Recent Papers

ESTIMATING THE LIMITING RATE OF DECREASE OF SOLUTIONS OF AN ELLIPTIC SYSTEM

A NEW INSTRUMENT FOR DETERMINING THE INTENSITY OF γ-RADIATION—A GAUSS QUANTOMETER

This paper presents the design and testing of a gamma radiation quantometer intended to determine beam intensity by automatically integrating the depth dose, or transition, curve in an absorber. The authors argue that replacing Simpson-type integration used in earlier Wilson quantometers with a six-…

REDUCTION OF SYSTEMS

ATMOSPHERIC OZONE OVER THE TROPICAL BELT OF THE ATLANTIC OCEAN

This paper examines variations in total atmospheric ozone over the tropical Atlantic between 25° N and 25° S using ozonometric and radiosonde observations from the fourteenth cruise of the research vessel Mikhail Lomonosov in August to November 1963. It compares the observed latitudinal ozone distri…

New Books

This bibliographic notice surveys recently published mathematical books and collected volumes available in 1965, with emphasis on differential equations, mathematical physics, operator theory, numerical methods, and related areas of analysis. It lists monographs, textbooks, translated works, proceed…

PHENOMENOLOGICAL THEORY OF THE SYMMETRY OF ORDERED PHASES

This paper develops a phenomenological symmetry method for determining the complete symmetry of stable ordered phases, focusing on ordinary superstructures whose translational periods do not vary within a single phase region. For binary substitutional solutions on Bravais lattices, the concentration…

Integral Representations of Holomorphic Functions of Several Complex Variables

The paper studies integral representations for holomorphic functions of several complex variables that retain a feature of the one-variable Cauchy formula, namely kernels with first-degree denominators or one-variable Cauchy integrals. It first proves reconstruction formulas for functions holomorphi…

A CONTINUOUS MEDIUM WITH SPINOR AND VECTOR CHARACTERISTICS

The paper develops a variational formulation for a relativistic continuous medium in a four-dimensional Riemannian space whose state includes spinor and vector characteristics, with coupling to gravitational and electromagnetic fields. It first defines covariant differentiation and parallel transpor…

ON THE EQUILIBRIUM SHAPE OF A TWIN WHOSE GROWTH IS INHIBITED BY AN OBSTACLE

This paper investigates the equilibrium shape of twin lamellae in bismuth single crystals when their growth into the crystal is either unobstructed or arrested by obstacles. Using optical observations during deformation, the authors compare the geometry of freely growing and pinned twins with predic…

ON SELF-SIMILARLY STABLE SOLUTIONS OF THE TRAVELING-WAVE TYPE FOR CERTAIN QUASILINEAR EQUATIONS, INCLUDING THE EQUATIONS OF WATER FLOW IN AN INCLINED CHANNEL

The paper studies self-similar traveling wave solutions with discontinuities for a scalar quasilinear equation and for equations describing water flow in an inclined channel. It defines stability under the addition of small dissipation and proves that, for a symmetric source term with a single sign …

RECURRENT SOLUTIONS OF DIFFERENTIAL EQUATIONS

This note studies the existence of completely recurrent solutions of nonautonomous differential equations in a Banach space. It develops characterizations of completely recurrent mappings through a shift dynamical system and uses these properties to prove criteria for equations of the form dx/dt = f…

HOMEOMORPHIC MAPPINGS IN THREE-DIMENSIONAL EUCLIDEAN SPACE THAT PRESERVE ANGLES FOR RAYS

This paper studies homeomorphic mappings of domains in three-dimensional Euclidean space that preserve angles only for rays issuing from each point, a weaker condition than uniform preservation of angles for arbitrary curves. It proves that any such mapping is a Möbius transformation on the domain. …

