Showing 50 of 25357 papers

THE CONJUGATION PROBLEM FOR THREE ANALYTIC FUNCTIONS

M. Ya. Kurganskaya, Yu. I. Cherskii
1970 SovietRxiv: ru-197001.39115

This paper studies a conjugation problem for three analytic functions connected by boundary conditions on a smooth closed contour through two branches of the square root. The authors reduce an associated jump problem to two classical Riemann boundary value problems, construct canonical factorizing f…

ON EMBEDDING THEOREMS FOR BESOV SPACES WITH MIXED NORM

R. D. Kulov
1970 SovietRxiv: ru-197001.39088

This note establishes embedding theorems for Besov spaces with mixed norm on Euclidean space and for weighted Besov spaces on the half-space. The author defines the relevant spaces through mixed Lebesgue norms and difference norms of derivatives, then states conditions under which functions or their…

ON SOME QUANTITATIVE CHARACTERISTICS OF ALGORITHMIC LANGUAGES

N. P. Ter-Zakharyan
1970 SovietRxiv: ru-197001.39012

This note studies quantitative characteristics of algorithmic languages, focusing on how briefly algorithms can be encoded and compared through translators between languages. It defines reducibility, message complexity, additive, asymptotic, and multiplicative boundedness of translators, and corresp…

CRYSTAL STRUCTURE OF Na-TITANOGERMANATE

V. Ya. Verkhovskii, È. A. Kuz'min, V. V. Ilyukhin, N. V. Belov
1970 SovietRxiv: ru-197001.38937

The paper reports an X-ray crystallographic determination of hydrothermally synthesized sodium titanogermanate, Na2(TiO)[GeO4], in order to assess its structural relation to analogous silicates and the role of germanium in tetrahedral coordination. Using three-dimensional Patterson analysis and refi…

A VACUUM-LIKE STATE OF A MEDIUM

E. B. Gliner
1970 SovietRxiv: ru-197001.38936

The paper argues that a vacuum-like state of matter with energy momentum tensor proportional to the metric and equation of state p equals minus the energy density can serve as the initial state for any of the three Friedmann cosmological models. It analyzes the causal and quantum limits of such a me…

THE PINCH EFFECT IN SEMICONDUCTORS UNDER CONDITIONS OF STRONG DEGENERACY OF AN ELECTRON–HOLE PLASMA

I. I. Boiko
1970 SovietRxiv: ru-197001.38794

This paper analyzes the pinch effect in a bipolar semiconductor plasma when one or both carrier species are strongly degenerate, a regime not covered by the usual nondegenerate gas model. For an infinite plate carrying longitudinal current, the carrier distribution is reduced under quasineutrality a…

GEOMETRY OF SPACES OF CONSTANT CURVATURE AS A SPECIAL CASE OF THE THEORY OF PHYSICAL STRUCTURES

Yu. I. Kulakov
1970 SovietRxiv: ru-197001.38778

The paper proposes an axiomatic construction of locally Euclidean, locally symplectic, and locally non-Euclidean geometries of constant curvature as instances of the theory of physical structures. It formulates a principle of phenomenological symmetry for a set of points equipped with symmetric or a…

Mappings of Families of Sets

A. D. Aleksandrov
1970 SovietRxiv: ru-197001.38717

This paper studies one-to-one mappings between affine spaces that carry the family of all translates of a bounded set onto the family of translates of its image. Using an iterative construction of associated centrally symmetric sets, it proves that tangent supporting hyperplanes at suitable extreme …

APPLICATION OF THE CONTOUR INTEGRAL METHOD TO THE SOLUTION OF MULTIDIMENSIONAL MIXED PROBLEMS FOR PARABOLIC SYSTEMS OF SECOND ORDER

M. L. Rasulov
1970 SovietRxiv: ru-197001.38370

The paper applies the contour integral method to multidimensional mixed problems for second order parabolic systems in a three-dimensional domain, with boundary conditions that include a time derivative. Under assumptions on the spectrum of the coefficient matrix, regularity and boundedness of the c…

