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In this paper, we discuss properties of the singular value decomposition (SVD-decomposition) within the framework of the analysis of the numerical rank in ill-posed problems for determining frequency properties of discrete sequences consisting of trigonometric binomials. The properties of the numerical rank of the SVD-decomposition are indicated. We propose an algorithm for determining the frequencies of trigonometric binomials involved in the original function that forms a discrete sequence; this algorithm is based on estimates of the numerical rank. We obtain a stable criterion for estimating the numerical rank based on the arithmetic-mean estimators of the pseudo-null-space of the trajectory matrix. Also, we present the results of numerical experiments that demonstrate the consistency of the arithmetic-mean estimator of the pseudo-zero-space for the analysis of the spectrum of noisy sequences. [ABSTRACT FROM AUTHOR]

In the paper, we consider a nonlinear integrodifferential equation of the third order with delay. We establish sufficient conditions guaranteeing the global existence and boundedness of the solutions of the analyzed equation. We use the Lyapunov second method to prove the main result. An example is also given to illustrate the applicability of our result. The result of this paper is new and improves previously known results. [ABSTRACT FROM AUTHOR]

In a joint work with S. Bianchini [8] (see also [6, 7]), we proved a quadratic interaction estimate for the system of conservation lawsut+fux=0,ut=0=u0x,where u : [0, ∞) × ℝ → ℝn, f : ℝn → ℝn is strictly hyperbolic, and Tot.Var.(u0) ≪ 1. For a wavefront solution in which only two wavefronts at a time interact, such an estimate can be written in the form∑tjinteraction timeσαj−σαj′αjαj′αj+αj′≤CfTot.Var.u02,where αj and αj′ are the wavefronts interacting at the interaction time tj, σ(·) is the speed, |·| denotes the strength, and C(f) is a constant depending only on f (see [8, Theorem 1.1] or Theorem 3.1 in the present paper for a more general form).The aim of this paper is to provide the reader with a proof for such a quadratic estimate in a simplified setting, in which:• all the main ideas of the construction are presented;• all the technicalities of the proof in the general setting [8] are avoided. [ABSTRACT FROM AUTHOR]

In this paper, we examine the problem on the spatial free deceleration of a rigid body in a resistive medium under the assumption that the interaction of the homogeneous axisymmetric body with the medium is concentrated on the frontal part of the surface, which has the shape of a flat circular disk. In earlier works of the author, under the simplest assumptions on interaction forces, the impossibility of oscillations with bounded amplitude was proved. Note that an exact analytic description of forces and moments of the body-medium interaction is unknown, so we use the method of "embedding" of the problem into a wider class of problems; this allows one to obtain a sufficiently complete qualitative description of the motion of the body. For dynamical systems considered, we obtain particular solutions and families of phase portraits of quasi-velocities in the three-dimensional space that consist of countable sets of nonequivalent portraits with different nonlinear qualitative properties. [ABSTRACT FROM AUTHOR]

The paper is a continuation of previous papers of the authors dealing with the exploration of shortwave diffraction by smooth and strictly convex bodies of revolution (the axisymmetric case). In these problems, the boundary layer method contains two large parameters: one is the Fock parameter M and the second is Λ that characterizes the oblongness of the scatterer. This naturally gives the possibility of using the two-scaled asymptotic expansion, where both M and Λ are regarded as independent. The approximate formulas for the wave field in this situation depend on the mutual strength between the large parameters and may vary. In the paper, we carry out numerical experiments with our formulas, in the case where the Fock analytical solution is in good coincidence with the exact solution of a model problem, in order to examine the influence of the parameter Λ on the wave field. It follows from our numerical experiments that the influence of the oblongness of the scatterer on the wave field is really insignificant if the method of Leontovich-Fock parabolic equation does not meet mathematical difficulties. [ABSTRACT FROM AUTHOR]

The aim of the investigation is a closed retrial queueing system with a finite source. The server can be reached from the source (primary request) or from the orbit (secondary request). If an incoming (primary or secondary) job finds the server busy, two modes are distinguished: the job is transferred to the orbit (no collision) or the job under service is interrupted and both of them are transferred to the orbit (collision). Requests in the orbit can retry reaching the server after a random waiting time. The nonreliable case when the server is subject to breakdown is also investigated. In case of breakdown, when the server is under repair, also two cases can be investigated. For the first, primary calls from the source can reach the system, and they will be sent to the orbit. For the second, the source is blocked, so primary customers are not able to step into the system. This paper focuses on the unreliable system with collision and blocking of parameters. These types of systems can be solved by numerical, asymptotical, and simulation methods. Our goal is to provide a new approach to the algorithmic solution for calculating the steady-state probabilities of the system. Using these quantities the main performance characteristics (utilization of the server, response time, etc.) can be calculated. Examples illustrate the effect of different parameters on the distribution of requests in the system. [ABSTRACT FROM AUTHOR]

