Recent Papers

Direct decompositions of idempotents in semigroups

This paper develops a semigroup-theoretic framework intended to unify structure-theoretic and category-theoretic theories of direct decompositions. It defines direct decompositions of idempotent elements in semigroups with zero and identity, introduces regularity, splitting, normality, subordination…

Groups with one class of inaccessible isoorder $\Pi d$-subgroups

This note studies finite groups in relation to classes of isoordinal subgroups, where subgroups are grouped by having the same order, with particular attention to unattainable, that is non-subnormal, Pi d-subgroups. After recalling notions of Pi-solvability and Pi-separability, the paper establishes…

Spheres and Geodesics in Riemannian Spaces with a Pole

This paper studies Riemannian spaces of positive curvature with a pole, focusing on spheres centered at the pole and the behavior of geodesics relative to the corresponding balls. Using comparison arguments and variational methods for geodesic digons, it proves that all such spheres are strictly con…

Corrections to the Article “On Affine Connections Associated with a Skew-Symmetric Tensor” (DAN, Vol. 128, No. 4, 1959)

Congruence of Centroidal Geodesic Curves of a Metric Space of Linear Elements

This paper develops an invariant differential geometry for congruences of centroidal geodesic curves in a metric space of linear elements with Euclidean connection and three-dimensional base space. Using Laptev’s group-theoretic method, it defines the underlying affine and metric connection structur…

The use of the characteristic functional and semi-invariants in the ergodic theory of stationary processes

This paper studies ergodic and mixing properties of stationary stochastic processes using characteristic functionals, moments, and semi-invariants. It formulates necessary and sufficient conditions for ergodicity, mixing in the wide sense, mixing of finite degree, and mixing of all degrees, includin…

A supplement to S. M. Nikol'skii's embedding theorem for the class $H^{*_{(r_1,\dots, r_n)}}_{p_1,\dots, p_n}$

This note extends S. M. Nikolskii’s embedding theorem for anisotropic smoothness classes with mixed integrability exponents to a periodic setting in which the exponents may lie on both sides of a fixed exponent. The proof follows Nikolskii’s approximation method, using generalized Jackson approximat…

A Theorem on the Existence and Embedding of Subgroups in a Finite Group

This paper studies existence and embedding questions for subgroups of finite groups using Chunikhin’s notions of block, separable, and reduced block divisors of a group order. It proves lemmas showing that separable and block-separable divisors are inherited by subgroups and factor groups, then deri…

On Strongly Elliptic Monge–Ampère Equations

This paper studies strongly elliptic Monge-Ampère equations with continuous coefficients and formulates conditional, or generalized, solutions through weak limits of curvature, mean curvature, and area set functions associated with convex surfaces. Building on earlier existence results, it gives suf…

PROJECTIVE AND PROJECTIVE-METRIC TRANSPORTS IN MANIFOLDS WITH AFFINE CONNECTION AND IN RIEMANNIAN SPACES

The paper studies transports of local centro-projective spaces and their duals over a differentiable manifold equipped with an affine connection. Using an auxiliary object with a specified transformation law, it establishes coordinate-invariant correspondences between tangent vectors, covectors, and…

On the Cohomology of Complex Homogeneous Manifolds

The paper studies the Dolbeault cohomology groups of simply connected compact complex homogeneous manifolds that need not be Kähler. Using Wang’s description of such manifolds and Bott’s reduction to relative Lie algebra cohomology, it relates a non-Kähler homogeneous manifold X to an associated com…

THE MULTIPLICATIVE GROUP OF A DIVISION RING

This paper studies the multiplicative group of a noncommutative associative division ring and its relation to the center of the ring. Extending results of Hua and Scott, it proves that the multiplicative group is not locally nilpotent and that every locally nilpotent normal subgroup is contained in …

Structure of Rings of Continuous Functions on the Circle with Two Generators

This paper studies closed rings of continuous functions on the unit circle generated by two functions that separate points, and asks when such a ring fails to coincide with the full ring of continuous functions. Extending results of Wermer, it replaces analyticity assumptions by Hölder-type smoothne…

Periodic solution of a system of ordinary differential equations with a small parameter multiplying the derivatives

The paper studies a singularly perturbed system of ordinary differential equations in which the fast variables have a unique nondegenerate periodic motion for each fixed value of the slow variables. Using a phase coordinate, a reduction to equations with the phase as independent variable, and an ave…

On Some Problems in the Topology of Manifolds Related to the Theory of Thom Spaces

This paper studies cobordism-type groups of smooth manifolds embedded in Euclidean space whose normal bundles have prescribed structure groups, especially the stable oriented, unitary, and symplectic cases, and interprets these groups through the homotopy groups of Thom spaces. Using Thom’s construc…

On the Spectral Theory of Linear Operators in a Banach Space

This note studies spectral decomposition conditions for linear operators in Banach spaces, introducing the class of S-operators whose real spectrum can be localized by invariant subspaces associated with finite intervals. It proves that a locally correct operator, equivalently the generator of a str…

