Recent Papers

ON A PARTICULAR CASE OF THE DIRICHLET PROBLEM FOR THE DARBOUX EQUATION FOR A SPACE CUT ALONG AN ELLIPSOIDAL DISK

DISTRIBUTION OF THE MAGNETIC FIELD

This paper reports experimental measurements of the azimuthal magnetic field and inferred current distribution in a quasi-stationary coaxial plasma injector operated with millisecond discharge pulses in nitrogen. Using probe coils and Rogowski belts, the authors mapped averaged current lines for dif…

A GENERALIZED M. RIESZ FORMULA AND EXTENSION OF CONVOLUTION

This note studies a generalized M. Riesz identity for trigonometric polynomials and uses it to investigate when a convolution operator defined on polynomials of order at most n admits a norm-preserving extension to periodic function spaces. It establishes general criteria and examples for such exten…

GENERAL BOUNDARY CONDITIONS FOR MARKOV PROCESSES WITH A COUNTABLE SET OF STATES

This paper studies Markov processes on a countable state space specified by transition density coefficients and asks how such processes can be continued after the first accumulation time of jumps. Under a finiteness condition expressed through nonnegative bounded solutions of the eigenvalue equation…

ZERO-SETS AND A HOMEOMORPHISM WITH FINITE DIRICHLET INTEGRAL

This note studies boundary zero-sets of simply connected plane domains in the compactification by prime ends under homeomorphisms whose coordinate functions have finite Dirichlet integral. It introduces a metric condition for a boundary set, expressed by divergence of an integral involving the Hausd…

EXTENSION OF FUNCTORS FROM THE CATEGORY OF BANACH SPACES TO THE CATEGORY OF \((\alpha)\)-SPACES

This note studies the extension of functors from the category of Banach spaces to the category of separable locally convex spaces of type alpha. Using the representation of alpha spaces by spectra of Banach subspaces, local completion, beta strengthening, and limits in the category of alpha spaces, …

INTERPOLATION OF LINEAR OPERATORS AND ESTIMATES OF FOURIER COEFFICIENTS

This paper develops interpolation theorems for linear and quasilinear operators on symmetric Banach function and sequence spaces, expressed through conditions on their fundamental functions or sequences. These results are applied to operators generated by Fourier coefficients, yielding estimates for…

ELECTRON TEMPERATURE IN STELLAR ENVELOPES CONTAINING HIGH-ENERGY ELECTRONS

This paper examines the electron temperature in the envelopes of cool stars when high energy electrons interact with photospheric radiation and generate ionizing Lyman continuum radiation through the inverse Compton effect. Assuming hydrogen photoionization by this nonthermal radiation, recombinatio…

FINITE-DIMENSIONAL REPRESENTATIONS OF CERTAIN BICOMPACT TOPOLOGICAL SEMIGROUPS

This paper studies finite-dimensional representations of bicompact topological semigroups, focusing on when such representations, especially irreducible ones, separate points. It proves that every totally disconnected bicompact topological semigroup has enough representations by finite semigroups, a…

ON THE ASYMPTOTICS OF SOLUTIONS OF THE DIRICHLET PROBLEM NEAR AN IRREGULAR BOUNDARY

The paper studies the asymptotic behavior of solutions to the Dirichlet problem for the Laplace equation near an irregular boundary point, using spherical sections of the domain and eigenvalues of the Beltrami operator to control radial growth. It proves comparison estimates for boundary norms, uniq…

ILL-POSED PROBLEMS IN HILBERT SPACE AND STABLE METHODS FOR THEIR SOLUTION

THERMODYNAMIC PROPERTIES OF SUPERCONDUCTORS WITH A NONMAGNETIC IMPURITY.