In this paper a closed retrial queueing system is considered with a finite number of customers. If an arriving (primary or secondary) request finds the server busy, two modes are possible: the job is transferred to the orbit (no conflict) or the job under service is interrupted and both of them are transferred to the orbit (conflict). Jobs in the orbit can retry reaching the server after a random time. The unreliable case where the server is subject to breakdown is also investigated. These types of systems can be solved by numerical, asymptotical, and simulation methods. The novelty of the investigations is that it provides a new approach to an algorithmic solution for calculating the steady-state probabilities of the system. With the help of these probabilities the main performance measures can be computed. Several sample examples illustrate the effect of different parameters on the distribution on requests in the system. [ABSTRACT FROM AUTHOR]

The aim of the paper is to present an orthogonal basis for the discrete wavelets in the general structure of the spline-wavelet decomposition. Decomposition of an original numerical flow without embedding in the standard functional spaces is discussed. It makes it possible to concentrate on simplification of the realization formulas: here, the simple formulas of decomposition and reconstruction are presented, an orthogonal wavelet basis is constructed, and an illustrative example is given. Finally, some estimates of the complexity of the method discussed for different software environments are provided. Bibliography: 6 titles. [ABSTRACT FROM AUTHOR]

The paper describes the congruent centralizer of the matrix $$ {\Delta}_n=\left(\begin{array}{llll}\hfill & \hfill & \hfill & 1\hfill \\ {}\hfill & \hfill & \dots \hfill & i\hfill \\ {}\hfill & 1\hfill & \dots \hfill & \hfill \\ {}1\hfill & i\hfill & \hfill & \hfill \end{array}\right) $$ , representing one of three blocks in the Horn-Sergeichuk canonical form, i.e., the set of matrices X such that X Δ X = Δ. [ABSTRACT FROM AUTHOR]

Control problems in dynamic systems allowing pulse forces due to the presence of unilateral active constraints are considered. This paper gives an analysis of controls used during impact interactions. A new kind of pulse controls arising at the time of impact is introduced. These problems are typical for the so-called vibroimpact systems with numerous applications, whose number is constantly increasing in recent years. The goal of the paper is to describe the phase of a controllable impact and to determine the constraint reactions. [ABSTRACT FROM AUTHOR]

This paper is devoted to the study of Abelian afi-groups. A subgroup A of an Abelian group G is called its absolute ideal if A is an ideal of any ring on G. We will call an Abelian group an afi-group if all of its absolute ideals are fully invariant subgroups. In this paper, we will describe afi-groups in the class of fully transitive torsion groups (in particular, separable torsion groups) and divisible torsion groups. [ABSTRACT FROM AUTHOR]

This paper studies a nonparametric kernel estimator of a mean residual life function. We find asymptotic decompositions for the mean, variance, and mean square deviation of the estimator. [ABSTRACT FROM AUTHOR]

In this paper, we present a general procedure for solving of homogeneous equations that describe penetration and diffusion of X-rays in plane geometry. Starting from Van Kampen's and Case's observation that it suffices that 'solutions' be distributions, elementary solutions of a homogeneous equation are found. We also prove that general solutions can be obtained by superposition of elementary solutions. [ABSTRACT FROM AUTHOR]

In this paper, we propose robust numerical methods for finding the maximum likelihood estimation of the generalized inverse Gaussian distribution. A comparative analysis of the existing algorithms and the results of numerical experiments are presented. Special attention is paid to reproducibility of the tests. [ABSTRACT FROM AUTHOR]

The classes of right and left γ-generating matrices were introduced by D. Z. Arov in the 1980s. These matrices play an important role in the description of solutions of the indeterminate Nehari problem. In the present paper, the classes of the so-called generalized right and left γ-generating matrices, being resolvent matrices of the Nehari-Takagi problem, are introduced. For matrices of these classes, some factorization theorems are proved, and the connection between the class of generalized γ-generating matrices and the class of generalized j -inner matrix valued functions is found. Subclasses of singular, regular, and strongly regular generalized -generating matrices are introduced and studied. [ABSTRACT FROM AUTHOR]

