed by the authors.
Abstract: It is shown that for a bounded and convex domain Ω ⊂ ℝ3
, the Maxwell constants are bounded from below and above by the Friedrichs and Poincare constants of Ω, respectively. Bibliography: 14 titles.
28 citations
TL;DR: In this article, the authors develop a theory of equipped graded graphs (or Bratteli diagrams) and an alternative theory of projective limits of finite-dimensional simplices, where an equipment is an additional structure on the graph, namely, a system of cotransition probabilities on the set of its paths.
Abstract: In this paper, we develop a theory of equipped graded graphs (or Bratteli diagrams) and an alternative theory of projective limits of finite-dimensional simplices. An equipment is an additional structure on the graph, namely, a system of “cotransition” probabilities on the set of its paths. The main problem is to describe all probability measures on the path space of a graph with given cotransition probabilities; it goes back to the problem, posed by E. B. Dynkin in the 1960s, of describing exit and entrance boundaries for Markov chains. The most important example is the problem of describing all central measures, to which one can reduce the problems of describing states on AF-algebras or characters on locally finite groups. We suggest an unification of the whole theory, an interpretation of the notions of Martin, Choquet, and Dynkin boundaries in terms of equipped graded graphs and in terms of the theory of projective limits of simplices. In the last section, we study the new notion of “standardness” of projective limits of simplices and of equipped Bratteli diagrams, as well as the notion of “lacunarization.”
28 citations
TL;DR: In this article, the minimal and maximal operators generated by the Bessel differential expression on a finite interval and a half-line are studied and all nonnegative self-adjoint extensions of the minimal operator are described.
Abstract: The minimal and maximal operators generated by the Bessel differential expression on a finite interval and a half-line are studied. All nonnegative self-adjoint extensions of the minimal operator are described. We obtain a description of the domain of the Friedrichs extension of the minimal operator in the framework of extension theory of symmetric operators by applying the technique of boundary triplets and the corresponding Weyl functions, and by using the quadratic form method.
26 citations
TL;DR: In this article, an upper bound for the infinity norm of the inverse for matrices in two subclasses of H-matrices, both of which contain the class of Nekrasov matrices, was established.
Abstract: The paper considers upper bounds for the infinity norm of the inverse for matrices in two subclasses of the class of (nonsingular) H-matrices, both of which contain the class of Nekrasov matrices. The first one has been introduced recently and consists of the so-called S-Nekrasov matrices. For S-Nekrasov matrices, the known bounds are improved. The second subclass consists of the socalled QN- (quasi-Nekrasov) matrices, which are defined in the present paper. For QN-matrices, an upper bound on the infinity norm of the inverses is established. It is shown that in application to Nekrasov matrices the new bounds are generally better than the known ones. Bibliography: 15 titles.
25 citations
TL;DR: In this article, a survey of integrable cases in dynamics of two-, three-, and four-dimensional rigid bodies under the action of a non-conservative force field is presented.
Abstract: This paper is a survey of integrable cases in dynamics of two-, three-, and four-dimensional rigid bodies under the action of a nonconservative force field. We review both new results and results obtained earlier. Problems examined are described by dynamical systems with so-called variable dissipation with zero mean.
24 citations
TL;DR: In this article, the authors continue the analysis of strongly elliptic modifications of the total variation image inpainting model formulated in the space BV(Ω) and investigate the corresponding dual variational problems.
Abstract: We continue the analysis of some strongly elliptic modifications of the total variation image inpainting model formulated in the space BV(Ω) and investigate the corresponding dual variational problems. Remarkable features are the uniqueness of the dual solution and the uniqueness of the absolutely continuous part ∇
a
u of the gradient of BV-solutions u on the whole domain. Additionally, any BV-minimizer u automatically satisfies the inequality 0 ≤ u ≤ 1, which means that u measures the intensity of the grey level. Outside of the damaged region we even have the uniqueness of BV-solutions, whereas on the damaged domain the L
2-deviation $$ {\left\Vert u-\upsilon \right\Vert}_{L^2} $$
of different solutions is governed by the total variation of the singular part ∇
s
(u − υ) of the vector measure ∇(u − υ). Moreover, the dual solution is related to the BV-solutions through an equation of stress-strain type. Bibliography: 23 titles.
23 citations
TL;DR: In this article, the conditions of solvability and the structure of the generalized Green operator of a linear Noetherian matrix differential-algebraic boundary-value problem are found.
