Recent Papers

On the Dual of a Subspace of a Countable Inductive Limit

The paper studies when the natural map from the inductive limit of the intersections of a subspace with the terms of a countable inductive system into the subspace has a bijective adjoint on duals. It relates this question to weak homomorphisms and surjectivity of adjoint operators, then uses invers…

GENERAL INTEGRAL REPRESENTATIONS

The note develops new general integral representations for holomorphic functions in one and several complex variables, extending earlier operator methods introduced by the author. It defines composite inverse operator families and applies them to functions on star-shaped domains in one complex varia…

ON THE KUHN—TUCKER THEOREM

This note studies when optimality in a convex programming problem with concave, possibly nondifferentiable objective and constraint functions is equivalent to the existence of a saddle point of the corresponding Lagrange function. Using geometric separation arguments, limiting cones, and support fun…

SOLUTION OF A CLASS OF MAGNETOHYDRODYNAMIC PROBLEMS WITH MAGNETIC-FIELD AMPLIFICATION

This paper analyzes kinematic magnetohydrodynamic field amplification by a convective vortex cell intended as a simplified model for processes relevant to the solar dynamo. The induction equation is solved for an incompressible toroidal vortex with both meridional circulation and an azimuthal veloci…

ON THE NATURE OF THE SOLUTIONS OF LINEAR EVOLUTIONARY SYSTEMS WITH ELLIPTIC SPATIAL PART

The paper studies weak and generalized solutions of linear evolutionary systems whose spatial part is elliptic in the sense of Petrovsky, including cases beyond hypoelliptic equations and systems with complex-valued solutions constrained by cones. It develops several lateral smoothing estimates in l…

SOME ANALYTIC QUESTIONS AND THE INVERSE STURM–LIOUVILLE PROBLEM FOR AN EQUATION WITH A HIGHLY SINGULAR POTENTIAL

This paper studies the direct and inverse spectral theory for a half-line Sturm-Liouville equation whose potential has a singularity at the origin stronger than the Bessel type. Under specified growth, smoothness, and integrability assumptions on the singular part and perturbation, the authors estab…

ON THE POSSIBILITY OF THE PRODUCTION OF ELECTRON–POSITRON PAIRS IN VACUUM UPON FOCUSING LASER RADIATION

This paper examines whether focused coherent laser radiation can produce electron, positron pairs from the vacuum, a quantum electrodynamic effect requiring fields near the critical Schwinger value. Using the nonlinear effective Lagrangian for slowly varying electromagnetic fields, the authors deriv…

ON THE CLASSICAL SOLUTION OF THE MULTIDIMENSIONAL STEFAN PROBLEM

The paper studies the multidimensional two-phase Stefan problem in a rectangular spatial domain, focusing on a regular classical solution with a moving phase-separation surface. For the two-dimensional case, with extension indicated to higher dimensions, the authors replace the Stefan condition by a…

ON THE EMBEDDING OF STONE–ČECH COMPACTIFICATIONS OF DISCRETE SPACES IN BICOMPACTS

The paper studies when compact Hausdorff spaces contain Stone-Cech compactifications of discrete spaces, reducing the problem to the existence of continuous maps onto Tikhonov cubes and to dyadic systems of zero-sets. It introduces the cardinal invariants massiveness and tightness, proves mapping th…

ON THE BOUNDARY VALUES OF GENERALIZED SOLUTIONS OF ELLIPTIC EQUATIONS

The paper studies boundary values and traces of generalized solutions of properly elliptic differential equations in a bounded smooth domain. Using Sobolev type spaces with boundary components and integration by parts identities, it proves equivalence between a norm involving interior Sobolev regula…

THE CRYSTAL STRUCTURE OF KURNAKOVITE

EMBEDDING THEOREMS AND BEST APPROXIMATIONS

ON THE LOCATION OF THE POINTS OF MAXIMAL DEVIATION IN CHEBYSHEV APPROXIMATION OF CONTINUOUS FUNCTIONS

This note studies the location of points of maximal deviation in best uniform trigonometric approximation of continuous periodic functions. Extending related results for algebraic polynomial approximation, it analyzes differences of successive best approximating trigonometric polynomials, introduces…

NONLINEAR EQUATIONS WITH MONOTONE OPERATORS

The paper studies existence and uniqueness for nonlinear Hammerstein type integral equations and systems in Lebesgue spaces, allowing measurable sets of finite or infinite measure and avoiding assumptions such as complete continuity, self-adjointness, or restrictions like \(p \geq 2\). It formulates…