The paper deals with the inverse problem of reconstructing a Riemannian manifold from its boundary data. This problem has been solved by the boundary control method, and at the moment there are several variants of solving it. In the paper, one more version of the procedure, which recovers the manifold from scalar spectral or dynamical data, is proposed. This version is the simplest one in regard to the devices in use: geometrical optics, polar representation of operators, etc. are not employed and only a controllability property of a relevant dynamical system is applied. Without substantial changes, this version is applicable to a more complicated (vector) problem of electrodynamics for the Maxwell system. The simplicity of the procedure proposed provides additional chances for its numerical realizability. At the end of the paper, a plan of numerical experiment is discussed. To draw attention to such new options is one of the main aims of the paper. Bibliography: 9 titles. [ABSTRACT FROM AUTHOR]

The paper is devoted to Koosis' approach to the Carleson theorem. We show that this approach also works for other related questions. The main emphasis in this paper is on the method. Bibliography: 10 titles. [ABSTRACT FROM AUTHOR]

In this paper, we describe the range of the Lp-norm of a function under fixed Lp-norms with two other different exponents p and under a natural multiplicative restriction of the type of the Muckenhoupt condition. Particular cases of such results are simple inequalities as the interpolation inequality between two Lp-norms as well as such nontrivial inequalities as the Gehring inequality or the reverse Hölder inequality for Mackenhoupt weights. The basic method of our paper is the search for the exact Bellman function of the corresponding extremal problem. Bibliography: 5 [ABSTRACT FROM AUTHOR]

The paper is devoted to two new directions in developing the classical geometric subjects related to studying the problem of unique determination of closed convex surfaces by their intrinsic metrics. The first of these directions is the study of unique determination of domains (i.e., open connected sets) in Euclidean spaces by relative metrics of the boundaries of these domains. It appeared about 25–30 years ago and was developed owing to the efforts of Russian scientists. The first part of the paper (Secs. 3–7) contains an overview of the results referring to this direction. The foundations of the second direction are presented in the second part of the paper, i.e., in Sec. 8, for the first time. This direction is closely related with the first one and consists of studying the problem of unique determination of conformal type. The main result of the section is the theorem on the unique determination of bounded convex domains by relative conformal moduli of their boundary conductors. [ABSTRACT FROM AUTHOR]

We introduce interpolation analogs of the Schur Q-functions — the multiparameter Schur Q-functions. We obtain for them several results: a combinatorial formula, generating functions for one-row and two-row functions, vanishing and characterization properties, a Pieri-type formula, a Nimmo-type formula (a quotient of two Pfaffians), a Giambelli-Schur-type Pfaffian formula, a determinantal formula for the transition coefficients between multiparameter Schur Q-functions with different parameters. We write an explicit Pfaffian expression for the dimension of a skew shifted Young diagram. This paper is a continuation of the author's paper math. CO/0303169 and a partial projective analog of the paper q-alg/9605042 by A. Okounkov and G. Olshanski and the paper math. CO/0110077 by G. Olshanski, A. Regev, and A. Vershik. Bibliography: 36 titles. [ABSTRACT FROM AUTHOR]

In this paper, we study continuous approximations to the Clarke subdifferential and the Demyanov­Rubinov quasidifferential. Different methods have been proposed and discussed for the construction of the continuous approximations. Numerical methods for minimization of the locally Lipschitzian functions which are based on the continuous approximations are described and their convergence is studied. To test the proposed methods, numerical experiments have been carried out and discussed in the paper. [ABSTRACT FROM AUTHOR]

In this paper, we prove that any dynamical system has a unique maximal factor of zero Rokhlin entropy, the so-called Pinsker factor. It is also proven that if the system is ergodic and this factor has no atoms, then the system is a relatively weakly mixing extension of its Pinsker factor. [ABSTRACT FROM AUTHOR]

The paper is devoted to the general problem of obtaining interpolation theorems for operators that are bounded on cones in normed spaces and to some specific results pertaining to the particular problem of interpolation of operators that are bounded on cones in weighted spaces of numerical sequences. This setting is a natural generalization of the classical problem of interpolation of the boundedness property for a linear operator that is bounded between two Banach couples. We introduce the general concept of a Banach triple of cones possessing the interpolation property with respect to a given Banach triple. We provide sufficient conditions under which a triple of cones (Q,Q,Q) in weighted spaces of numerical sequences possesses the interpolation property with respect to a given Banach triple of weighted spaces of numerical sequences (F, F, F). Appropriate interpolation theorems generalize the classical result about interpolation of linear operators in weighted spaces and are of interest for the theory of bases in Fréchet spaces. Bibliography: 10 titles. [ABSTRACT FROM AUTHOR]