Abstract: The conditions of solvability and the structure of the generalized Green operator of a linear Noetherian matrix differential-algebraic boundary-value problem are found. The sufficient conditions for reducibility of the generalized matrix differential-algebraic equation to the traditional differential-algebraic equation with the unknown function in the form of a vector-column are obtained. In the solution of a generalized matrix differential-algebraic boundary-value problem, the original conditions of solvability and the structure of the general solution of a matrix Sylvester-type equation are used.
23 citations
TL;DR: In this article, the authors studied the class of orientation-preserving Morse-Smale diffeomfication on a connected closed smooth manifold of dimension n ≥ 4, and established the topoligical type of the supporting manifold which was determined by the relation between the numbers of saddle and node periodic orbits.
Abstract: We study the class G(M
n
) of orientation-preserving Morse–Smale diffeomorfisms on a connected closed smooth manifold M
n
of dimension n ≥ 4 which is defined by the following condition: for any f ∊ G(M
n
) the invariant manifolds of saddle periodic points have dimension 1 and (n − 1) and contain no heteroclinic intersections. For diffeomorfisms in G(M
n
) we establish the topoligical type of the supporting manifold which is determined by the relation between the numbers of saddle and node periodic orbits and obtain necessary and sufficient conditions for topological conjugacy. Bibliography: 14 titles.
23 citations
TL;DR: In this paper, integral and supremum type tests of exponentiality based on Ahsanullah's characterization of the exponential law are constructed and conditions of local optimality of new statistics are given.
Abstract: We construct integral and supremum type tests of exponentiality based on Ahsanullah’s characterization of the exponential law. We discuss limiting distributions and large deviations of new test statistics under the null-hypothesis and calculate their local Bahadur efficiency under common parametric alternatives. Conditions of local optimality of the new statistics are given. Bibliography: 33 titles.
TL;DR: In this article, the authors continue the analysis of modifications of the total variation image inpainting method formulated on the space BV (Ω) and treat the case of vector-valued images where they do not impose any structure condition on the density F and the dimension of the domain Ω is arbitrary.
Abstract: We continue the analysis of modifications of the total variation image inpainting method formulated on the space BV (Ω)
M
and treat the case of vector-valued images where we do not impose any structure condition on the density F and the dimension of the domain Ω is arbitrary. We discuss the existence of generalized solutions of the corresponding variational problem and show the unique solvability of the associated dual variational problem. We establish the uniqueness of the absolutely continuous part ∇
a
u of the gradient of BV -solutions u on the domain Ω and get the uniqueness of BV -solutions outside the damaged region D. We also prove new density results for functions of bounded variation and for Sobolev functions. Bibliography: 36 titles.
TL;DR: In this article, the authors investigate parameter-dependent general inhomogeneous boundary value problems for systems of linear differential equations, of order n ∈ N, given on a finite interval.
Abstract: We investigate parameter-dependent general inhomogeneous boundary-value problems for systems of linear differential equations, of order n ∈ N, given on a finite interval. We find sufficient conditions under which the solutions to the problems together with their derivatives up to order n − 1 are continuous in the uniform norm with respect to the parameter. We also present sufficient conditions under which the Green matrices corresponding to these problems converge uniformly in the parameter.
TL;DR: In this paper, sufficient conditions for the existence and global asymptotic stability of unique equilibrium point of a Cohen-Grossberg neural network of neutral type were obtained, and an example is presented.
Abstract: Sufficient conditions for the existence and global asymptotic stability of unique equilibrium point of a Cohen–Grossberg neural network of neutral type are obtained. An example is presented.
TL;DR: An integral representation for the generalized hypergeometric function unifying known representations via generalized Stieltjes, Laplace, and cosine Fourier transforms is found in this article using positivity conditions for the weight in this representation.
Abstract: An integral representation for the generalized hypergeometric function unifying known representations via generalized Stieltjes, Laplace, and cosine Fourier transforms is found. Using positivity conditions for the weight in this representation, various new facts regarding generalized hypergeometric functions, including complete monotonicity, log-convexity in upper parameters, monotonicity of ratios, and new proofs of Luke’s bounds are established. In addition, two-sided inequalities for the Bessel type hypergeometric functions are derived with the use of their series representations. Bibliography: 22 titles.