VIBRATIONS OF A ROTATING DISK UNDER PARTIAL BRAKING

This paper studies axisymmetric vibrations and stresses in a homogeneous isotropic elastic circular disk whose rotation is reduced by partial braking through a rigid rim. Because residual angular velocity couples radial and tangential displacements through rotational inertia, the authors formulate c…

EXISTENCE OF PERIODIC MOTIONS AND MOTIONS OF SPECIAL TYPE OF HAMILTONIAN SYSTEMS WITH A SMALL PARAMETER

This paper studies Hamiltonian systems in action angle variables that are small perturbations of an integrable system, under a nondegeneracy condition on the Hessian of the unperturbed Hamiltonian near a fixed action value. A variational method is proposed, based on minimizing a functional that meas…

CONGRUENCES MODULO A POWER OF A PRIME NUMBER

The paper studies the number of solutions to congruences modulo a prime power of the form F(x,y) congruent to 0 modulo p^m, where F is an absolutely irreducible polynomial and the variables range over incomplete residue intervals. Using a Hensel-type lifting argument, algebraic number theory, estima…

CRYSTAL STRUCTURE OF MAGNESIUM METHOXYCHLORIDE

On the Efficiency of Large Systems

The paper proposes a macromodel for evaluating the efficiency of large information control systems consisting of a controlled object and a controlling subsystem linked by a flow of control information. It defines efficiency as the difference between the positive effect released in the object and the…

EMBEDDING THEOREMS FOR FUNCTIONS DEFINED IN UNBOUNDED DOMAINS, AND THEIR APPLICATION TO THE SPECTRAL THEORY OF ELLIPTIC SELF-ADJOINT OPERATORS

The paper studies weighted Sobolev-type spaces for functions on unbounded domains and addresses the failure of compact embeddings in such settings. For a broad class of unbounded domains, it establishes sharp weighted embedding estimates and compactness theorems for embeddings between spaces of diff…

A NEW SOLUTION OF THE DIFFERENTIAL EQUATIONS OF MOTION OF A BODY HAVING A FIXED POINT, UNDER THE CONDITIONS OF S. V. KOVALEVSKAYA

This paper addresses the motion of a rigid body with a fixed point under Kovalevskaya-type inertia and center-of-mass conditions, in the presence of a nonzero gyrostatic moment. Starting from the standard differential equations for angular velocity and the gravity direction cosines, the authors impo…

KINETICS OF UNIPOLAR CHARGING OF BETA-ACTIVE “HOT” PARTICLES IN AN ELECTRIC FIELD

This paper examines the kinetics of unipolar charging of highly radioactive beta-emitting aerosol particles in an external electric field, a problem relevant to electrostatic precipitation and atmospheric or industrial electric fields. The authors model a particle as an absorbing sphere emitting ele…

A BICOMPACTUM WITH NONCOINCIDING INDUCTIVE DIMENSIONS

The paper addresses P. S. Aleksandrov’s question on whether the small and large inductive dimensions must coincide for bicompact spaces. It constructs a Hausdorff bicompactum using lexicographically ordered compact continua, dense decompositions, marked transfinite sequences, Cantor set mappings, an…

MEASUREMENT OF HEAT FLOW THROUGH THE BOTTOM OF THE ARCTIC OCEAN IN THE REGION OF THE MID-OCEAN GAKKEL RIDGE

This paper reports geothermal measurements across the Gakkel Ridge, an active mid-ocean ridge system in the Arctic Ocean, to assess whether heat flow is elevated in its rift zone relative to average oceanic values. Using a thermoprobe deployed from drifting ice, the authors measured geothermal gradi…

On Integral Conservation Laws for Continuous Media in General Relativity

This paper addresses the formulation of integral conservation laws for continuous media in general relativity, where conventional treatments are complicated by nonunique energy momentum complexes and ambiguous integration in curved spacetime. Using Sedov’s variational principle, tetrad variables, an…

ON THE INDECOMPOSABILITY OF TRANSITIVE SUBGROUPS OF THE GROUP \(SF(X)\)

The paper studies transitive subgroups of the finitary symmetric group on an infinite set, focusing on whether such groups can decompose as products of proper elementwise commuting normal subgroups. After establishing a lemma on the equivalence of the actions induced by an intransitive normal diviso…

