Recent Papers

ON THE CAUCHY PROBLEM FOR SYSTEMS OF LINEAR PARTIAL DIFFERENTIAL EQUATIONS WITH VARIABLE COEFFICIENTS

ON THE SMOOTHNESS OF THERMAL POTENTIALS. III

ON FINITELY MULTIPLE OPEN MAPPINGS

This paper studies finite-to-one and exactly k-to-one open mappings between Hausdorff topological spaces, focusing on how such maps affect weight, paracompactness, and metrizability. The main argument proves that a finite-to-one open mapping does not decrease the weight of a locally bicompact space,…

On Multiply Complete Systems and Non-Self-Adjoint Operators Depending on the Parameter \(\lambda\)

This paper develops the notion of multiple completeness for systems of elements in a Hilbert space and gives criteria under which such systems form bases, including Riesz bases with parentheses. These abstract results are applied to non-self-adjoint operator pencils depending on a parameter, in part…

HYPOELLIPTIC EQUATIONS IN CONVOLUTIONS

This paper studies local properties of pseudodifferential operators with nonhomogeneous symbols, treating them as a broad generalization of constant-strength differential operators. It develops a calculus for regular symbols in weighted spaces of tempered distributions, including boundedness, smooth…

ON THE THEORY OF FINITE FACTORIZABLE GROUPS

This paper studies finite groups that can be factorized as the product of two proper subgroups, focusing on how solvability and nonsimplicity are influenced when at least one factor has only one class of noninvariant conjugate subgroups. It presents examples showing that some natural restrictions on…

A SKOLEM METHOD FOR THE ELIMINATION OF POSITIVE QUANTIFIERS IN SEQUENTIAL CALCULI

The paper studies Skolem-style elimination of positive quantifiers in Gentzen sequential calculi for classical, intuitionistic, minimal, and positive predicate logic, with attention to equality and function symbols. It defines positive and negative quantifier complexes for pure sequents and formulat…

On a Problem of I. M. Gelfand

The paper addresses an integral-geometric reconstruction problem posed by I. M. Gelfand for a compactly supported infinitely differentiable function on an oriented real affine space with a nondegenerate quadratic form of signature \((p,q)\). Given integrals of the function over selected hyperplanes …

A NOTE ON THE THEORY OF THE RICCATI EQUATION

DOUBLE OPERATOR STIELTJES INTEGRALS AND MULTIPLIER PROBLEMS

The paper develops further properties of double operator Stieltjes integrals associated with two spectral measures, emphasizing their action on symmetric normed ideals of bounded operators. It extends earlier results from one-dimensional settings to general measure spaces and compact manifolds, repl…

THE METHOD OF GRIDS FOR FINITE AND INFINITE DOMAINS WITH PIECEWISE SMOOTH BOUNDARY

The paper develops a composite grid method for the Dirichlet problem for Laplace’s equation in finite and infinite simply connected domains with piecewise smooth boundaries and finitely many corner angles, including cases where boundary data may have jump discontinuities at corners. The construction…

ON A GENERAL APPROACH TO THE SOLUTION OF LINEAR PROGRAMMING PROBLEMS OF BLOCK STRUCTURE

The paper develops a general geometric framework for solving linear programming problems with block structure, where a subset of constraints has a form that permits easier subproblem analysis. It reduces the original problem to minimization of a convex piecewise-linear function of a vector of estima…

ON THE ASYMPTOTICS OF SOLUTIONS OF A MIXED PROBLEM

EMBEDDING OF TREE-LIKE COMPACTA IN \(E^3\)

The paper studies embeddings of tree-like one-dimensional compacta in three-dimensional Euclidean space and their relation to cellular decompositions by finite unions of cubes. It outlines a proof that every tree-like compactum in E3 can be approximated by an arbitrarily small homeomorphic shift ont…

ON THE UNIQUENESS OF THE SOLUTION OF THE EXTERIOR INVERSE PROBLEM FOR A NEWTONIAN POTENTIAL

ON STABILITY WITH RESPECT TO THE FIRST APPROXIMATION

DISCRETE PERIODIC PROCESSES

The paper studies discrete periodic processes through a scheduling model in which materials enter and leave a bunker at prescribed indexed times with specified periods and quantities. Under the condition that average inflow equals average outflow, it derives a periodic expression for the bunker rema…

ON UNIVALENT FUNCTIONS WITHOUT COMMON VALUES IN A MULTIPLY CONNECTED DOMAIN

The paper studies regular univalent functions without common values in finitely connected plane domains bounded by analytic Jordan curves. Using Dirichlet integrals and Bergman kernels of the first and second kind, it derives inequalities for systems of such functions, including versions for the sub…

INTEGRAL GEOMETRY ON THE MANIFOLD OF \(k\)-DIMENSIONAL PLANES

This paper studies the integral transform that assigns to a rapidly decreasing smooth function on complex space its integrals over k-dimensional affine planes with compatible translation-invariant measures. It constructs a differential form valued operator on the complex Grassmannian, using derivati…