ANALOGY OF SYSTEMS OF DIFFERENTIAL EQUATIONS NEAR A SINGULAR POINT

The paper studies nonlinear systems of ordinary differential equations near a singular point by comparing them with their linear part, under smallness conditions on the nonlinear term expressed through a Lipschitz function. It proves the existence of local homeomorphisms that relate stable solutions…

ABSORPTION OF MICRORADIO WAVES IN AIR BY WATER-VAPOR DIMERS

This paper addresses the observed excess absorption of centimeter, millimeter, and near submillimeter radio waves by atmospheric water vapor relative to calculations based on water monomers. After rejecting explanations based on inaccurate monomer line widths or isotopic water molecules, the authors…

ELECTRON-OPTICAL REGISTRATION OF X-RAY DIFFRACTION

This paper examines electron-optical registration as a means of reducing the exposure time required to record X-ray diffraction patterns. The authors describe an experimental setup in which a diffraction image formed on a fluorescent screen is optically transferred to an electron-optical converter a…

GROUPS WITH PRESCRIBED PROPERTIES OF SYSTEMS OF INFINITE SUBGROUPS

This paper studies infinite groups defined by restrictions on their infinite subgroups, especially groups in which all infinite abelian subgroups are invariant and locally finite groups in which no infinite proper subgroup coincides with its normalizer. It establishes structural results for these cl…

ON PARABOLIC EQUATIONS WITH CONTINUOUS COEFFICIENTS

The note examines whether linear parabolic equations with merely continuous leading coefficients necessarily possess classical solutions, bounded adjoint solutions, or solutions with bounded derivatives in the self-adjoint case. It constructs a one-dimensional uniformly parabolic equation whose coef…

SELENIUM AS A POLYMERIC SEMICONDUCTOR AND THE MECHANISM OF ITS CONDUCTIVITY

This paper examines the electrical conductivity, thermoelectric power, and Hall effect of high purity selenium in solid and liquid states from 20 to 450°C, including the melting region, with attention to the role of oxygen and compensating impurities. The authors interpret the temperature dependence…

MAGNETOHYDRODYNAMIC INSTABILITIES DURING AN ELECTRICAL EXPLOSION

This study investigates the mechanism by which conductors are destroyed during electrical explosion, motivated by the observation that the explosion threshold energy exceeds the melting energy but is below the vaporization energy. Using pulsed x-ray shadow photography of copper, lead, tungsten, moly…

ON SOME NEW RESULTS IN THE THEORY OF RESOLVENTS OF HERMITIAN OPERATORS

The paper develops a theory of resolvent matrix functions for simple closed Hermitian operators in Hilbert space with equal deficiency indices, allowing the index to be infinite. Using a representation subspace, projector functions, and an associated operator function, it establishes a compact ident…

Bibliography of Journal Articles

This publication is a compiled bibliography of recent journal articles in differential equations, mathematical physics, integral equations, and numerical methods, with particular emphasis on Soviet mathematical literature from 1965 and early 1966. The entries are organized by subject area and list a…

THE INFLUENCE OF COULOMB COLLISIONS ON THE DRIFT INSTABILITY OF PLASMA

This paper analyzes how Coulomb collisions affect drift and drift-cyclotron instabilities in a low-pressure inhomogeneous magnetized plasma. Using the Landau collision integral rather than a model collision term, the authors derive local oscillation spectra in a geometrical-optics approximation for …

LAYERED GROWTH OF CRYSTALS

This paper investigates whether polymorphic transformations in organic crystals proceed by the same layer-by-layer growth mechanism known for crystal growth from liquids and vapors. Using optical microscopy and microcinematography, the authors observed the alpha to beta transformation of n-dichlorob…

ON THE GLOBAL BEHAVIOR OF PHASE TRAJECTORIES OF QUASILINEAR DIFFERENTIAL EQUATIONS WITH DELAYED ARGUMENTS

This paper studies the global asymptotic behavior of phase trajectories for quasilinear differential equations with delayed arguments and small nonlinear perturbations. It formulates the phase space for such delay systems, compares the associated period mapping with that of an auxiliary ordinary dif…