ON THE SOLVABILITY OF QUASILINEAR PARABOLIC SYSTEMS

S. I. Pokhozhaev
1970 SovietRxiv: ru-197001.38299

The paper studies boundary value problems for quasilinear parabolic systems in the Douglis, Nirenberg, and Solonnikov sense, with linear boundary conditions and zero initial data in anisotropic Sobolev spaces. Using an abstract solvability theorem for nonlinear equations in Banach spaces together wi…

SURFACES OF NEGATIVE EXTERNAL CURVATURE IN A RIEMANNIAN SPACE WITH NONPOSITIVE RIEMANNIAN CURVATURE

I. S. Brandt
1970 SovietRxiv: ru-197001.38153

The paper extends Efimov-type results on complete surfaces of negative curvature from Euclidean three-space to three-dimensional Riemannian spaces with nonpositive sectional curvature. For a complete surface with negative extrinsic curvature, it derives generalized fundamental equations in asymptoti…

THE HYSTERANT OPERATOR

M. A. Krasnosel'skii, B. M. Darinskii, I. V. Emelin, P. P. Zabreiko, E. A. Livshitz, A. V. Pokrovskii
1970 SovietRxiv: ru-197001.38109

This paper introduces the hysterant operator as a mathematical tool for describing hysteresis-type nonlinearities arising in Prager-Ishlinskii models of elastic-plastic behavior. The authors define an elementary hysterant first for continuous piecewise-linear inputs and then extend it to arbitrary c…

ON A CONCAVE \(n\)-PERSON GAME AND ONE MODEL OF PRODUCTION

S. I. Zukhovitskii, R. A. Polyak, M. E. Primak
1970 SovietRxiv: ru-197001.38023

The paper studies normalized equilibrium points in concave n-person games and develops iterative methods generalizing the conditional-gradient approach for computing them under convexity and regularity assumptions. It proves convergence results for three step-size rules, including subsequential conv…

FROM THE EXISTENCE OF A NONMEASURABLE SET OF TYPE \(A_2\) THERE FOLLOWS THE EXISTENCE OF AN UNCOUNTABLE SET CONTAINING NO PERFECT SUBSET OF TYPE \(CA\)

V. A. Lyubetskii
1970 SovietRxiv: ru-197001.38011

The paper addresses two classical descriptive set theory questions in their formal set theoretic formulation: the existence of an uncountable coanalytic set containing no perfect subset, and the existence of a non-Lebesgue-measurable set of projective type. It proves in Zermelo-Fraenkel set theory t…

ON PROBLEMS OF DISCRETE OPTIMIZATION

V. A. Emelichev
1970 SovietRxiv: ru-197001.37639

This note formulates a general scheme for a method used in several classes of discrete optimization problems, including production allocation, integer linear programming, discrete programming, concave programming, and reliability problems. The problem is to minimize a function on a finite feasible s…

ON FREDHOLM THEORY FOR NONLINEAR OPERATOR EQUATIONS

Unknown
1970 SovietRxiv: ru-197001.37583

This note develops partial Fredholm-type solvability results for nonlinear operator equations in Banach spaces with completely continuous operators that possess an asymptotic derivative. Using a finite-dimensional algebraic lemma and the Schauder-Tikhonov fixed point principle, it proves necessary a…

THE CRYSTAL STRUCTURE OF LANDAUITE \

L. E. NIKOLAEVA, Academician N. V. BELOV
1970 SovietRxiv: ru-197001.37021

The paper determines the crystal structure of landauite from the Burpala massif using X-ray diffraction data, Patterson projections, electron-density maps, and least-squares refinement. It evaluates alternative chemical and symmetry models and finds that the centrosymmetric space group A2/a with the…

ISOMETRIC EMBEDDINGS AND IMMERSIONS

M. L. Gromov
1970 SovietRxiv: ru-197001.36592

This note formulates general theorems on the space of isometric immersions and embeddings of pseudo-Riemannian manifolds, extending results of Nash, Kuiper, Janet, Cartan, Burstin, and Smale-Hirsch type immersion theory. Using bundle-theoretic conditions on isometric morphisms, monomorphisms, and se…