DISSOCIATION OF OXYGEN MOLECULES IN COLLISIONS

This paper examines the high temperature dissociation of oxygen molecules in collisions with O2 and O, addressing the inadequacy of extrapolating lower temperature rate constants to regimes above about 10,000 K. Shock tube experiments in a 10 percent O2 and 90 percent Ar mixture used ultraviolet abs…

FINITELY CONVERGENT ALGORITHMS FOR SOLVING COUNTABLE SYSTEMS OF INEQUALITIES AND THEIR APPLICATION TO PROBLEMS OF SYNTHESIS OF ADAPTIVE SYSTEMS

The paper studies finitely convergent iterative algorithms for solving countable systems of inequalities that arise in the synthesis of adaptive control systems, where the inequalities are revealed sequentially and may contain unknown quantities. It develops several correction algorithms for quadrat…

ON THE PROBLEM OF OPTIMIZING ALGORITHMS FOR APPROXIMATE INTEGRATION OF FUNCTIONS OF MANY VARIABLES

This note studies optimization of cubature formulas for approximate integration of functions of many variables in weighted Hilbert spaces defined by Fourier transform weights. The full minimax problem is reduced to optimizing coefficients for fixed nodes, with special attention to lattice node syste…

THE SCHAUDER PRINCIPLE AND THE STABILITY OF PERIODIC SOLUTIONS

This note relates the Schauder fixed point principle to stability questions for periodic solutions of nonlinear differential equations. It proves two abstract results for completely continuous operators in Banach spaces: a characterization of asymptotic stability in terms of isolation and index of a…

ON THE QUESTION OF THE SCHWARZSCHILD METRIC IN A SYNCHRONOUS REFERENCE SYSTEM

The paper examines transformations of the Schwarzschild metric to a synchronous reference system and argues that the usual choice of the arbitrary radial function removes the horizon singularity but gives an unsatisfactory flat-space limit. It proposes choosing the function so that, when the gravita…

A VARIATIONAL PRINCIPLE IN FRACTURE MECHANICS

This paper proposes a variational formulation for quasi-brittle fracture that does not require the crack path to be prescribed in advance. Starting from an energy balance for a body with internal ruptures, it derives separate variational conditions for changes in crack trajectory and for motion of a…

ON THE ORIGIN OF TURBULENT MOTION

This paper examines the transition from laminar to turbulent motion through measurements of the frequency spectra of longitudinal velocity fluctuations in air flowing through a circular tube. Using hot-wire anemometry and low-frequency spectral analysis at several radial positions, the authors compa…

SOLUTION OF THE CAUCHY PROBLEM AND ITS ASYMPTOTICS AS \(t\to\infty\) FOR THE LINEARIZED EQUATIONS OF A ROTATING VISCOUS FLUID

The paper studies the Cauchy problem for the linearized Navier Stokes equations of an incompressible viscous fluid subject to uniform rotation. Using Fourier transformation, Bochner’s formula, and Sonine formulas for cylindrical functions, it constructs explicit fundamental kernels for the velocity …

SPATIAL DOUBLY PERIODIC PROBLEMS OF THE THEORY OF ELASTICITY

A method is developed for spatial doubly periodic boundary value problems in elasticity for an infinite body perforated by parallel cylindrical cavities whose circular cross sections form an oblique lattice. Using Galerkin’s general solution of Lamé equations and addition theorems for modified Besse…

THE LINEAR CONJUGATION PROBLEM FOR A HOLOMORPHIC VECTOR IN A BANACH SPACE

The paper studies a linear conjugation problem for a holomorphic vector with values in a Banach space of infinite sequences on a Lyapunov contour, with boundary relation determined by an infinite functional matrix. Under bounded invertibility and compactness assumptions on the matrix coefficient, it…

ON THE MINIMAX PROBLEM

This paper studies minimax optimization problems of the form minimizing the maximum of a smooth function over an auxiliary set. It derives first-order stationarity conditions using directional derivatives of the max function and replaces generally discontinuous criteria by equivalent continuous func…

A SYMMETRY THEOREM FOR SHALLOW EQUILIBRIUM FORMS OF GEOMETRICALLY NONLINEAR SHALLOW AND NONSHALLOW SHELLS

This paper generalizes a previously established symmetry principle for shallow geometrically nonlinear shells to a more exact nonlinear shell theory and to shallow equilibrium forms of nonshallow shells. Using compatibility and equilibrium equations in orthogonal curvilinear coordinates, the author …