In this paper, we discuss optimal control problems whose behavior is described by elliptic equations with Bitsadze-Samarski nonlocal boundary conditions. A necessary and sufficient optimality condition is given. The existence and uniqueness of a solution of the conjugate problem are proved. A numerical method of solution of an optimal problem by means of the Mathcad package is presented. [ABSTRACT FROM AUTHOR]

In this paper, for removable sets in Finsler spaces, a condition of girth smallness relative to some curve families is established. Bibliography: 8 titles [ABSTRACT FROM AUTHOR]

The paper introduces the notion of normal ring sets and considers the problem of decomposition and composition for them. [ABSTRACT FROM AUTHOR]

Let TH be the space of ( T + H)-matrices of order n. The paper considers the following question: Which unitary matrices U satisfy the condition ∀A ∈ TH → U* AU ∈ TH? A criterion for verifying whether a given matrix U has this property is proposed. Bibliography: 4 titles. [ABSTRACT FROM AUTHOR]

This paper is a review of studies in differential geometry of distributions for 35 years (1975-2009) based on abstracts published in the review journal 'Referativny Zhurnal, Series Mathematics.' [ABSTRACT FROM AUTHOR]

In this paper, we calculate the maximal dimension of the Lie group of automorphisms of an n-dimensional Riemann-Cartan manifold. [ABSTRACT FROM AUTHOR]

In this paper, numerical characteristics of identities of finite-dimensional nonassociative algebras are studied. Main attention is paid to the question on the change of the PI-exponent after adjoining an external unit element. We construct an example of a four-dimensional simple algebra such that its PI-exponent increases by one after adjoining an external unit element. [ABSTRACT FROM AUTHOR]

In this paper a robust sequential test is constructed for a discrete observation model, for which probabilities of first-type and second-type errors under Tukey-Huber type distortions do not exceed the specified values. No additional 'commensurability' condition is imposed on the model, and test construction does not require cumbersome calculations. Theoretically studied properties of the constructed test are illustrated by numerical examples. [ABSTRACT FROM AUTHOR]

This article deals with the oscillation of a certain class of fourth-order delay differential equations. Some new oscillation criteria (including Hille- and Nehari-type criteria) are presented. The results obtained in the paper improve some results from [C. Zhang, T. Li, B. Sun, and E. Thandapani, Appl. Math. Lett., 24, 1618 (2011)]. Two examples are presented to illustrate our main results. [ABSTRACT FROM AUTHOR]

A subgroup A of an Abelian group G is called its absolute ideal if A is an ideal of any ring on G. An Abelian group is called an RAI-group if there exists a ring on it in which every ideal is absolute. The problem of describing RAI-groups was formulated by L. Fuchs (Problem 93). In this paper, absolute ideals of torsion Abelian groups and torsion Abelian RAI-groups are described. [ABSTRACT FROM AUTHOR]

In this paper, vector groups whose holomorphs are isomorphic are studied. In connection with the studied problem, the concepts of a semi-characteristic and Γ( G)-decomposition of a group are introduced. The properties of such decompositions are described. Isomorphism conditions of holomorphically isomorphic vector groups are found. [ABSTRACT FROM AUTHOR]

In this paper, we study torsion groups containing proper fully invariant subgroups isomorphic to the group itself, the so-called IF-groups. We introduce the concept of an admissible sequence of Ulm-Kaplansky invariants for primary groups by use of which a description of IF-groups is obtained in some important classes of p-groups. [ABSTRACT FROM AUTHOR]

In the paper we define and study the resampling estimators of such main characteristics of the renewal process as the renewal function and the distribution function of the ith renewal time moment. An algorithm of the expectation and the mean squared error calculation for these estimators are proposed. Numerical examples show that the suggested estimators have less bias than the usual estimators based on the empirical distribution function of the time between successive renewals. [ABSTRACT FROM AUTHOR]

Simulation allows one to realize models of complex systems, processes, or components and carry out experiments on them with the purpose to determine how the real systems perform. The aim of this paper is to present a simulator able to analyze the stochastic behavior of multi-server queueing systems with general distributions for interarrival and service times, for which very few analytical results are available. The simulator, developed using the symbolic and numerical power of the software Mathematica, is based on a discrete-event simulation model. In particular, a case study is presented: the simulation of a real system represented by a bank, according to real data collected on interarrival times of the users and service times of the servers. Moreover, the optimization of this system is proposed through an objective function that takes into account various parameters, among which is the average sojourn time of a customer in the queue. [ABSTRACT FROM AUTHOR]

