Recent Papers

Corrections to the paper “Density near the forward stagnation point of a blunt body in a supersonic rarefied gas flow” (DAN, vol. 161, no. 2, 1965)

AN ANALOGUE OF STONE’S THEOREM IN A SPACE WITH AN INDEFINITE METRIC

The paper formulates an analogue of Stone’s theorem for spaces with an indefinite metric, denoted by \(\Pi_\varkappa\), and for strongly continuous one-parameter groups of \(J\)-unitary operators. It proves that the generator of such a group has the form \(iH\), where \(H\) is \(J\)-self-adjoint and…

ON THE COMPUTATION OF STEADY SEA AND OCEAN CURRENTS

This paper develops a computational formulation for steady wind driven and climatologically forced currents in seas and oceans, using hydrostatic balance and vertical momentum exchange appropriate to shallow basins. The authors derive velocity, transport, surface slope, and integral stream function …

On the Energy Spectrum of an Electron in a “Defective” One-Dimensional Periodic Lattice

The paper studies the energy spectrum and density of states of an electron in a one-dimensional periodic lattice containing randomly distributed delta-function defects, with particular attention to behavior near band edges where perturbation expansions fail. By reducing the phase recurrence for Bloc…

DEPENDENCE OF THE ABSORPTION COEFFICIENT OF THE $1s$ BAND OF SINGLE CRYSTALS ON THE POLARIZATION AND ORIENTATION OF THE RADIATION

This paper analyzes how the absorption coefficient of the 1s band in single crystals depends on the polarization and orientation of x-ray radiation, using the quasi-atomic character of 1s states and crystal symmetry. General expressions are derived for polarized and unpolarized radiation, including …

ANTI-SCUFFING PROPERTIES OF OILS AS A FUNCTION OF THE RATE OF THEIR DECOMPOSITION IN THE FRICTION ZONE

This paper proposes a criterion for evaluating the anti-scuffing properties of lubricating oils based on the rate of their chemical decomposition in the friction zone, rather than on machine-dependent critical load values. It develops a model in which scuffing begins when oil entering the contact is…

Measurements of Solar-Origin Protons with Energies of $1\div5$ MeV during the Flights of the Venera-2, Venera-3, and Zond-3 Stations

Measurements from the Zond-3, Venera-2, and Venera-3 interplanetary stations are used to examine six increases in solar proton fluxes with energies of 1 to 5 MeV during 1965. The authors compare semiconductor proton detector data with Geiger counter readings, neutron monitor records, geomagnetic dis…

A BOUNDARY-VALUE PROBLEM FOR AN EQUATION OF MIXED TYPE WITH TWO LINES OF DEGENERATION

The paper studies a boundary value problem for the mixed type equation y(y minus 1)u_xx plus u_yy equals zero in a specially constructed finite domain containing intervals of both degeneration lines y equals 0 and y equals 1. It formulates admissible singular behavior and boundary data on elliptic a…

ON THE QUESTION OF THE INTERACTION OF SPINOR AND GRAVITATIONAL FIELDS

The paper addresses the formulation of Dirac-type equations for spinor fields in a curved Riemannian space-time without relying on the Fock-Ivanenko tetrad formalism, whose tetrads are not uniquely fixed by the metric. Starting from the mass-shell relation in a gravitational field, the authors deriv…

THE SAMPLE MEAN AS AN ESTIMATE OF A SHIFT PARAMETER

This paper studies when the sample mean is an admissible or optimal unbiased estimator of a shift parameter in families of one-dimensional distributions with finite moments. It introduces nested classes of unbiased estimators obtained by adding to the sample mean polynomials of degree at most k in t…

SUBGROUPS OF PERIODIC GROUPS

The paper studies infinite periodic groups in which any two elements generate a finite subgroup, termed F2-groups, a class containing all locally finite groups. Using normalizer criteria, conjugacy class arguments, and finite group results including the Feit-Thompson theorem, it proves that every F2…

SOME QUESTIONS IN THE THEORY OF ATMOSPHERIC CONDENSATION NUCLEI

This paper develops a theoretical treatment of atmospheric condensation nuclei by introducing an activity parameter that links nucleus composition and dry size to equilibrium supersaturation and droplet growth. From this framework, it derives relations between size distributions, activity spectra, a…

