Recent Papers

AXIOMATICS OF MEASURE THEORY IN LINEAR SPACES

This note proposes an axiomatic treatment of measure theory in real linear spaces that avoids assuming a locally convex topology and instead formulates compatibility between the linear and measure structures through measurable partitions and generalized convolutions. The argument centers on linear m…

GROUPS SATISFYING THE WEAK MINIMAL CONDITION

This paper introduces the weak minimal condition for subgroups, excluding infinite descending chains in which each successive subgroup has infinite index, as a relaxation of the usual minimal condition. It proves basic closure properties, including stability under extensions, and shows that for loca…

CURRENT–VOLTAGE CHARACTERISTIC OF A SEMICONDUCTOR–DIELECTRIC HETEROCONTACT

This paper analyzes the current-voltage characteristic of electron emission from a semiconductor into a dielectric, motivated by experimental observations of cubic current laws in semiconductor-dielectric structures. The authors argue that such behavior need not be attributed solely to trap filling …

ON A LINEAR FORM IN LOGARITHMS OF ALGEBRAIC NUMBERS

This note establishes an effective lower bound for a nonhomogeneous linear form in logarithms of algebraic numbers under a rational linear independence assumption on the logarithms. It defines height-like parameters through the lengths of the algebraic numbers and states an explicit inequality depen…

THE CRYSTAL STRUCTURE OF BARIUM TETRAGERMANATE

The study determines the crystal structure of barium tetragermanate, BaGe4O9, in order to test earlier proposals that compounds of this type contain Ge3O9 rings and octahedrally coordinated germanium. Single-crystal X-ray diffraction data were collected with anomalous scattering from barium used to …

ON A. N. TIKHONOV’S FIXED-POINT PRINCIPLE IN EQUATIONS WITH OPERATORS WEAKLY CLOSED ON THE KERNEL

The paper studies solvability of nonlinear operator equations in locally convex and reflexive Banach spaces, extending ideas related to A. N. Tikhonov’s fixed point principle. It proves an existence theorem for equations \(F(x)=0\) under a boundary positivity condition on a set surrounding the origi…

ON THE SOLVABILITY OF THE FIRST BOUNDARY-VALUE PROBLEM FOR A SECOND-ORDER ELLIPTIC EQUATION WITH DIVERGENT PRINCIPAL PART IN \(W_2^1\)

This paper studies the first Dirichlet problem in \(W_2^1\) for uniformly elliptic second-order equations in divergence form whose lower-order coefficients have integrability at or below the usual \(L_p\), \(p>n/2\), threshold. It introduces mixed-norm spaces \(L_{(r_1,r_2)}\), proves embedding and …

Corrections to the article On the Axiom of Complete Induction (DAN, Vol. 173, No. 2)

ON THE ACCURACY OF THE APPROXIMATION OF THE DISTRIBUTION OF A SUM OF INDEPENDENT RANDOM VARIABLES TO THE NORMAL DISTRIBUTION

This paper studies the uniform accuracy of the normal approximation for normalized sums of independent identically distributed random variables, especially when higher moments needed for classical asymptotic expansions are infinite. It introduces functionals of truncated moments and tail integrals t…

Asymptotic Properties of Solutions of Systems of Integral Equations on the Half-Line

This paper studies the asymptotic behavior of positive solutions to systems of integral equations on the half-axis with nonnegative matrix kernels of finite forward range. By comparing two solutions and deriving a recursive integral equation for their componentwise ratio, it establishes conditions u…

NONUNITARY OPERATORS WITH ABSOLUTELY CONTINUOUS SPECTRUM ON THE UNIT CIRCLE

This paper studies criteria under which nonunitary operators are linearly similar to unitary or self-adjoint operators with absolutely continuous spectrum. Using characteristic matrix and operator functions, it proves boundedness conditions that imply similarity for the simple parts of bounded opera…

PROJECTIVE SETS OF TOPOLOGICAL SPACES OF WEIGHT \(\tau\)

This paper studies projective hierarchies of classes of sets in topological spaces of weight τ, including the spaces Dτ, Jτ, Dων, and Jων, under the assumption that τ is strongly inaccessible. Using set-theoretic operations with variable bases and ΔΣ-operations, it characterizes how projections of F…