This paper analyzes thermodynamic properties of a two-band superconductor with overlapping energy bands near the Fermi surface in the presence of a small concentration of nonmagnetic impurities. Using temperature Green’s functions and impurity-averaged self-energies, it derives equations for the ban…

IMBEDDING THEOREMS FOR MIXED SPACES

ANNUAL VARIATIONS OF COSMIC RAYS AND THE CHANGE IN THE INTENSITY OF COSMIC RADIATION AS A FUNCTION OF THE EARTH’S HELIOLATITUDE

This paper examines the origin of annual variations in cosmic-ray intensity, using 1960 data from a worldwide network of hard-component and neutron-component stations together with aerological temperature corrections. The authors compare observed seasonal behavior with calculated meteorological effe…

ON THE POSSIBILITY OF UNIDIRECTIONAL GENERATION IN A GAS TRAVELING-WAVE LASER

This paper analyzes the conditions for unidirectional generation in a gas traveling-wave laser when four waves can oscillate at two frequencies, with counterpropagating waves allowed at each frequency. Using Lamb’s density-matrix method without the usual approximation that the cavity mode spacing gr…

CRYSTAL GROWTH DURING POLYMORPHIC TRANSFORMATION IN GLUTARIC ACID AND HEXACHLOROETHANE

This paper examines crystal growth during solid solid polymorphic transformations in glutaric acid and hexachloroethane, extending earlier work on organic crystals. Using polarizing microscopy, controlled heating and cooling, and X-ray methods, the authors observe the formation and growth of faceted…

ON AN INVARIANT EQUIPPING OF A SURFACE OF A SPACE WITH AFFINE CONNECTION

The paper addresses the problem of constructing an invariant equipment for an m-dimensional surface in a space with affine connection, allowing arbitrary ambient dimension and possible curvature and torsion. It develops a tensorial method based on higher order tangent spaces, covectors annihilating …

New Books

This bibliographic notice surveys recently published books and collected volumes in mathematics and mathematical physics, with emphasis on differential equations, boundary-value problems, functional analysis, operator theory, numerical methods, and related computational programs. It provides publica…

WEIGHT SPACES OF FUNCTIONS WITH DOMINANT MIXED DERIVATIVES AND DIFFERENTIAL PROPERTIES OF FUNCTIONS FROM THESE SPACES

This paper studies weighted function spaces on the positive orthant whose smoothness is governed by dominant mixed derivatives, motivated by boundary questions for degenerate hyperelliptic equations. It defines weighted analogues of Sobolev, Besov, and Nikol’skii type spaces using mixed derivatives,…

ON THE TRANSCENDENCE AND ALGEBRAIC INDEPENDENCE OF VALUES OF CERTAIN HYPERGEOMETRIC \(E\)-FUNCTIONS

This paper studies transcendence and algebraic independence of values at nonzero algebraic points of certain hypergeometric E-functions and their derivatives. It strengthens a coefficient arithmetic lemma used in Shidlovskii’s method by allowing different prime ideals for different subintervals of t…

EQUATIONS OF MOTION OF A MACHINE UNIT WITH A VARIATOR

This paper derives equations of motion for a machine unit consisting of an engine, ideal variator, and working machine, treating the prescribed time-varying transmission ratio as a nonholonomic constraint. Using Appell’s equations, the authors formulate equivalent differential equations in terms of …

ANALYTIC THEORY AND PROBLEMS OF THE REAL THEORY OF DIFFERENTIAL EQUATIONS CONNECTED WITH THE FIRST METHOD AND WITH METHODS OF ANALYTIC THEORY

ON ASYMPTOTIC SERIES IN THE THEORY OF NONLINEAR SYSTEMS OF ORDINARY DIFFERENTIAL EQUATIONS. I

INTEGRAL GEOMETRY IN EUCLIDEAN SPACE AND ITS CONNECTION WITH BOUNDARY-VALUE PROBLEMS

This note studies the real Euclidean analogue of reconstructing a function in three-dimensional affine space from its integrals over straight lines belonging to a three-parameter complex. The authors formulate the space of lines as a pseudo-Riemannian manifold, identify the relevant Laplace-Beltrami…

EQUATIONS FOR FINITE-DIMENSIONAL PROBABILITY DISTRIBUTIONS OF A TURBULENCE FIELD

This note develops evolution equations for finite-dimensional probability distributions of the velocity field in incompressible turbulence. Starting from the Navier-Stokes equations and the pressure representation in terms of velocity, it derives equations for n-point characteristic functions and, b…