ON THE RELATION BETWEEN THE HYDRODYNAMIC AND ELECTRICAL CHARACTERISTICS OF A DISCHARGE IN A LIQUID

This paper examines the relation between electrical energy release and hydrodynamic behavior in moderate current discharges in water, where magnetic forces and strongly supersonic channel expansion can be neglected. Using an approximate energy balance for the discharge channel, an acoustic treatment…

EQUIAFFINE GEOMETRY OF A DUAL FIELD AND ITS APPLICATION TO THE THEORY OF STEADY FLUID FLOW

This paper develops an equiaffine geometric description of a dual field in three-dimensional space, consisting of a vector and a covector with unit contraction, using Cartan’s exterior forms. It derives invariant vectors, covectors, and tensors associated with such fields and relates them to line co…

THE TRICOMI PROBLEM FOR AN ELLIPTIC-HYPERBOLIC EULER—POISSON—DARBOUX EQUATION

The paper studies a Tricomi-type boundary value problem for an elliptic-hyperbolic Euler-Poisson-Darboux equation and for a related equation reducible to it by a power substitution. Under stated restrictions on the parameters, the problem is transformed by a one-to-one change of variables into the s…

ON LOGIC OF HIGHER LEVELS

This note strengthens earlier results on logics of higher levels, focusing on definability, spectra of formulas, and the expressive limits of finite and transfinite levels of higher-order languages. It proves that for each natural level there are formulas not equivalent to any set of lower-level for…

THE METHOD OF DIFFERENTIAL DESCENT FOR SOLVING MULTIDIMENSIONAL VARIATIONAL PROBLEMS

This paper studies differential descent trajectories for minimizing functionals and solving nonlinear operator equations in Hilbert spaces, with extensions indicated for Hilbert and Banach manifolds. It establishes local convergence criteria based on inequalities relating a functional or residual no…

COMPARISON THEOREMS FOR VOLTERRA EQUATIONS WITH RETARDED ARGUMENT

AN ANOMALY IN THE COMPOSITION OF THE IONS FORMED AND CERTAIN PHENOMENA IN THE LOWER IONOSPHERE

This paper examines discrepancies between observed lower ionospheric behavior and models that treat the effective recombination coefficient as constant at altitudes of 100 to 200 km. Using calculated ion formation rates for solar radiation in different spectral intervals, it argues that absorption-i…

ON THE APPROXIMATION OF FUNCTIONS BY FOURIER–JACOBI SUMS

This note studies uniform approximation of functions by partial sums of Fourier series in orthonormal Jacobi polynomials on the interval with Jacobi weight. For functions whose r-th derivative satisfies a Lipschitz condition of order gamma, it derives upper estimates for the supremum norm of the Fou…

A CRITERION FOR THE DISCRETENESS OF THE SPECTRUM OF A SELF-ADJOINT SYSTEM OF FIRST-ORDER DIFFERENTIAL EQUATIONS WITH SLOWLY VARYING COEFFICIENTS

This paper studies the spectrum of a self-adjoint first-order differential system on the real line with a constant diagonal principal part and continuous Hermitian, slowly varying coefficients, including a form related to the Dirac operator considered by Titchmarsh. Using splitting principles and lo…

AN ITERATIVE METHOD FOR SOLVING A CONVEX PROGRAMMING PROBLEM

The paper develops an iterative method for minimizing a linear functional over a closed convex set, including sets defined by systems of smooth convex inequalities. It introduces Fejér and convergent Fejér operators, gives constructions of such operators from defining convex functions and gradients,…

ON FUNCTIONS OF SPECIAL OPERATORS IN THE THEORY OF ELASTIC-HEREDITARY MEDIA

The paper examines how functions of integral operators with fractional exponential kernels can be used in applying Volterra’s principle to elastic hereditary media, especially when elastic solutions contain irrational or transcendental functions of material constants. It develops series representati…

HYDRODYNAMIC STABILITY OF A SPHERICAL FLAME

This paper analyzes the hydrodynamic stability of a freely expanding spherical laminar flame and addresses why experiments show instability only at Reynolds numbers far above those suggested by Landau’s plane-flame theory. The authors formulate a stability criterion based on growth of the disturbanc…

On the initial direction of the crystallization process when immersing a plate in a melt