INVESTIGATION OF THE GAS-DYNAMIC STABILITY OF A DETONATION WAVE OF ARBITRARY PROFILE

This paper examines the gas dynamic stability of plane detonation waves for arbitrary heat release kinetics, motivated by cases where Arrhenius temperature dependence is not an adequate description. The authors propose a stepwise model of the detonation zone, representing it as an initiating shock f…

CRYSTAL OPTICS TAKING INTO ACCOUNT THE MAGNETOELECTRIC EFFECT

This paper develops a formulation of crystal optics that includes the magnetoelectric effect, allowing the electric and magnetic inductions to depend linearly on both electric and magnetic fields. It derives tensor restrictions from energy conservation and absence of absorption, decomposes the magne…

FACTORIZATION OF FINITE GROUPS

This paper studies factorizations of finite groups through additions to normal subgroups and through decompositions associated with invariant and chief series. It proves several criteria concerning when additions yield complements, including generalizations of results of Hall, Huppert, Roquette, Sch…

FIXED POINTS OF NONCOMPACT MAPPINGS

This note develops a finite-dimensional projection construction for proving fixed point existence for mappings on weakly compact convex subsets of Banach spaces, extending the Schauder and Tikhonov principle beyond compact or weakly continuous operators. The authors associate to a mapping a family o…

COMPLEXES OF \(k\)-DIMENSIONAL PLANES IN THE SPACE \(C^n\) AND THE PLANCHEREL FORMULA FOR THE GROUP \(GL(n,C)\)

This paper studies integral-geometric transforms that assign to a rapidly decreasing smooth function on complex affine space its integrals over planes belonging to an algebraic complex of k-dimensional planes. It defines admissible complexes, for which an inversion formula follows from earlier gener…

ON EQUATIONS AND BOUNDARY-VALUE PROBLEMS IN THE THEORY OF TWO-PHASE FILTRATION FLOWS IN A POROUS MEDIUM

This paper reformulates the equations for isothermal two-phase filtration of incompressible immiscible fluids in an inhomogeneous porous medium, including relative permeabilities, capillary pressure, gravity, and density differences. By taking either phase pressure and saturation as unknowns, the au…

X-RAY DIFFRACTION STUDY OF STRUCTURAL FEATURES OF CRYSTALS OF CUBIC BORON NITRIDE

Single-crystal Laue X-ray diffraction was used to examine structural features of about 50 individual cubic boron nitride crystals, addressing lattice perfection, twinning, accessory phases, and defect distributions not accessible from earlier powder studies. The study found that only some visually s…

ON THE DIMENSION OF THE PRODUCT OF ONE-DIMENSIONAL BICOMPACTA

The paper studies dimension properties of products of one-dimensional bicompacta, proving that for a finite product of n bicompact spaces with large inductive dimension one, the covering, small inductive, and large inductive dimensions all equal n. The argument develops partition lemmas for normal s…

$\theta$-PROXIMITIES AND $\theta$-ABSOLUTES

This paper extends the concept of theta-proximity to arbitrary Hausdorff spaces and relates it to irreducible theta-perfect mappings of completely regular spaces and their bicompact extensions. Using centered systems of open sets, it proves representation and uniqueness theorems showing that every t…

ON EXPANSION IN EIGENFUNCTIONS OF THE SCHRÖDINGER OPERATOR WITH A STRONGLY SINGULAR POTENTIAL

This paper studies spectral expansion for Schrödinger operators in Euclidean space with strongly singular potentials that become infinite on a set, motivated by approximating an impenetrable barrier by finite barriers. Using semigroup convergence for truncated potentials and scattering solutions sat…

SPHERICAL SOUND WAVES IN RIEMANNIAN SPACE

The paper studies spherically symmetric sound waves in a medium interacting with its own gravitational field within a Riemannian, relativistic hydrodynamic framework. It formulates the governing equations for velocity, specific volume, entropy, and metric functions, recovers the Oppenheimer Volkov e…

ON SOME PROPERTIES OF NONCONSERVATIVE SYSTEMS OF CLASSICAL STATISTICAL MECHANICS

This paper examines classical statistical mechanical systems whose energy is not conserved because external generalized forces act on the particles. Starting from non-Hamiltonian equations of motion, it derives a generalized Liouville equation and identifies a phase-space divergence condition as the…