TL;DR: In this paper, the theory of almost geodesic mappings of spaces with affine connection was further developed and the authors devoted to the further development of the theory was devoted to their work.
Abstract: This paper is devoted to the further development of the theory of almost geodesic mappings of spaces with affine connection.
TL;DR: Growth and distortion theorems for the functions indicated in the title are proved by the symmetrization method as discussed by the authors, and Sharp estimates for the moduli of the functions considered and their derivatives at inner and boundary points are established, and an estimate for the Schwarzian derivative is obtained.
Abstract: Growth and distortion theorems for the functions indicated in the title are proved by the symmetrization method. Sharp estimates for the moduli of the functions considered and their derivatives at inner and boundary points are established, and an estimate for the Schwarzian derivative is obtained. Bibliography: 14 titles
TL;DR: In this article, the uniqueness of solutions to the Cauchy problem for the Fokker-Planck-Kolmogorov equation with a singular diffusion matrix in the class of probability measures is studied.
Abstract: We study the uniqueness of solutions to the Cauchy problem for the Fokker–Planck–Kolmogorov equation with a singular diffusion matrix in the class of probability measures. A survey of known result and methods is given. In addition, we obtain new sufficient conditions for the uniqueness in the case of unbounded coefficients and a partially singular diffusion matrix and also in the case where the diffusion matrix is a squared Lipschitzian matrix.
TL;DR: A survey of the results on the structure of Chevalley groups over a ring R can be found in this paper, where the authors generalize and improve previously known results on: (1) the relative local-global principle; (2) generators of a relative elementary group; (3) relative multicommutator formulas; (4) the nilpotent structure of relative K1; (5) the bounded length of commutators.
Abstract: UDC 512.5 The article contains a survey of the recent author’s results on the structure of a Chevalley group G(R) over a ring R. They generalize and improve previously known results on: (1) the relative local-global principle; (2) generators of a relative elementary group; (3) relative multicommutator formulas; (4) the nilpotent structure of a relative K1; (5) the bounded length of commutators. The proof of the first two items is based on computations with generators of the elementary group translated into the language of parabolic subgroups. The other results are proved by means of enlarging a relative elementary group, constructing a generic element, and using the localization procedure in the universal ring. Bibliography: 40 titles.
TL;DR: For the non-degenerate Beltrami equations in the quasidisks and in particular in smooth Jordan domains, the authors proved the existence of regular solutions of the Riemann-Hilbert problem with coefficients of bounded variation and boundary data that are measurable with respect to the absolute harmonic measure (logarithmic capacity).
Abstract: For the nondegenerate Beltrami equations in the quasidisks and, in particular, in smooth Jordan domains, we prove the existence of regular solutions of the Riemann–Hilbert problem with coefficients of bounded variation and boundary data that are measurable with respect to the absolute harmonic measure (logarithmic capacity).
TL;DR: In this paper, the authors present equivalent variational formulations of the problem of unilateral contact of elastic bodies with nonlinear Winkler surface layers in the form of a nonquadratic variational inequality and a nonlinear variational equation.
Abstract: We present equivalent variational formulations of the problem of unilateral contact of elastic bodies with nonlinear Winkler surface layers in the form of a nonquadratic variational inequality and a nonlinear variational equation. The existence and uniqueness of solutions of these variational problems are studied. To solve the nonlinear variational equation corresponding to the original contact problem, we propose a class of parallel iterative domain decomposition methods. In each step of these methods, it is necessary to simultaneously solve the linear variational equations for separate bodies equivalent (in a weak sense) to the problems of elasticity with the Robin boundary conditions in possible contact zones. The numerical investigation of the efficiency of proposed methods is carried out with the use of finite-element approximations.
TL;DR: In this paper, the authors studied the behavior of concentration functions of weighted sums with respect to the arithmetic structure of coefficients and proved some refinements of a result of Vershynin.
Abstract: Let X,X1, . . . , Xn be independent, identically distributed random variables. In this paper, we study the behavior of concentration functions of the weighted sums $$ {\displaystyle \sum_{k=1}^n{a}_k{X}_k} $$
with respect to the arithmetic structure of coefficients ak. Such concentration results recently became important in connection with the study of singular values of random matrices. In this paper, we formulate and prove some refinements of a result of Vershynin (2014).
TL;DR: The notion of graph generated by the mutual orthogonality relation for the elements of an associative ring is introduced in this paper, where the main attention is paid to the commutative rings and to the matrix ring over a field and its various sub-rings and subsets.