CONDITION FOR COMPLETE REGENERATION IN AN OPTRON WITH A PHOTORESISTOR

The paper develops a general condition for complete regeneration in a regenerative optocoupler using a photoresistor, extending earlier treatments that assumed more restricted device characteristics and input configurations. Starting from a system of equations for an optocoupler with electrical and …

THE FACTOR OF CHEMICAL INDIFFERENCE OF MUTUALLY SUBSTITUTING ATOMS IN CRYSTALS OF SOLID SOLUTIONS FORMED BY INTERMETALLIC COMPOUNDS

This paper examines the conditions governing isomorphous substitution of atoms in solid solutions formed by intermetallic compounds. It argues that, beyond similarities of chemical nature, crystal structure, and atomic size, a more fundamental criterion is the mutual chemical indifference of atoms o…

ON AVERAGING IN SYSTEMS OF NONLINEAR INTEGRO-DIFFERENTIAL EQUATIONS

This paper studies averaging methods for nonlinear integro-differential equations with a small parameter, motivated in part by equations arising in the dynamics of imperfectly elastic bodies. It formulates and proves averaging theorems for systems with slow variables on finite intervals of order inv…

ON THE CENTRAL LIMIT THEOREM

This note derives a central limit theorem for certain narrow-sense stationary random processes by reducing the problem to the known central limit theorem for stationary sequences of martingale differences. For an ergodic measure-preserving transformation and an associated decreasing filtration, it g…

ON FUNCTORS DEFINED BY REFLEXIVE \(K\)-SPACES

The paper extends Berman’s study of functors on locally convex spaces by associating to each reflexive K-space with a suitable topologizing system a functor defined through spaces of measurable vector-valued functions. It proves comparison and representation results for these spaces, including condi…

SOLUTION OF THE MILNE PROBLEM FOR THE KINETIC EQUATION OF BHATNAGAR, GROSS, AND KROOK

The paper solves the Milne boundary problem for the one-dimensional Bhatnagar, Gross, and Krook kinetic equation with an absorbing wall, motivated by dilute gas mixtures, low-temperature plasma, chemical kinetics, and neutron transport. Using a one-sided Fourier transform, the boundary condition is …

FINITE CONTROL OVER DISTRIBUTED LINEAR SYSTEMS

This paper formulates and solves a finite control problem for a distributed linear system governed by a one-dimensional wave equation, seeking a boundary control that brings the system to rest in a prescribed finite time. The solution applies a Fourier transform in time, the Paley-Wiener theorem, an…

ON THE ORDER OF GROWTH OF SUMS OF INDEPENDENT RANDOM VARIABLES

The paper studies almost sure growth rates for sums of independent random variables under moment conditions expressed through a general even increasing function g. It proves upper bounds of the form S_n = o(g^{-1}(A_n psi(A_n))) for functions psi whose associated series converges, with appropriate c…

DIFFRACTION ON A BOUNDED BODY

The paper proposes a numerical algorithm for scalar diffraction by a bounded body when the incident wavelength is comparable with the object size and the exterior medium may have coordinate-dependent properties. The exterior boundary-value problem with impedance conditions is reduced by introducing …

ON THE FORMULATION OF THE PROBLEM OF THE INTERACTION WITH THE GROUND OF A ROLLING WHEEL WITH AN ELASTIC TIRE DURING ITS OSCILLATIONS

The paper examines the formulation of equations for a rolling wheel with an elastic tire undergoing oscillations, focusing on the relation between tire deformation and ground reaction. Using transverse oscillations of the wheel rim as an example, it models the tire as a weightless elastic beam on an…

ON THE IMPOSSIBILITY OF CRYSTALLINE ORDERING IN ONE-DIMENSIONAL QUANTUM SYSTEMS

The paper examines whether crystalline ordering can occur in one-dimensional quantum systems of identical Bose or Fermi particles at nonzero temperature. Using Bogolyubov’s inequality for temperature Green’s functions, the authors derive a bound on density correlation functions near a reciprocal lat…

LIE SUBGROUPS OF THE LORENTZ GROUP WITH A FINITE GROUP OF COMPONENTS

The paper classifies Lie subgroups of the Lorentz group that have positive dimension and a finite group of connected components. Using the spinor representation of the Lorentz group and the known classification of its real Lie subalgebras, it determines the normalizers of the connected subgroups and…