GENERAL MIXED PROBLEMS FOR GENERAL TWO-DIMENSIONAL HYPERBOLIC SYSTEMS

ON SHARP ESTIMATES OF EIGENFUNCTIONS OF THE BIHARMONIC OPERATOR

The paper establishes sharp uniform estimates in a closed bounded domain for eigenfunctions of the biharmonic operator with homogeneous boundary conditions, a problem relevant to eigenfunction expansions for self-adjoint operators. For domains with sufficiently smooth boundary, the argument combines…

ON THE THEORY OF THE LAPLACE TRANSFORM

ASYMPTOTICS IN THE GENERAL HARDY–LITTLEWOOD PROBLEM

The note studies a generalized Hardy, Littlewood additive problem for representations of an even integer \(n\) in the form \(p+\varphi(\xi,\eta)=n\), where \(p\) is prime and \(\varphi\) is a positive primitive binary quadratic form with nonsquare discriminant. Using the theory of binary quadratic f…

ON THE QUESTION OF HARMONIC ANALYSIS OF BOUNDED SOLUTIONS OF OPERATOR EQUATIONS

This note studies harmonic analysis and almost periodicity of bounded solutions to linear operator differential equations in Hilbert and Banach spaces, with emphasis on parabolic equations whose coefficients are periodic in time. Using spectral properties of infinitesimal generators, compact resolve…

DIFFERENCE SCHEMES WITH FRONT STRAIGHTENING FOR SOLVING MULTI-FRONT PROBLEMS OF STEFAN TYPE

This paper develops finite difference methods for one-dimensional Stefan-type problems with multiple moving phase fronts governed by a parabolic equation. The authors introduce a front-straightening change of variables that maps each moving subdomain to a fixed interval, then formulate implicit iter…

STATISTICAL DISTRIBUTIONS IN MEDIA PERTURBED BY FOREIGN PARTICLES

The paper develops a functional statistical thermodynamic treatment of a solvent perturbed by a dissolved foreign particle, with emphasis on interactions that combine a strong impenetrable core and a weaker, longer range attractive tail. Using a generating functional for the configurational integral…

ON THE APPROXIMATION OF A FUNCTION BY RATIONAL FRACTIONS

This note studies when a continuous complex function can be uniformly approximated on a prescribed closed bounded set by rational functions. Using analytic capacity, Ahlfors functions, and auxiliary estimates for coverings by squares, it proves that approximation is possible if integrals of the func…

ON STABILITY IN THE CRITICAL CASE OF A DOUBLE ZERO ROOT FOR SYSTEMS WITH AFTEREFFECT

EXPANSION IN EIGENFUNCTIONS OF A ONE-DIMENSIONAL DIRAC SYSTEM

The paper studies eigenfunction expansions for a one-dimensional Dirac system on the half-line with real locally summable coefficients and a real boundary condition at the origin. Using the spectral function and spectral matrix associated with the boundary-value problem, it compares the generalized …

GEOMETRY OF AN \(m\)-SURFACE IN AFFINE SPACE

This paper studies the affine differential geometry of nonplanar m-dimensional surfaces in n-dimensional affine space without restrictions on m and n and without assuming maximal dimensions for all higher order tangent spaces, apart from ordinary points. It introduces surfaces of differential class,…

New Books

This bibliographic notice lists recently published mathematical books and article collections issued mainly in 1965 and 1966 by Soviet and translated publishers. The entries cover complex analysis, operational calculus, stability theory, linear operators in Hilbert space, mathematical physics, bound…

ON A VARIANT OF THE AVERAGING METHOD OF FUNCTIONAL CORRECTIONS FOR SOLVING LINEAR INTEGRAL EQUATIONS OF MIXED TYPE

ON THE DIFFERENTIABILITY OF NONLINEAR OPERATORS IN THE SPACES \(\mathscr L_p\)

This note studies Fréchet differentiability of nonlinear Uryson integral operators acting from one Lebesgue space into another on finite measure sets. It introduces function spaces for kernels and uses continuity or complete continuity of associated superposition operators to give sufficient conditi…

ON SOME DIFFERENTIAL-TOPOLOGICAL INVARIANTS OF NON-SIMPLY CONNECTED MANIFOLDS

The paper studies when a high-dimensional open smooth manifold with two ends and finite fundamental group is diffeomorphic to a product with the real line. It defines an obstruction in the reduced Grothendieck group of projective modules over the group ring, proves a duality relation for this invari…

ASYMPTOTIC BEHAVIOR OF THE SPECTRAL MATRIX OF A ONE-DIMENSIONAL DIRAC SYSTEM

This paper studies the high-energy asymptotic behavior of the spectral matrix associated with a one-dimensional Dirac system on the half-line with a real boundary condition. After reducing the relativistic Dirac equation to a first-order two-component system, the author defines the corresponding spe…