On General Systems of Differential Equations

The paper studies how to define principal terms, characteristic forms, and ellipticity for general systems of linear differential equations, where the analogue of the principal part is not uniquely determined. It introduces an order for a system via the order matrix, proves the existence of admissib…

On the domains of univalence of certain classes of analytic functions

This paper studies disks of univalence for polynomials obtained as integrals of polynomials whose derivative zeros lie outside a prescribed region, refining Kakeya’s radius estimate. Using a lemma on products of complex factors with bounded arguments, it derives a radius determined by the positive s…

On Differentiation of Complex Functions

This paper studies differentiation properties of complex functions on arbitrary sets and of functions approximable by rational functions. It first gives an analogue of Denjoy’s theorem, describing the possible sets of derivative numbers of an arbitrary complex function at almost every point. It then…

The Area Principle in the Problem of Non-Overlapping Domains

The paper develops an area principle for systems of conformal maps from the unit disk onto pairwise non-overlapping simply connected domains in the extended plane. By applying an area computation to auxiliary functions regular in the complement of truncated image domains, it derives coefficient ineq…

On a Sufficient Criterion for Hölder Continuity of a Mapping

This paper establishes a sufficient condition for Hölder continuity of continuous mappings from a domain in Euclidean space into a higher-dimensional Euclidean space whose weak first derivatives satisfy an integral isoperimetric-type inequality. The argument derives a growth estimate for the integra…

Integral Equations with Almost Difference Kernels

This paper studies one-dimensional integral equations in Lp spaces whose kernels are almost of difference type, represented through Fourier transforms by operator symbols depending on both position and frequency. It establishes boundedness criteria for such operators, including cases with absolutely…

On the Embedding of Uniform Spaces into Hilbert and Euclidean Spaces

This note addresses conditions under which uniform spaces can be embedded uniformly in generalized Hilbert spaces, in response to questions about uniform analogues of classical metrization and embedding theorems. It proves that any uniform space satisfying the condition that every uniform cover admi…

The method of modules in space

This paper extends the modulus method and its extremal length interpretation from the geometric theory of functions of one complex variable to three-dimensional Euclidean domains. It defines moduli for families of rectifiable curves and quadrable surfaces using admissible metrics, and proves distort…

ON THE CONCEPT OF A GENERALIZED SOLUTION

The paper examines the definition of generalized solutions for quasilinear hyperbolic systems in divergence form, focusing on Gelfand’s proposal to select limits of solutions of viscous regularizations. It argues that hyperbolicity alone does not make this definition intrinsic, since the limiting di…

On densely embedded ideals of semigroups

This note studies when a semigroup can occur as a densely embedded ideal of a larger semigroup, a notion arising in the abstract characterization of transformation semigroups. After recalling annihilators and characteristic ideals, it proves that any semigroup with a nontrivial annihilator cannot be…

A Characteristic Difference Scheme for a Nonstationary Kinetic Equation

This paper develops characteristic difference schemes for a nonstationary one-group kinetic Boltzmann equation describing neutron transport in a reactor with isotropic scattering, initial data, and absorbing boundary conditions. The method integrates the equation along neutron characteristics, intro…

On Tables and Interpolation of Functions from a Certain Class

The paper studies interpolation and tabulation of periodic functions of several variables whose Fourier coefficients satisfy a product type algebraic decay condition. Using Korobov type lattice points on a parallelepipedal grid, it constructs approximate Fourier coefficients from only N function val…

On the Construction of Envelopes of Holomorphy for Domains of a Special Type

The paper studies envelopes of holomorphy for domains formed by adjoining a complex neighborhood of a real domain to the forward and backward tube domains associated with the light cone. Using boundary values of holomorphic functions of controlled growth, the edge of the wedge theorem, and propertie…

Primarily factorizable groups

The paper studies groups in which every p-subgroup is complemented for each prime p, termed primarily factorizable groups, as a variant of fully factorizable groups. It introduces fully primitive components, p-projections, almost commutative and primary sets, and uses these notions to describe perio…

On Estimates of Green's Tensors for Some Boundary Value Problems

The paper derives estimates for Green tensors associated with boundary value problems in bounded three dimensional domains, extending Odqvist’s results for the stationary Navier, Stokes system with no slip boundary conditions. It establishes pointwise and Hölder type bounds, including logarithmic fa…

On Hyperbolic Equations with Discontinuous Coefficients

The paper studies mixed problems for second order linear hyperbolic equations with coefficients that may have jump discontinuities across prescribed surfaces, including transmission conditions for the solution and conormal derivative. Using approximation of discontinuous coefficients by smooth funct…

On the interpolation of stationary processes with discrete time

The paper studies linear interpolation of a discrete-time stationary random process when its values are known except on a finite set, using Hilbert space projection and the spectral representation of the process. It characterizes interpolability in terms of the spectral density and a minimal polynom…

On the application of the parameter variation method to the computation of eigenvalues and eigenvectors of matrices

The paper develops a parameter variation method for computing eigenvalues and eigenvectors of a matrix whose entries depend differentiably on a parameter. Starting from a known eigenvalue at an initial parameter value, it differentiates the characteristic equation and expresses the resulting differe…

