Showing 50 of 25357 papers

ON THE EIGENFUNCTIONS OF THE FIRST BOUNDARY-VALUE PROBLEM FOR ELLIPTIC EQUATIONS DEGENERATING AT POINTS

A. I. Achildiev
1969 SovietRxiv: ru-196901.35356

The paper studies eigenfunctions of first boundary value problems for elliptic equations whose coefficients degenerate at an interior point, using weighted Hilbert spaces and a normality condition near the singularity. The method removes a small ball around the degeneracy, solves the corresponding r…

TRACE FORMULA FOR A SYSTEM OF THREE PARTICLES

V. S. Buslaev, S. P. Merkur'ev
1969 SovietRxiv: ru-196901.35344

This note derives trace formulas for the connected part of the resolvent of the quantum mechanical Hamiltonian for three nonrelativistic particles with pairwise interactions, under regularity and spectral assumptions on the pair potentials. Using Faddeev’s framework, Hilbert’s identity, and direct i…

EXCITATION OF VIBRATIONS AND DISSOCIATION OF DIATOMIC MOLECULES IN ATOM–MOLECULE COLLISIONS IN A HIGH-TEMPERATURE GAS

B. V. Kuksenko, S. A. Losev
1969 SovietRxiv: ru-196901.35233

This paper investigates vibrational excitation and dissociation of diatomic oxygen in atom molecule collisions in a high temperature argon gas. Using a classical mechanical treatment with an anharmonic intramolecular potential, the authors compute level to level transition and dissociation probabili…

EXPONENTIAL STABILIZATION OF LINEAR SYSTEMS

E. D. Yakubovich
1969 SovietRxiv: ru-196901.34602

This paper studies exponential stabilization of finite-dimensional linear control systems with respect to a prescribed positive definite quadratic form and a prescribed decay rate. It formulates algebraic conditions under which feedback matrices can be chosen so that the Lyapunov inequality holds wi…

ON ENTROPY IN NONEQUILIBRIUM STATISTICAL MECHANICS

Yu. E. Murakhver
1969 SovietRxiv: ru-196901.33459

This paper examines the definition of entropy in nonequilibrium statistical mechanics, focusing on the relation between Planck, Boltzmann, and Gibbs coarse-grained entropies for an isolated classical system divided into weakly interacting subsystems. It defines coarse-graining by assigning a constan…

Detection of Soft X-ray Radiation Using Electron-Optical Converters

V. A. BRYZGUNOV, M. M. BUTSLOV, M. A. MOKULSKII
1969 SovietRxiv: ru-196901.33433

This paper examines the use of electron-optical converters for recording soft X-ray radiation, focusing on the difficulty of reducing exposure while preserving image quality in X-ray diffraction imaging. The authors describe a four-stage converter with a thin mica input window, an internal photocath…

ON AN EXPANSION IN EIGENFUNCTIONS CORRESPONDING TO A CERTAIN PART OF THE SET OF EIGENVALUES OF A NON-SELF-ADJOINT DIFFERENTIAL OPERATOR OF SECOND ORDER

O. A. Akperova, M. G. Dzhavadov
1969 SovietRxiv: ru-196901.33345

This note studies expansions in eigenfunctions associated with only the negative eigenvalues of a second order non-self-adjoint boundary value problem, \(y''+2A\lambda y'+B\lambda^2y=0\), \(y(0)=y(1)=0\), under the condition \(A^2-B<0\). The proof reduces the question to an auxiliary elliptic proble…

THE HOROCYCLIC POCKET

D. A. De Spiller
1969 SovietRxiv: ru-196901.32972

The paper proves a conjecture of V. A. Efremovich that the horocyclic pocket, defined as the universal covering of the Beltrami pseudosphere or equivalently by gluing two horocyclic domains in the Lobachevsky plane along their boundary horocycle, is not equimorphic to any surface of revolution. The …

ON COMPOSITION BLOCKS OF FINITE GROUPS

S. A. Chunikhin
1969 SovietRxiv: ru-196901.32692

This paper studies factorizations of arbitrary finite groups in terms of composition blocks, defined from the arithmetically connected classes of indices in an invariant or composition series. It introduces properly embedded systems of subgroups, invariant-index systems, and total permutability, the…

HYPERFINE STRUCTURE OF THE PARAMAGNETIC-RESONANCE SPECTRA OF Cu(II) IN CERTAIN OXIDE GLASSES

L. D. BOGOMOLOVA, V. N. LAZUKIN, E. N. PODZRINA, N. V. PETROVYKH
1969 SovietRxiv: ru-196901.32676

Electron paramagnetic resonance spectra of impurity Cu(II) were studied in binary oxide glasses based on phosphate, silicate, and borate formers with alkali or alkaline-earth modifiers, at room and liquid-nitrogen temperatures. The spectra are interpreted with an axial spin Hamiltonian and indicate …