ON THE CONSTRUCTION OF SMALL SOLUTIONS OF A CLASS OF NONLINEAR INTEGRAL EQUATIONS

Investigation of a regenerative optocoupler with optical feedback

This paper analyzes an optoelectronic cell, or regenerative optron, with direct electrical coupling and positive optical feedback, focusing on the conditions under which it exhibits a bistable current-voltage characteristic. Using a piecewise approximation for the light-emitting diode output and equ…

ON FUNCTIONAL EQUATIONS OF DIRICHLET FUNCTIONS

This paper studies shortened functional equations for general Dirichlet series whose completed forms satisfy a gamma-factor functional equation. It proves a main lemma giving an identity between weighted sums over the two Dirichlet series and residues, under explicit analytic and growth conditions o…

ON SOME INTEGRAL RINGS ASSOCIATED WITH A FINITE GROUP

This paper studies integral rings associated with a finite group, principally the integral character ring and the integral group ring over the ring of integers of a finite extension of the rationals. It proves that finite order units in the character ring are precisely roots of unity times linear ch…

LIMITS OF POSITIVE MOLECULAR MEASURES IN CERTAIN UNIFORM SPACES

This note studies approximation of positive bounded measures on separated uniform spaces by finite molecular measures within the dual scheme of Katětov, Raikov, and Pták. It characterizes when positive elements in the completion of the space generated by points can be represented as measures or Dani…

EQUATIONS FOR GREEN’S FUNCTIONS

This paper derives equations for Green’s functions in an electrically neutral Coulomb system with collisions, starting from the Bogolyubov, Lenard kinetic equation supplemented by a spatially inhomogeneous self-consistent field term. The linearized kinetic equation is varied with respect to an exter…

THE BEHAVIOR OF INTEGRAL CURVES OF A SYSTEM OF DIFFERENTIAL EQUATIONS CLOSE TO A HOMOGENEOUS ONE

ON THE INFLUENCE OF A DOUBLE GRATING OF SPECIAL GEOMETRIC SHAPE ON THE RADIATION OF AN ACTIVE PLANE-PARALLEL LAYER

This paper gives a rigorous electrodynamic treatment of how a symmetric double metallic grating of special geometry affects radiation from an active plane-parallel layer when the electric field is parallel to the grating strips. The boundary-value problem for the Helmholtz equation is formulated in …

ELLIPTIC BOUNDARY-VALUE PROBLEMS WITH A PARAMETER ONLY IN THE BOUNDARY CONDITIONS

This paper studies elliptic boundary value problems for systems in which a complex parameter appears only in the boundary conditions, while the differential equations themselves are parameter independent. Under ellipticity, solvability assumptions for the Dirichlet problem, and a local or global con…

RADIATION OF \(n\)–\(p\) JUNCTIONS ON CRYSTALS OF SOLID SOLUTIONS OF INDIUM PHOSPHIDE—GALLIUM ARSENIDE

This paper investigates electroluminescence from n-p junctions fabricated on single-crystal solid solutions in the indium phosphide, gallium arsenide system across several compositions. Junctions were formed by zinc diffusion, and recombination radiation spectra were measured through crystal cleavag…

ON THE ZERO-MANIFOLDS OF SOLUTIONS OF MULTIDIMENSIONAL DIFFERENTIAL EQUATIONS OF SECOND ORDER

The paper studies zero sets of solutions to completely solvable multidimensional second order linear differential equations with real continuous coefficients. It introduces zero-manifolds and an associated mapping from the domain into a unit sphere, using local diffeomorphism and inverse mapping arg…

ON A PROBLEM OF MIXED TYPE FOR THE EQUATION \(y(y-1)u_{xx}+u_{yy}=0\)