ON SINGULAR INTEGRAL EQUATIONS IN A CONE

This paper studies singular integral operators with homogeneous degree zero symbols in weighted Sobolev type spaces on Euclidean space and in cones. It establishes necessary and sufficient conditions on the weight exponent for boundedness in one dimension and in higher dimensions, including cases ou…

On the Problem of Extending Linear Positive Functionals

This paper studies when a linear positive functional defined on a subspace of a real Banach space with a cone can be extended to the whole space while preserving linearity and positivity. It gives several necessary and sufficient criteria in terms of closures of algebraic sums involving the cone and…

THE PHASE PROBLEM AND THE CORRELATION PROPERTIES OF X-RAY BEAMS

This paper examines the crystallographic phase problem for non-centrosymmetric crystals and proposes using two-beam interference of X-ray radiation to obtain phase information not available from reflection intensities alone. Starting from first-order correlation functions for coherent electromagneti…

WAVE ADIABATS FOR MEDIA WITH AN ARBITRARY EQUATION OF STATE

This paper studies wave adiabats for gases or liquids with nonconvex, anomalous equations of state, where the usual entropy increase condition is insufficient to select admissible shock states. It proposes stability and continuity requirements, states several theorems on the local structure, monoton…

ROTATION AND ORIENTATION OF COSMIC DUST GRAINS

The paper proposes a mechanism for the rotation and orientation of nonspherical cosmic dust grains based on statistical fluctuations in impacts from directed particle or photon fluxes, a factor neglected in earlier models of grain alignment. Using Poisson estimates for unequal impacts on opposite si…

INVESTIGATION OF A WEAK SOLUTION OF A MIXED PROBLEM FOR A HYPERBOLIC EQUATION WITH A NONLINEAR PART

This paper studies weak solutions of a mixed initial boundary value problem for a hyperbolic equation with a nonlinear term, where the linear part is generated by a self-adjoint positive operator. The solution is defined through an integral identity with test functions adapted to the operator domain…

ON THE PROBLEM OF MINIMALITY FOR SUBGROUPS IN LOCALLY FINITE GROUPS

This paper studies the minimality condition for subgroups in locally finite and periodic groups, continuing earlier work on quasi-extremal and extremal groups. It reduces the minimality problem for locally finite groups to the case of infinite simple quasi-extremal groups with involutions, and descr…

ON A BOUNDARY VALUE PROBLEM FOR LINEAR PARABOLIC EQUATIONS WITH DISCONTINUOUS COEFFICIENTS

The paper studies the first boundary value problem for linear parabolic equations in a bounded cylinder, allowing discontinuous leading coefficients and unbounded lower order coefficients and free terms. For the case in which relevant spatial integrability exponents may be below the dimension, it fo…

Adsorption Mechanism of the Escape of the Lunar Atmosphere

This paper addresses the apparent absence of a significant lunar atmosphere despite evidence that volcanic activity, meteorite impacts, and radioactive decay could release gases from the Moon. It argues that thermal escape alone cannot account for the loss of heavier atmospheric constituents, and th…

CRYSTAL STRUCTURE OF THE SUBOXIDE $\mathrm{Ti_2ZrO}$

This paper reports a neutron and X-ray diffraction study of a newly observed suboxide phase in the titanium, zirconium, oxygen system, with composition corresponding to Ti2ZrO. Cast and quenched alloys were examined, and reflection intensities were compared with multiple structural models to determi…

ON DYADIC BICOMPACTS

THREE THEOREMS ON NONLINEAR EQUATIONS

This paper proves three results on nonlinear equations involving monotone operators in Banach spaces. It first establishes convergence of the least squares method for equations with strongly monotone operators under either finite-dimensional continuity with completeness of the approximating system o…

On Bicompacta with Noncoinciding Dimensions

The paper addresses Aleksandrov’s problem on the possible noncoincidence of covering dimension and small inductive dimension for bicompact spaces, with attention to examples satisfying separability and the first axiom of countability. It constructs a separable bicompactum whose topology is defined o…