STABILITY REGIONS OF COMPLEX SELF-ADJOINT SYSTEMS OF DIFFERENTIAL EQUATIONS

This note studies the topology of the set of strongly stable periodic complex self-adjoint first-order differential systems with nonsingular skew-Hermitian leading matrix and Hermitian coefficient matrix. Using Krein multiplier theory, the problem is reduced to the structure of curves in the group o…

ON INVERSE THEOREMS OF UNIFORM APPROXIMATION

This note generalizes inverse theorems of uniform approximation by rational functions with prescribed poles in complementary components of a bounded plane set. It establishes a lemma bounding such rational functions and their derivatives on and near the boundary using Green functions, level curves, …

SOME ESTIMATES FOR A SINGULAR INTEGRAL \

The paper derives estimates for a Cauchy principal value singular integral on an interval in terms of interior suprema and moduli of continuity with explicit dependence on distances from the endpoints. Using these estimates, it defines a family of Banach spaces controlled by prescribed majorant func…

On Some Function-Theoretic Sieve Methods in Number Theory

Turán proposes a function theoretic sieve method for additive prime problems that replaces parts of the Hardy, Littlewood, Vinogradov circle method by Dirichlet series and contour integration. The paper formulates the method for representations of an integer as a prime plus values of a positive defi…

SOME LIMIT THEOREMS FOR SOLUTIONS OF DIFFERENTIAL EQUATIONS WITH A RANDOM RIGHT-HAND SIDE

This note studies the asymptotic behavior of solutions to differential equations with random right-hand sides containing a small parameter, especially in the case where the averaged first-order drift vanishes and the relevant time scale is of order 1 over epsilon squared. Under bounded smoothness, m…

AN EXTENDED CONCEPT OF QUASICONFORMALITY OF A PLANE MAPPING AND LINEAR SYSTEMS OF DIFFERENTIAL EQUATIONS OF MIXED TYPE

This note extends Lavrent’ev’s notion of plane quasiconformality by introducing a three characteristic framework based on commutative rings associated with generalized complex numbers and parameter dependent curves. It defines t-convergence, t-continuity, t-differentiability, regularity, and t-quasi…

ON THE \(J\)-FUNCTOR OF CELL COMPLEXES

The paper studies the complex J-functor for cell complexes, especially cases where the usual exact sequence for a pair fails, and introduces homology groups measuring this failure. Using Thom complexes, the author constructs a homomorphism from a kernel in complex K-theory to Q/Z and shows that it d…

ON A CERTAIN METHOD FOR SOLVING THE MIXED PROBLEM FOR A HYPERBOLIC EQUATION WITH DISCONTINUOUS COEFFICIENTS

THE INTEGRAL OVER AN ELLIPSOID AND THE SECOND BORN APPROXIMATION

This paper studies the high frequency behavior of the kernel appearing in the second Born approximation for a scattering equation, expressing it through an integral of the potential over ellipsoids with foci at two observation points. It develops basic properties of this ellipsoidal integral, includ…

ON EFFECTIVELY TOPOLOGICAL SPACES

The paper develops constructive analogues of basic notions from general topology by defining effectively metric and effectively topological spaces, effectively open and closed sets, computable and effectively continuous mappings, and effective versions of separation axioms. It examines how classical…

Bibliography of Journal Articles

This article is a bibliographic survey of journal publications relevant to differential equations and adjacent areas of analysis, mathematical physics, numerical methods, stability theory, integral equations, and boundary value problems. It compiles alphabetically arranged entries, chiefly from 1965…

A NEW CLASS OF FINITE-DIFFERENCE OPERATORS

This paper introduces a parameter-dependent class of finite-difference operators for the numerical integration of systems of ordinary differential equations, extending standard multistep operators by allowing shifted derivative terms. It establishes a representation of these operators as linear comb…

ON SEMI-ISOMORPHISMS AND STRUCTURAL ISOMORPHISMS OF CANCELLATIVE SEMIGROUPS

The paper studies semi-isomorphisms and structural isomorphisms of cancellative semigroups, extending a result of Scott by removing the assumption that the target semigroup is cancellative. It proves that every semi-isomorphism from a cancellative semigroup onto an arbitrary semigroup is necessarily…

APPROXIMATION OF FUNCTIONS BY FOURIER–JACOBI SUMS

This note studies the convergence rate of partial sums of Fourier-Jacobi expansions for functions on the interval [-1,1] with Jacobi weights. It derives an upper estimate for the associated Lebesgue function when the Jacobi parameters are at least -1/2, noting the sharpness of the endpoint order, an…

ON THE QUESTION OF THE STABILITY OF SMALL PERIODIC SOLUTIONS

The paper studies bifurcation and stability of small nonzero periodic solutions of a parameter dependent system of ordinary differential equations with periodic right hand sides and a persistent zero solution. Assuming that the monodromy matrix of the linearized system has the multiplier 1 associate…