ON LOCAL COHOMOLOGY GROUPS

This note studies two notions of local cohomology at a point in a paracompact Hausdorff space: the direct limit of the reduced cohomology of punctured neighborhoods and the inverse limit of relative cohomology groups. Using an exact sequence obtained from the Leray spectral sequence for the inclusio…

SPONTANEOUS GROWTH OF FILAMENTOUS SINGLE CRYSTALS OF MAGNESIUM OXIDE

This paper reports the spontaneous formation of filamentous single crystals of magnesium oxide on fired periclase specimens with a spinel bond. The authors examine the macrostructure and microstructure of specimens fired at 1650 degrees Celsius and relate whisker growth to zonal differences produced…

Asymptotic behavior of solutions of nonlinear controlled systems

Formation of a long spark in air under the action of weakly focused laser radiation

This paper investigates the formation and dynamics of long sparks in air produced by weakly focused radiation from a high power neodymium glass laser. Using time resolved photography and measurements of the laser field in near and far zones, the authors observe a spark more than two meters long, com…

ORIENTING FIELD AND DIPOLE POLARIZATION

The paper addresses the unresolved relation between the dielectric constant of a liquid and the molecular dipole moment, noting limitations of the Debye and Onsager treatments and the need for a unified approach for pure liquids and solutions. It argues that the orienting field must be weaker than t…

SCHOTTKY EMISSION AND CURRENTS IN DIELECTRICS

This paper analyzes emission currents in dielectrics when the Schottky effect lowers the metal dielectric contact barrier, modifying the boundary conditions of the kinetic problem. Using the known general solution for emission currents and introducing scaled variables, the authors derive the current…

ELLIPTIC (CO)BOUNDARY MORPHISMS

This paper introduces elliptic boundary and coboundary morphisms for Sobolev sections over a closed smooth manifold with an embedded submanifold, combining pseudodifferential operators with restriction and adjoint restriction maps in a matrix framework. It formulates ellipticity through the usual sy…

Sufficient conditions for the absence of periodic trajectories of autonomous systems in the case of multiply connected regions

Two-dimensional autonomous systems of the form \begin{equation} \dot{x}=P(x,y),\quad\dot{y}=Q(x,y)\tag{1} \label{1} \end{equation} are considered, where the right-hand sides have isolated singular points $O_j$ of the pole type. The concept of a "quasi-residue" $J_j$ of a singular point $O_j$ is intr…

DIFFERENTIATION IN LINEAR TOPOLOGICAL SPACES

This paper develops a theory of differentiation for mappings between real linear topological spaces, not necessarily normed, using derivatives defined by uniform convergence on specified systems of subsets and with respect to chosen subspaces. It introduces first and higher derivatives, including we…

On spatial quasiconformal mappings satisfying the Hölder condition at boundary points

This note studies boundary regularity of spatial quasiconformal mappings in three-dimensional Euclidean space. Extending known interior Hölder estimates, it uses modulus estimates for separating surface families, including an inversion lemma, to prove Hölder continuity at boundary points for mapping…

A finite difference method for solving degenerate elliptic and parabolic equations

This paper develops finite difference schemes for boundary value problems for degenerate elliptic equations and for related degenerate parabolic equations in bounded domains where coefficients may vanish on part of the boundary. The authors specify how boundary or boundedness conditions depend on th…

ELECTRON-MICROSCOPIC STUDY OF CHROMIUM AND MOLYBDENUM DEFORMED UNDER HIGH-PRESSURE CONDITIONS

This study examines how high all-round pressure affects the fine deformation structure of high-purity chromium and molybdenum, metals whose plasticity increases markedly under such conditions. Specimens were compressed or hydroextruded at 14 to 18 kbar at room temperature and 250 degrees Celsius, th…

SOME METRIZATION THEOREMS FOR FEATHERED SPACES

This paper proves several metrization results for feathered, or p, spaces under normality and covering assumptions. It first shows that a weakly paracompact p-space with a G-delta diagonal has a uniform base, yielding metrizability in the paracompact case, and then establishes that a collectionwise …