This paper analyzes an idealized Stefan problem for the initial phase changes that occur when an infinite plate below its melting temperature is immersed in a stirred melt above its crystallization temperature. Three possible initial regimes are formulated mathematically: simultaneous crystallizatio…

ON CONDITIONS FOR THE SOLVABILITY OF THE CHAPLYGIN PROBLEM

The paper studies solvability conditions for the Chaplygin comparison problem for differential equations in a partially ordered functional setting. It gives a necessary condition, and in the linear case a sufficient one, in terms of preservation of negativity for solutions of an adjoint variational …

MOTION OF A NEUTRAL FERMION POSSESSING AN ANOMALOUS MAGNETIC MOMENT IN AN ELECTRIC FIELD

This paper analyzes the motion of a neutral Dirac fermion with an anomalous magnetic moment in a static electric field directed along the z axis. By using commuting momentum operators and a polarization tensor operator to classify spin states, the Dirac equation is reduced to coupled equations for t…

ASYMPTOTICS OF THE ERROR OF CUBATURE FORMULAS WITH A BOUNDARY LAYER REGULAR IN THE SENSE OF S. L. SOBOLEV

This note derives asymptotic estimates for the error norms of cubature formulas in weighted Sobolev type spaces \(H_2^{(\mu)}(\Omega)\), under regularity and growth assumptions on the weight function. It introduces cubature formulas with a boundary layer regular in the sense of S. L. Sobolev, charac…

Investigation of computational algorithms for the approximate integration of differential equations using the finite difference method

This review discusses P. S. Bondarenko’s monograph on finite difference algorithms for the approximate integration of differential equations, with particular attention to the distinction between abstract algorithms using exact arithmetic and real algorithms using fixed precision arithmetic with roun…

ON SOME PROPERTIES OF WEIGHT CLASSES

This note studies density and trace properties in weighted Sobolev spaces, with weights depending on the distance to a boundary or to a coordinate hyperplane. It gives conditions under which functions in first order weighted spaces on a cube can be approximated in the weighted norm by smooth functio…

A NEW OPTICAL AND CATHODOLUMINESCENT MATERIAL WITH GLASS-FIBER PROPERTIES

This paper describes a cathodoluminescent crystal-fiber material produced by heat treatment of glasses close to zinc orthosilicate composition, in which elongated willemite crystallites form within a lower-index glassy phase and act as light-guiding fibers. Electron microscopy and optical testing sh…

THE STRUCTURE OF ELEMENTARY REPRESENTATIONS OF A SEMISIMPLE COMPLEX LIE GROUP

This note studies elementary representations of a connected semisimple complex Lie group, obtained by analytic continuation of the principal series and parametrized by characters of a Cartan subgroup. It defines spectral bases and indicators for these signatures and proves a criterion for complete i…

NONSTATIONARY PROBLEMS OF QUANTUM MECHANICS AND THE LAPLACE TRANSFORM

This paper develops an exact treatment for a class of nonstationary Schrödinger equations in which the time-dependent perturbation is a rank-one projection operator with a coefficient linear, or in a related case linear-fractional, in time. Using a Laplace-transform type contour integral representat…

A RELAXATION METHOD FOR FINDING A COMMON POINT OF CONVEX SETS AND ITS APPLICATION TO OPTIMIZATION PROBLEMS

This paper develops a general relaxation method for finding a point common to a family of closed convex sets in a linear topological space, using generalized projections defined by a nonnegative distance-like function. Under stated compactness, convexity, and continuity conditions, it proves converg…

ON REMAINDER TERMS

The paper studies remainder terms in multidimensional central limit and asymptotic expansion theorems for normalized sums of independent identically distributed random vectors with finite moments. It addresses whether logarithmic factors in known convergence estimates for convex or Borel sets can be…

AN ANALOGUE OF THE RADÓ—CARTAN THEOREM FOR SOLUTIONS OF ELLIPTIC EQUATIONS

This note proves an analogue of the Radó-Cartan removability theorem for solutions of second-order elliptic equations. For a continuously differentiable function satisfying a linear elliptic equation off the boundary of its zero set, under standard Hölder regularity assumptions on the coefficients, …

CAPACITY OF A SET IN SIGNAL SPACE AND A RIEMANNIAN METRIC

This paper defines the capacity of a subset of an input signal space for a statistical channel given by a family of probability measures, and relates this quantity to distinguishability and Shannon information. It proves basic properties of capacity, including subadditivity and multiplicativity for …