Interpolation and quadrature formulas on the classes $W_s^\alpha$ and $E_s^\alpha$

The paper studies interpolation and quadrature for periodic functions of several variables in the classes defined by Fourier coefficient decay conditions, denoted W_s^alpha and E_s^alpha. It estimates the optimal mean-square error when function values are sampled at N points of Korobov-type parallel…

On a theorem of V. Ponomarev

This note strengthens a theorem of V. Ponomarev on extending open mappings to Čech compactifications by removing a compactness assumption in the single-valued case and giving a simpler proof in the multivalued setting. It proves that a continuous, closed and open mapping from a normal space onto a n…

On Critical Points of Periodic Functionals

This paper studies critical points of functionals on the unit sphere of a Banach space that are invariant under a periodic transformation. Using Krasnosel’skii’s generalization of Lyusternik and Shnirelman category theory, it defines genus for invariant compact sets and proves the existence of sets …

On Some Interpolation Problems in the Class $H_p$ for $p<1$

This paper studies extremal interpolation in Hardy classes \(H_p\) for \(0<p<1\), extending earlier results known for \(p\geq 1\). It proves that minimal interpolating functions have the same structural form previously established for \(p\geq 1\), using a transformation that relates a minimal functi…

On the Question of the Group of Abelian Extensions of Abelian Groups

This paper studies the construction of the group Ext(F,T) of abelian extensions for various classes of abelian groups, using standard exact sequences for Hom and Ext. It derives descriptions of Ext(F,T) when F is torsion-free of finite rank and T is periodic, including rank-one and complete torsion-…

Application of the Small Parameter Method for Constructing Solutions of Differential Equations with Delayed Argument

The paper develops a small-parameter approach for constructing solutions of differential equations with delayed argument, treating the delay as the perturbation parameter. Starting from the solution of the corresponding equation without delay, it defines successive linear approximations whose differ…

Asymptotic Expansions of Eigenvalues of a Boundary Value Problem with a Parameter

The paper studies asymptotic eigenvalue formulas for a first order matrix boundary value problem with a complex spectral parameter, polynomial parameter dependence in the boundary conditions, and a diagonal leading matrix with sufficiently smooth entries. It constructs a refined asymptotic represent…

Generalized Abel Integral Equation

The note solves a generalized Abel integral equation on a finite interval with two weakly singular one-sided integrals and variable coefficients. Using Carleman’s continuation into the complex plane, the equation is transformed into a Riemann boundary-value problem for an analytic function on the pl…

The Family of Axial Planes of a Two-Dimensional Surface in Four-Dimensional Projective Space and Some Problems Related to This Family

The paper studies two-dimensional surfaces in four-dimensional projective space through a moving projective frame adapted to their Laplace transforms and introduces the two-parameter family of axial planes determined by osculating planes of the conjugate net. It derives formulas for these planes, de…

On extremal problems for functions satisfying additional constraints inside a domain and their application to approximation problems

The paper develops a general framework for extremal problems involving analytic functions subject both to global growth bounds in a domain and additional constraints on a subset of that domain. Using duality in locally convex spaces, it derives abstract extremal identities and applies them to bounde…

On an Analogue of the Poisson Formula for Fourier Cosine Transforms

This paper develops an analogue of the Poisson summation formula for sums weighted by the number of integral ideals of given norm in selected algebraic number fields. Using Mellin inversion, the functional equation of the Dedekind zeta function, and generalized Fourier kernels expressed through Bess…

On groups with a $k$-reducible basis

This note studies finitely presented groups whose defining bases are \(k\)-reducible, generalized \(k\)-reducible, irreducible, or \(\delta\)-bases, in the sense related to work of Tartakovskii. It compares \(k\)-reducibility with the \(\delta\)-basis condition via suitable length functions, and pro…

On Expansion in Eigenfunctions of a Non-Self-Adjoint Differential Operator of Arbitrary Even Order on the Half-Axis $[0,\infty)$

This paper studies expansions in eigenfunctions for a non-self-adjoint differential operator of arbitrary even order on the half-axis, with complex summable coefficients and general boundary conditions at the origin. Using asymptotic solutions in sectors of the spectral parameter plane and finite-in…

On a theorem of M. Riesz

This paper extends the M. Riesz interpolation theorem for linear operators between Lebesgue spaces to questions of complete continuity. It proves that if a linear operator is completely continuous from one Lebesgue space into another, with finite target exponent, and continuous between a second pair…

Estimates of trigonometric sums with completely uniformly distributed functions

This paper studies trigonometric sums associated with completely uniformly distributed functions, improving earlier estimates of order O(P^{3/4} log P). It constructs a class of functions using blocks determined by primes and carefully chosen residue coefficients, and proves that their shifted linea…

The characteristic functions of a certain integral equation

This note studies an integral equation on a closed Riemann surface that is analogous to an equation used in Vekua’s theory of generalized analytic functions, but that may possess eigenfunctions. Using properties of an elementary function of the first kind, divisors, and the Riemann Roch theorem, the…