This paper studies a boundary value problem for the mixed type equation y(y minus 1)u_xx plus u_yy equals 0 in a domain containing both parabolic degeneration lines y equals 0 and y equals 1. The author formulates a regularity class allowing prescribed singular behavior at selected boundary and char…

ON THE THEORY OF INVARIANT SURFACES

ANISOTROPY OF ATOMIC DISPLACEMENTS

This study examines whether neutron irradiation produces crystallographically anisotropic atomic displacements in the alpha phase of carbon steel. Using X-ray diffraction, the authors measured integrated intensities for many reflections from irradiated and unirradiated specimens, including multiple …

ON A CLASS OF FUNCTION SPACES

MATHEMATICAL CONSIDERATION OF CERTAIN PROBLEMS ON LONGITUDINAL VIBRATIONS OF COMPOSITE BEAMS CONSISTING OF ELASTIC AND VISCOELASTIC PARTS

INVESTIGATION OF THE HYDRODYNAMICS AND MASS TRANSFER OF A “SHARP” GAS JET WITH A LIQUID

This study examines the hydrodynamics and gas-liquid mass transfer of a submerged, “sharp” gas jet, a configuration relevant to oxygen blowing in metallurgical processes. Based on theoretical considerations, photographic measurements, and experiments with several liquids and nozzle diameters, the au…

THE SOMMERFELD EFFECT IN A SYSTEM WITH RANDOMLY VARYING NATURAL FREQUENCY

This paper examines the Sommerfeld effect in a linear oscillatory system driven by the inertial forces of an unbalanced rotor when the system’s natural frequency varies randomly. Using equations for a rotor on an elastic support with limited motor power, the authors apply Krylov, Bogoliubov averagin…

ON EXISTENCE THEOREMS IN THE CALCULUS OF VARIATIONS

This note formulates an existence theorem for time-optimal control processes under a compactness condition on trajectories and a convexity condition on sets determined by the maximizers of the Hamiltonian. The proof embeds the original controlled system into a convexified system, applies the known F…

ON THE LENGTH OF MOLECULAR THREADS

This paper estimates the longitudinal dimensions of molecular threads presumed to form on the cold tip of an electron projector and to produce Müller-type “molecular” emission patterns. Treating the threads as cylindrical metal-like conductors in an electric field, the author balances electrostatic …

Change of the Generation Channel in a Four-Level Quantum Oscillator

This paper analyzes changes of the generation channel in a four-level quantum generator, focusing on transitions from generation at one frequency to another and on simultaneous multifrequency operation. Using simplified rate-balance equations for unsplit levels, it derives level populations and thre…

On solutions in generalized functions of ordinary differential equations with polynomial coefficients

This note studies ordinary differential equations with polynomial coefficients that are not of Fuchs type, focusing on solutions in spaces of generalized functions that permit regularization of exponential singularities. For equations of a specified form with an isolated singularity at zero, it anal…

ON PERIODIC SOLUTIONS OF PARABOLIC EQUATIONS

PRELIMINARY RESULTS OF A STUDY OF SOLID INTERPLANETARY MATTER IN THE VICINITY OF THE MOON

This paper reports preliminary measurements of solid interplanetary matter near the Moon obtained by the Luna-10 artificial lunar satellite using piezoelectric impact sensors mounted on the spacecraft skin. Between April 3 and May 12, 1966, the instruments recorded 198 particle impacts over 11 hours…

REFLECTION OF FAST IONS FROM A DENSE MEDIUM AT GLANCING ANGLES

This paper analyzes the reflection of fast ions incident on a dense medium at glancing angles, in the regime where binary collisions and predominantly small angle scattering apply. Starting from the Boltzmann kinetic equation, the collision term is approximated by angular diffusion together with uni…

Cherskii, Yu. I.** On the integro-differential equation of Wiener–Hopf and its applications. *Izv. vyssh. ucheb. zavedenii. Matematika*, 1965, No. 2, pp. 188–200.