ON BASES OF PRIMITIVE-RECURSIVELY CLOSED CLASSES OF FUNCTIONS

The paper studies when a primitive-recursively closed class of functions admits a finite basis from which all functions in the class can be obtained by substitution alone. It proves that such a class has a finite basis exactly when it contains a universal function for its unary members, deriving con…

A general boundary value problem for elliptic systems of second order with constant coefficients. II

INVESTIGATION OF THE DEFECT OF AN ABSTRACT CAUCHY PROBLEM

This paper studies the defect of the abstract Cauchy problem \(dx(t)/dt=Ax(t)\) for a closed linear operator in a Banach space, especially when the operator domain is not dense. It defines the defect as the dimension of the quotient between the closure of the domain and the closure of the initial ma…

THE METHOD OF PROJECTIONS IN THE STUDY OF SOLUTIONS OF ELLIPTIC EQUATIONS

This paper develops a projection method for studying bounded lower semicontinuous solutions of elliptic inequalities in a domain of Euclidean space. It defines lower and upper projections of a function onto planes and shows that, under assumptions involving absolute continuity of the support mapping…

ON A BASIS FOR RECURSIVELY ENUMERABLE SETS

The paper introduces the class of predicates defined as the intersection of s-rudimentary predicates with predicates computable by a Turing machine with logarithmic slowdown, and compares it with several previously studied restricted classes used in Kleene normal form and enumeration theory. It prov…

SIMPLE BASES IN CLOSED CLASSES OF FUNCTIONS OF THE ALGEBRA OF LOGIC

The paper studies simple bases, minimal complete systems that cannot be simplified by identifying variables, for closed classes of functions in the algebra of logic. Building on Post’s classification of closed Boolean function classes and known criteria for completeness via precomplete subclasses, i…

ON FREE POLYNILPOTENT GROUPS

The paper studies subgroups of free polynilpotent groups, defined through iterated terms of the lower central series and viewed as free groups in products of nilpotent varieties. Extending earlier results on free soluble groups, it gives a criterion for when a subgroup lying between successive itera…

THE INTEGRAL OVER A PARABOLOID AND THE FIRST BORN APPROXIMATION

The paper studies the first Born correction for the Helmholtz-type equation with an incident plane wave, focusing on its dependence on the potential and on the wave number as the latter tends to infinity. By rewriting the correction as a Fourier-type integral whose kernel is an integral of the poten…

ON SOME IDENTITIES OF THE GENERAL THEORY OF ORTHOGONAL POLYNOMIALS AND THEIR APPLICATIONS

This note derives identities in the general theory of orthogonal polynomials for sums involving derivatives, complementing the Christoffel-Darboux formula for orthonormal polynomial systems on an interval. It proves formulas for the kernel sum of first derivatives, its diagonal specialization, and c…

ON THE DECOMPOSITION OF MULTIDIMENSIONAL PROBABILITY LAWS

This paper develops multidimensional analogues of results on decompositions of probability laws, especially Raikov’s theorems on holomorphic characteristic functions and infinitely divisible laws without Gaussian components. It proves that a characteristic function holomorphic in a ridge domain cont…

ON THE DEPENDENCE BETWEEN STRESSES AND STRAINS IN THE NEIGHBORHOOD OF A CORNER POINT OF THE LOADING PATH

This paper examines the relation between stress and plastic strain increments in an infinitesimal neighborhood of a corner point of the loading path, within a previously proposed slip-based model of plane plastic deformation. For a state reached by monotonic loading, the authors derive integral cond…

WELL-POSEDNESS OF THE CAUCHY PROBLEM AND ANALYTICITY OF SOLUTIONS OF AN EVOLUTION EQUATION

This paper studies the Cauchy problem for the evolution equation dx/dt equals Ax in a Banach space, where A is a closed densely defined unbounded operator, and relates well-posedness to resolvent estimates and semigroup properties. It introduces the well-posedness set and the uniform well-posedness …

ON THE GENERATION OF CONTINUOUS EMISSION IN COLD STARS

This paper proposes a mechanism for the continuous emission observed during flares of cool G, K, and M stars, where brightness increases most strongly in the ultraviolet and the star becomes markedly bluer. It argues that a layer of fast electrons, possibly released with matter ejected from the stel…