THE GIBBS ENSEMBLE AND CHAINS OF EQUATIONS FOR CORRELATION FUNCTIONS OF WEAKLY RELATIVISTIC SYSTEMS

I. P. Pavlotsky
1969 SovietRxiv: ru-196901.32159

This paper develops a weakly relativistic formulation of classical statistical mechanics for systems in which terms beyond order v squared over c squared may be neglected. It constructs the one-particle and Gibbs phase spaces using synchronized laboratory time, derives quasicanonical equations of mo…

NEW LANTHANUM OXYTUNGSTATE \(2\mathrm{La}_2\mathrm{O}_3\cdot3\mathrm{WO}_3\)

T. I. Timchenko, L. V. Petushkova, E. A. Pobedimskaya, A. V. Pashkova
1969 SovietRxiv: ru-196901.32143

A new lanthanum oxytungstate with composition 2La2O3·3WO3 was obtained as single crystals from the La2O3, WO3, NaCl system, although it had not been found in the binary La2O3, WO3 system. The crystals formed under isothermal conditions through evaporation of NaCl and partly WO3, with the largest col…

REGIONAL FEATURES OF THE STRUCTURE OF THE EARTH’S CRUST OF THE RUSSIAN PLATFORM FROM DATA ON AVERAGED GRADIENTS OF THE GEOMAGNETIC FIELD

A. N. Korneva
1969 SovietRxiv: ru-196901.32022

This paper proposes a method for identifying regional crustal structures of the Russian Platform by transforming anomalous geomagnetic field maps into maps of averaged horizontal gradients. The procedure calculates maximum rates of change of the magnetic field within equal map squares and uses the r…

HIGH-TEMPERATURE CREEP OF SILICON SINGLE CRYSTALS

M. M. Myshlyaev, V. I. Nikitenko
1969 SovietRxiv: ru-196901.31957

This study examines whether the apparent differences between creep in homeopolar crystals and metals reflect bond type or the limited observation of early creep stages. Silicon single crystals were tested in uniaxial compression along the 111 direction in argon at 900 to 1300 degrees Celsius and 2 t…

ON THE OPTIMAL SYNTHESIS OF AUTOMATIC MACHINES

I. I. Artobolevsky, D. Ya. Il'inskii, I. I. Kapustin
1969 SovietRxiv: ru-196901.31389

The paper formulates the design of automatic machines as an optimization problem linking reliability, utilization, productivity, and production cost. It represents unit production cost as a separable nonlinear function of reliability related adjustment durations for machine mechanisms and input mate…

On Boundary Value Problems for Elliptic-Parabolic Equations

Yu. A. Dubinskii
1969 SovietRxiv: ru-196901.31372

The paper studies boundary-value problems for elliptic-parabolic differential equations in bounded cylinders, with an elliptic spatial operator and a finite-order time differential operator. Using localization, eigenfunction expansions, Sobolev-type spaces, and parameter-dependent elliptic estimates…

ON THE REDUCTION OF ONE CLASS OF INTEGRAL EQUATIONS OF THE FIRST KIND TO EQUATIONS OF THE SECOND KIND

Ya. N. Fel'd
1969 SovietRxiv: ru-196901.31206

The paper studies a class of two-dimensional integral equations of the first kind on an open Lyapunov surface, with kernels of the form \(Q(g,p)/R_{gp}\), arising in mathematical physics. It introduces an auxiliary singular kernel and uses potential-theoretic representations, limiting jump relations…

THE INFLUENCE OF CRYSTALLINE STRUCTURE ON THE ANGULAR AND ENERGY DISTRIBUTIONS OF IONS SCATTERED BY A SINGLE CRYSTAL

U. A. Arifov, A. A. Aliev
1969 SovietRxiv: ru-196901.30999

This paper examines how the crystallographic orientation of single-crystal molybdenum and tungsten affects the angular and energy distributions of secondary ions scattered under low-energy ion bombardment. Using energy analysis of ions emitted from heated crystal faces while varying the azimuthal ro…

On Solvability Conditions for Pseudodifferential Equations

Unknown
1969 SovietRxiv: ru-196901.30930

This paper studies necessary conditions for solvability and a priori estimates for pseudodifferential equations, extending earlier nonsolvability criteria of Lewy, Hörmander, Nirenberg, and Treves. It formulates conditions in terms of repeated commutators of an operator and its adjoint, and proves t…