THE RADON TRANSFORM IN SPACES OF MATRICES AND GRASSMANN MANIFOLDS

The paper generalizes the classical Radon transform from Euclidean hyperplanes to spaces of real and complex rectangular matrices and to real and complex Grassmann manifolds. It defines integration over matrix planes given by first-degree matrix equations, establishes basic invariance, homogeneity, …

Classification of the singular points of linear systems of total differential equations

A topological classification of the singular points of the system $$dx^i=\sum_{\mu=1}^{n-1}\sum_{j=1}^na^i_{j\mu}x^j\,dt^{\mu}\quad(i=1,\dots,n),$$ is provided, assuming that the conditions of complete integrability are satisfied, and the $n\times n$-matrices $(a^i_{j\mu})$, $\mu=1,\dots,n-1$ have n…

Permutation groups of representations of the groups $G_2$ and $SU_3$

This paper studies permutations of the parameters labeling irreducible representations of the Lie groups G2 and SU3 that leave representation characters, equivalently Casimir operator eigenvalues, invariant. Explicit transformation sets are given for the two groups and interpreted geometrically as r…

DETERMINATION OF THE DISPERSION OF ELASTIC VIBRATIONS IN THE CRYSTAL LATTICE OF POTASSIUM CHLORIDE FROM DIFFUSE X-RAY SCATTERING

This paper investigates the determination of elastic vibration dispersion in undeformed potassium chloride single crystals using diffuse X-ray scattering. Treating KCl as an alkali-halide crystal whose ionic masses and scattering factors permit a quasiacoustic approximation, the authors measure diff…

ISOTOPIC HYPERFINE STRUCTURE OF THE EPR SPECTRUM OF $\mathrm{Cu}^{2+}$ IN $\mathrm{ZnWO}_4$

Phase Holograms of Tracks in Bubble and Emulsion Chambers and Their Processing Capabilities

This paper investigates the use of phase holography for recording and processing particle tracks in bubble chambers and emulsion chambers, where high track density makes event selection difficult in conventional photography. Using artificial tracks in a gelatin bubble chamber as a model, the authors…

An exceptional case of a dual integral equation of convolution type

The paper studies the exceptional case of paired integral equations of convolution type in weighted Banach spaces, where the operator symbol is allowed to have zeros of finite integer order on the real axis. It introduces the notion of a left equivalent normalizer and constructs such an operator to …

Linear boundary value problems with small lag

It is proved that in linear boundary value problems, the property of a parameter being an eigenvalue or a regular value is preserved under small changes in the delay. Bibliography: 6 items.

Optimality Conditions in Control Problems with Intermediate Conditions

This paper derives optimality conditions for control problems in which trajectories of a nonlinear dynamical system must satisfy endpoint constraints and an additional intermediate constraint, with initial, intermediate, and terminal times possibly determined by constraint equations. Using Pontryagi…

Contact problem for a linear deformable foundation

A spatial contact problem regarding the pressure of a strip punch on an elastic foundation with an elastic modulus $E=E_m z^m$ ($0<m<1$) is solved. Using the method of Fourier integral transforms, the problem is reduced to dual integral equations of trigonometric type. By means of an existing soluti…

ON THE APPROXIMATION OF PERIODIC FUNCTIONS BY LINEAR METHODS OF SUMMATION OF FOURIER SERIES

The paper studies approximation of periodic functions by linear summation methods for Fourier series, using moduli of smoothness, best trigonometric approximation, conjugate functions, and bounded subadditive operators. It establishes direct and inverse estimates for iterated convolution differences…

PLANE AND AXISYMMETRIC FILTRATION PROBLEMS WITH FREE BOUNDARIES IN AN INHOMOGENEOUS MEDIUM

This paper studies plane and axisymmetric filtration problems with free boundaries in inhomogeneous media, focusing on cases where the image of the filtration domain in the complex potential plane is known. The problems are formulated as inverse mixed boundary value problems for a system generalizin…