A VARIATIONAL METHOD FOR SOLVING IRREGULAR ELLIPTIC EQUATIONS

This paper develops a variational framework for solving higher order elliptic equations with possibly irregular or degenerate coefficients on arbitrary open sets. It introduces weighted Sobolev type spaces and uses generalized Hardy inequalities to obtain embedding results, local summability and dif…

ON THE ACCURACY OF THE KIRCHHOFF–LOVE HYPOTHESIS IN DETERMINING CRITICAL FORCES IN THE THEORY OF ELASTIC STABILITY

The paper examines the accuracy of the Kirchhoff-Love hypothesis for calculating critical buckling forces in elastic stability problems. Using three-dimensional linearized equations of the nonlinear theory of elasticity, it analyzes a thick orthotropic plate compressed in one direction and derives a…

EUTECTIC STRUCTURE OF MUSCLE AND CONNECTIVE TISSUES

This paper applies an epitaxial model of eutectic crystallization to biological tissues, comparing metallic eutectics with muscle, connective tissue, and mineralized skeletal structures. It argues that, as in eutectic melts where small crystals of one component grow in crystallographically parallel …

GENERALIZED SELF-ADJOINT EXTENSIONS OF SYMMETRIC OPERATORS

The paper introduces generalized self-adjoint extensions of densely defined symmetric operators using a scale of Hilbert spaces generated by the graph norm on the domain of the adjoint. It shows that every closed symmetric operator can be extended from the domain of its adjoint into the correspondin…

ON SOLVABLE GROUPS OF FINITE RANK

This paper studies groups possessing rational series, whose factors embed in the additive group of rational numbers, and examines the relation between rational rank and special rank. Using properties of solvable torsion-free groups of finite rank and groups satisfying the weak minimal condition for …

SOLUTION OF THE GRAVITATIONAL EQUATIONS IN A HOMOGENEOUS, COMPLETELY ANISOTROPIC MODEL

This paper derives homogeneous but fully anisotropic cosmological solutions of the Einstein equations for a flat three-space filled with ideal matter in a comoving synchronous frame. Using scale factors along three spatial axes and the metric determinant, the analysis reduces the field equations for…

TRANSFORMATIONS PRESERVING HARMONIC COORDINATES

The paper studies coordinate transformations in an arbitrary Riemannian space that map every harmonic coordinate system to another harmonic coordinate system, treating the question locally and using Lie group methods for differential equations. It proves that, when such transformations form a contin…

INTEGER POINTS IN PERTURBED CIRCLES

The paper studies the lattice point discrepancy for plane convex domains whose boundary is a small smooth perturbation of a circle. Assuming a polar representation with the perturbation and its first four angular derivatives uniformly of order o(R), the argument applies Fourier coefficients of chara…

ON THE LIOUVILLE THEOREM FOR GENERALIZED ANALYTIC FUNCTIONS

This paper extends Liouville-type results for generalized analytic functions to first-order elliptic systems with constant coefficients in the plane. It studies entire regular solutions of the system ∂w/∂z̄ + aw + b w̄ = 0 subject to polynomial growth of order at most N, using Fourier transforms of …

ON ORIENTED QUASICONFORMAL MAPPINGS IN SPACE

The note studies oriented quasiconformal mappings in Euclidean space, defined in the Sobolev class by a distortion inequality with nonnegative Jacobian almost everywhere. Using an integral estimate for the Jacobian, it derives local \(L^n\) bounds for the differential in terms of one coordinate func…

MONOVALENT EUROPIUM IN NaCl—Eu AND KCl—Eu

A RAREFACTION WAVE AND THE EXPANSION OF A MEDIUM IN A VARIABLE GRAVITATIONAL FIELD

This paper analyzes the one-dimensional unsteady expansion of an ideal gas cloud ejected from a gravitating body, treating the cloud as small enough that its motion can be decomposed into center-of-mass motion and expansion relative to that center. Using gas-dynamic equations with a time-dependent N…

ON THE LENGTH OF THE RELAXATION ZONE OF IONIZATION BEHIND THE FRONT OF A STRONG SHOCK WAVE IN AIR

The paper examines the unexpectedly large length of the nonequilibrium ionization relaxation zone behind strong shock waves in air at velocities near 9 to 10 km/sec. The authors numerically solve coupled kinetic equations for dissociation, nitric oxide chemistry, ionization by heavy particles and el…