A PRIORI ESTIMATES IN \(\mathscr L_2\) OF SOLUTIONS OF GENERAL BOUNDARY-VALUE PROBLEMS FOR DEGENERATE ELLIPTIC EQUATIONS OF SECOND ORDER

V. P. Glushko
1969 SovietRxiv: ru-196901.30816

The paper extends earlier results on a priori estimates to a broad class of second order degenerate elliptic operators in bounded domains with smooth characteristic boundary components. It formulates local normal-coordinate conditions defining alpha-ellipticity, classifies boundary components accord…

WEAK SHOCK WAVES IN A THERMORELAXING MEDIUM\

G. M. Arutyunyan
1969 SovietRxiv: ru-196901.30662

This paper analytically investigates the structure of weak shock waves in thermorelaxing two-component media, such as emulsions or gases containing suspended particles, where compression produces intercomponent temperature differences and heat-exchange relaxation. Using the Mandelstam-Leontovich tre…

MEASURES OF KERNELS OF COMPREHENSION AXIOMS

D. A. Bochvar
1969 SovietRxiv: ru-196901.30548

Bochvar analyzes comprehension axioms in the formal system K0 through the introduced notion of a measure of a kernel. For a kernel of a comprehension axiom, the paper defines maximal included and minimal covering predicates, called internal and external measures, and formulates extensions of K0 in w…

SOLUTION OF PROBLEMS OF RIEMANN AND HILBERT TYPE FOR A GENERALIZED CAUCHY–RIEMANN SYSTEM WITH A SINGULAR LINE

N. Radzhabov
1969 SovietRxiv: ru-196901.30195

The paper studies Riemann and Hilbert type boundary value problems for a generalized Cauchy-Riemann system with a singular line, considering cases of positive and negative values of the parameter. Using integral representations of solutions in half-planes, the problems are reduced to classical conju…

ON CERTAIN \(\Delta\Sigma\)-OPERATIONS WHOSE BASES ARE OBTAINED BY UNITING THE CHAINS OF THE BASE OF THE ORIGINAL OPERATION

Z. I. Kozlova
1969 SovietRxiv: ru-196901.30165

This paper studies regularity conditions for properties of bases of Delta Sigma operations obtained by uniting chains of an original base, over an index space of strongly inaccessible cardinality. It defines regular and semiregular bases, proves lemmas giving sufficient closure conditions, and estab…

ON THE PROBABILITY OF DOUBLE BETA DECAY OF NUCLEI IN REGIONS FAR FROM THE BAND OF BETA STABILITY

E. E. BERLOVICH, Yu. N. NOVIKOV
1969 SovietRxiv: ru-196901.30134

This paper estimates the probability of double beta decay in nuclei far from the beta stability band, where the available decay energy and number of accessible final states may be much larger than in stable nuclei. The authors derive and use expressions for two-neutrino and neutrinoless double beta …

SYNTHESIS, X-RAY, AND THERMOGRAPHIC STUDY OF POTASSIUM–RARE-EARTH TUNGSTATES

P. V. Klevtsov, L. P. Kozeeva
1969 SovietRxiv: ru-196901.30041

Potassium rare-earth double tungstates KLn(WO4)2 for the lanthanide series from lanthanum to lutetium were synthesized as single crystals by crystallization from a K2WO4 and WO3 melt and examined by powder X-ray diffraction, optical goniometry, and differential thermal analysis. The study distinguis…

Investigation of Optical Breakdown in Air Induced by Ultrashort Pulses Using an Image Converter Streak Camera

B. Z. Gorbenko, Yu. A. Drozhbin, S. D. Kaitmazov, A. A. Medvedev, Academician A. M. Prokhorov, A. M. Tolmachev
1969 SovietRxiv: ru-196901.29875

This paper investigates the early dynamics of optical breakdown in air produced by a train of ultrashort mode-locked neodymium laser pulses. The authors use an FER-2 image-converter photochronograph with a modified laser-triggered spark-gap sweep circuit, reducing the trigger delay to about 10 to 15…

ON A PROPERTY OF PERIODIC MOTIONS OF A SINGLE-LOOP NONLINEAR IMPULSE SYSTEM WITH AN INTEGRATING ELEMENT

Unknown
1969 SovietRxiv: ru-196901.29818

This paper examines periodic motions in a single-loop nonlinear impulse control system containing an ideal impulse element, an integrating element, a static nonlinearity, and a linear dynamic element. By deriving the point transformation over one and multiple impulse periods, the analysis formulates…