In this paper, we consider topological (2 , 2)-transformation groups. [ABSTRACT FROM AUTHOR]

This paper is a survey of our recent results concerning metabelian varieties, and more specifically, varieties generated by wreath products of Abelian groups. We give a full classification of cases where sets of wreath products of Abelian groups $$ \mathfrak{X} $$ Wr $$ \mathfrak{Y} $$ = { X Wr Y | X ∈$$ \mathfrak{X} $$ , Y ∈ $$ \mathfrak{Y} $$ } and $$ \mathfrak{X} $$ wr $$ \mathfrak{Y} $$ = { X wr Y | X ∈ $$ \mathfrak{X} $$ , Y ∈ $$ \mathfrak{Y} $$ } generate the product variety $$ \mathfrak{X} $$ var ( $$ \mathfrak{Y} $$ ). [ABSTRACT FROM AUTHOR]

In this paper, recently published results on matrix spectral factorization is reviewed, and their connection to wavelet matrices is revealed. [ABSTRACT FROM AUTHOR]

In this paper, we indicate several aspects of the notion of homotopy Gerstenhaber algebras and give some important examples and applications. [ABSTRACT FROM AUTHOR]

Let Ω be a set and TΩ be the set of all 5-ary functions over Ω. In this paper, by considering five Mann’s compositions on TΩ, we obtain a (2 , 5)-semigroup and an abstract characterization of this algebra. [ABSTRACT FROM AUTHOR]

This paper is devoted to the numerical analysis of abstract parabolic problems u′( t) = Au( t), u(0) = u with hyperbolic generator A. We develop a general approach to establish a discrete dichotomy in a very general setting in the case of discrete approximation in space and time. It is a well-known fact that the phase space in the neighborhood of the hyperbolic equilibrium can be split in such a way that the original initial value problem is reduced to initial value problems with exponentially decaying solutions in opposite time directions. We use the theory of compact approximation principle and collectively condensing approximation to show that such a decomposition of the flow persists under rather general approximation schemes. The main assumption of our results are naturally satisfied, in particular, for operators with compact resolvents and condensing semigroups and can be verified for the finite element method as well as finite difference methods. [ABSTRACT FROM AUTHOR]

The Kopytov order for any algebras over a field is considered. The purpose of this paper is to investigate a generalization of the concept of prime radical to lattice ordered algebras over partially ordered fields. Prime radicals of l-algebras over partially ordered and directed fields are described. Some results concerning properties of the lower weakly solvable l-radical of l-algebras are obtained. Necessary and sufficient conditions for the l-prime radical of an l-algebra to be equal to the lower weakly solvable l-radical of an l-algebra are presented. [ABSTRACT FROM AUTHOR]

Consider reduced Abelian p-groups ( p ≥ 3) A and A. In this paper, we prove that the automorphism groups Aut A and Aut A are elementary equivalent if and only if the groups A and A are equivalent in second-order logic bounded by the cardinalities of the basic subgroups of A and A. [ABSTRACT FROM AUTHOR]

The determinant theory for matrices over a pseudo-complemented distributive lattice is presented. Previous results on this topic are special cases of the theorems proved in this paper. [ABSTRACT FROM AUTHOR]

Numerical methods are often used for the investigation of various queuing systems, where exact methods result in extremely complicated formulae. In this paper we are going to examine such a queuing system, which accepts bulk-arrivals, and where the first group of requests that appears initiates a vacation, during which the server is prepared for the service, and actual service can only begin after this period of time. We are going to give recursive formulae for the equilibrium distribution of this system. [ABSTRACT FROM AUTHOR]

In this paper, the numerical simulation method is used to study spectral properties of sample covariance matrices. [ABSTRACT FROM AUTHOR]

We obtain cubature formulas of volume potentials over bounded domains combining the basis functions introduced in the theory of approximate approximations with their integration over the tangential-halfspace. Then the computation is reduced to the quadrature of one dimensional integrals over the halfline. We conclude the paper providing numerical tests which show that these formulas give very accurate approximations and confirm the predicted order of convergence. Bibliography: 6 titles. [ABSTRACT FROM AUTHOR]

This paper presents a number of numerical quantities that admit interpretation in terms of classical and quantum mathematical physics. [ABSTRACT FROM AUTHOR]