Abstract: The notion of graph generated by the mutual orthogonality relation for the elements of an associative ring is introduced. The main attention is paid to the commutative rings and to the matrix ring over a field and its various subrings and subsets. In particular, the diameters of the orthogonality graphs of the full matrix algebra over an arbitrary field and its subsets consisting of diagonal, diagonalizable, triangularizable, and nilpotent matrices are computed. Bibliography: 36 titles.
TL;DR: A characterization of inherently non-finitely generated subvarieties of, based on identities that they cannot satisfy and monoids that they must contain, is given in this paper, which is decidable in polynomial time.
Abstract: Let denote the class of aperiodic monoids with central idempotents. A subvariety of that is not contained in any finitely generated subvariety of is said to be inherently non-finitely generated. A characterization of inherently non-finitely generated subvarieties of , based on identities that they cannot satisfy and monoids that they must contain, is given. It turns out that there exists a unique minimal inherently non-finitely generated subvariety of , the inclusion of which is both necessary and sufficient for a subvariety of to be inherently non-finitely generated. Further, it is decidable in polynomial time if a finite set of identities defines an inherently nonfinitely generated subvariety of .
TL;DR: Uraltseva et al. as mentioned in this paper considered the Cauchy problem for the one-dimensional Carleman equation with bounded energy and periodic initial data and obtained the local equilibrium conditions.
Abstract: UDC 517.9 We consider the Cauchy problem for the one-dimensional Carleman equation with bounded energy and periodic initial data and obtain the local equilibrium conditions. We prove exponential stabilization to the equilibrium state. Bibliography :1 0titles. Illustrations :3 figures. Dedicated to N. N. Uraltseva
TL;DR: In this article, a Liouville type theorem for mild bounded ancient solutions to the Navier-Stokes system in a half plane is proved, provided that a certain scale invariant quantity is bounded.
Abstract: A Liouville type theorem for mild bounded ancient solutions to the Navier-Stokes system in a half plane is proved, provided that a certain scale invariant quantity is bounded.
TL;DR: In this paper, the problem of geometric equivalence in the class of Boolean algebras with distinguished elements has been studied, and criteria for which a Boolean algebra is equationally Noetherian, weakly equationally noetherian or uω-compact.
Abstract: We study equations over Boolean algebras with distinguished elements. We prove criteria for which a Boolean algebra is equationally Noetherian, weakly equationally Noetherian, qω-compact, or uω-compact. Also we solve the problem of geometric equivalence in the class of Boolean algebras with distinguished elements.
TL;DR: In this article, the existence, uniqueness, and continuous dependence of solutions to a general class of thick fluids with variable threshold on the absolute value of the deformation rate tensor, the solutions of which belong to a time dependent convex set is established.
Abstract: In chemical engineering models, shear-thickening or dilatant fluids converge in the limit case to a class of incompressible fluids with a maximum admissible shear rate, the so-called thick fluids. These non-Newtonian fluids can be obtained, in particular, as the power limit of the Ostwald–de Waele fluids, and can be described as a new class of evolution variational inequalities, in which the shear rate is bounded by a positive constant or, more generally, by a bounded positive function. It is established the existence, uniqueness, and the continuous dependence of solutions to this general class of thick fluids with variable threshold on the absolute value of the deformation rate tensor, the solutions of which belong to a time dependent convex set. For sufficiently large viscosity, the asymptotic stabilization toward a unique steady state is also proved.
TL;DR: A scaling entropy sequence of an automorphism is an entropy-type metric invariant suggested by A. M. Vershik as discussed by the authors, which does not depend on the choice of a semimetric.
Abstract: A scaling entropy sequence of an automorphism is an entropy-type metric invariant suggested by A. M. Vershik. We confirm his conjecture that it does not depend on the choice of a semimetric. This means that it is indeed a metric invariant. We also calculate this invariant for several classical dynamical systems.
TL;DR: In this article, a vector tomography problem of reconstructing potential components of a three-dimensional vector field from its normal Radon transform was studied and the method of singular value decomposition was used.
Abstract: We study a vector tomography problem of reconstructing potential components of a three-dimensional vector field from its normal Radon transform. The method of singular value decomposition is used. For the subspace of potential fields with potentials vanishing on the boundary, we construct an orthogonal basis and compute its image under the normal Radon transform.