ON THE METHOD OF INCOMPLETE FACTORIZATION

Yu. I. Cherskii
1969 SovietRxiv: ru-196901.29624

The paper proposes a method of incomplete factorization for certain boundary value problems in the theory of analytic functions, where coefficients on one contour admit piecewise holomorphic continuation with jumps on another contour. The approach treats the original boundary condition as partially …

AN A PRIORI ESTIMATE OF THE PRINCIPAL RADII OF CURVATURE OF A CLOSED CONVEX HYPERSURFACE IN TERMS OF THEIR MEAN VALUES

A. V. Pogorelov
1969 SovietRxiv: ru-196901.29436

The paper studies closed convex hypersurfaces in Euclidean space whose elementary symmetric function of the principal radii of curvature is prescribed as a function of the exterior normal. It proves an a priori upper estimate for every radius of normal curvature in terms of the corresponding mean ra…

THE PHENOMENON OF A FLASH OF ABSORPTION OF LASER RADIATION AND THE GAS-DYNAMIC EFFECTS ASSOCIATED WITH IT

G. G. Vilenskaya, I. V. Nemchinov
1969 SovietRxiv: ru-196901.29333

This paper analyzes the absorption of laser radiation by vapor and condensate formed during rapid evaporation of an opaque solid surface. Using conservation laws, equilibrium equations of state, and estimates of radiation absorption by condensate particles and weakly ionized vapor, the authors deriv…

EXCITATION OF NONPOTENTIAL OSCILLATIONS IN THE PLASMA OF A SOLID

A. A. Ivanov, E. Z. Meilikhov, V. V. Parail, D. A. Frank-Kamenetskii
1969 SovietRxiv: ru-196901.29279

This paper analyzes the excitation of low-frequency nonpotential oscillations in the electron-hole plasma of a solid when an electric current flows across an external magnetic field. Using a hydrodynamic approximation with quasineutrality, Maxwell equations without displacement current, and conditio…

ON A SYSTEM OF BELTRAMI EQUATIONS DEGENERATING ON A LINE

A. Dzhuraev
1969 SovietRxiv: ru-196901.29185

The paper studies a first-order Beltrami equation whose ellipticity degenerates on a simple analytic curve where the coefficient satisfies a finite-order vanishing condition for its modulus. It analyzes two geometric cases, according to whether the characteristic direction is transverse or tangent t…

RECOMBINATION RADIATION UNDER THE PINCH EFFECT IN A NONDEGENERATE ELECTRON–HOLE PLASMA OF SEMICONDUCTORS

I. I. Boiko, V. V. Vladimirov
1969 SovietRxiv: ru-196901.29151

This paper analyzes recombination radiation from a nondegenerate electron-hole plasma in a semiconductor plate under current-induced pinch conditions. Using a one-dimensional plate model, the authors derive expressions for the spectral and integral radiation intensities in terms of carrier distribut…

ON CONDITIONS FOR THE EXISTENCE OF BOUNDED SOLUTIONS OF DIFFERENTIAL EQUATIONS IN A BANACH SPACE

N. V. Medvedev
1969 SovietRxiv: ru-196901.29059

The paper studies existence and uniqueness of bounded solutions on the whole real line for nonhomogeneous linear differential equations in a Banach space with generally unbounded time-dependent operators. It develops an approximation method based on bounded solutions of associated difference equatio…

ON THE DECOMPOSITION OF DIRECT PRODUCTS OF IRREDUCIBLE REPRESENTATIONS OF SPACE GROUPS

B. K. Novosadov, L. K. Saulevich, D. T. Sviridov, Yu. F. Smirnov
1969 SovietRxiv: ru-196901.28794

The paper addresses the decomposition of direct products of irreducible representations of crystal space groups, a problem needed for applying selection rules and constructing exciton and related states in solid-state physics. It formulates a method, mainly for symmorphic space groups, for determini…

Nonlinear Excitation of Drift Waves in an Inhomogeneous Plasma

Corresponding Member of the USSR Academy of Sciences B. B. Kadomtsev, O. P. Pogutse
1969 SovietRxiv: ru-196901.28588

This paper examines whether finite amplitude drift waves in an inhomogeneous magnetized plasma can exhibit nonlinear excitation mechanisms absent from linear theory. Using a drift kinetic treatment with quasineutrality, the authors analyze a standing drift wave and isolate the contribution of electr…

ON THE NORMAL SOLVABILITY OF NONLINEAR EQUATIONS

S. I. Pokhozhaev
1969 SovietRxiv: ru-196901.28390

The paper formulates a notion of normal solvability for nonlinear operator equations in Banach spaces, modeled on Hausdorff normal solvability for linear equations. It proves that if a continuously differentiable operator maps a Banach space into a reflexive Banach space and has weakly closed range,…