ON THE “CHAIN EFFECT” IN THE SCATTERING OF IONS BY A FACE OF A SINGLE CRYSTAL

V. M. Kivilis, È. S. Parilis, N. Yu. Turaev
1970 SovietRxiv: ru-197001.36543

The paper examines the “chain effect” in glancing scattering of argon ions by the [110] atomic chains on the (100) face of a copper single crystal. Using numerical calculations based on earlier scattering models, it analyzes how the reflected ion energy as a function of scattering angle changes with…

ON THE DENSITIES OF MEASURES CORRESPONDING TO SOLUTIONS OF CERTAIN DIFFERENTIAL EQUATIONS WITH RANDOM FUNCTIONS

Unknown
1970 SovietRxiv: ru-197001.36511

The paper studies absolute continuity of measures generated by solutions of differential equations with random Gaussian forcing in finite-dimensional Euclidean space. It compares a linear equation with a corresponding nonlinear equation containing an additional drift term, formulates conditions invo…

ILL-POSED PROBLEMS AND GEOMETRIES OF BANACH SPACES

V. P. Tanana
1970 SovietRxiv: ru-197001.36399

This paper studies stability of the residual method for ill-posed linear operator equations of the first kind in Banach spaces, where only a convex closed neighborhood filter of the exact right-hand side is given. The method selects the minimum-norm element among points whose image lies in the presc…

ON GRAVITATIONAL STRESSES

I. G. Fikhtengol'ts
1970 SovietRxiv: ru-197001.35981

The paper examines quantities constructed from the Ricci tensor and a separated term containing second derivatives of the metric, arguing that in harmonic coordinates the resulting quantities can be interpreted as gravitational stresses. It derives a decomposition of the Einstein tensor into two par…

ON THE STABILITY OF PERIODIC MOTIONS IN THE TRANSCENDENTAL CASE OF TWO PURELY IMAGINARY CHARACTERISTIC EXPONENTS

Yu. N. Bibikov
1970 SovietRxiv: ru-197001.35840

This paper studies Lyapunov stability of the zero solution of a periodic analytic system of differential equations whose linear approximation has two purely imaginary characteristic exponents and all remaining exponents with negative real parts. Focusing on Lyapunov’s generally transcendental case, …

INVESTIGATION OF THE PLASTICITY ZONE UNDER AFTEREFFECT FOR CERTAIN BODIES WITH CENTRAL AND AXIAL SYMMETRY

M. I. Rozovskii, N. N. Dolinina
1970 SovietRxiv: ru-197001.34705

This paper studies the time-dependent size of plastic zones in elastic-plastic bodies with aftereffect, focusing on a hollow sphere under internal and external pressure and related axially symmetric cylinder problems. Using operator constitutive relations for shear, volumetric response, and hardenin…

A GENERAL FIRST MAIN THEOREM OF VALUE DISTRIBUTION THEORY

I. M. Degtyarev
1970 SovietRxiv: ru-197001.34528

This note extends first main theorems in value distribution theory for holomorphic mappings to compact complex target manifolds without imposing Kähler, homogeneous, or projective structure. The main construction proves that on any compact complex manifold with a normalized volume form there is a co…

Measurement of Electric Fields in Turbulent Plasma by Stark Broadening of Hydrogen Spectral Lines

E. K. Zavoiskii, Yu. G. Kalinin, V. A. Skoryupin, V. V. Shapkin, G. V. Sholin
1970 SovietRxiv: ru-197001.34256

This paper examines the use of Stark broadening of hydrogen spectral lines as a noncontact optical diagnostic of electric fields associated with turbulent plasma heating by direct discharge current. The authors derive and apply criteria distinguishing quasistatic ion-acoustic fields from high-freque…

Method for determining the lower limit of the spectral linewidth of the luminescence line of the iodine atom $5^2P_{1/2}$ – $5^2P_{3/2}$ transition in a photodissociation laser

S. D. Velikanov, S. B. Kormer, V. D. Nikolaev, M. V. Sinitsyn, Yu. A. Solov'ev, V. D. Urlin
1970 SovietRxiv: ru-197001.34239

This paper presents a method for estimating the spectral width of the infrared luminescence line associated with the iodine atom transition in a photodissociation optical quantum generator operating at 1.315 micrometers. The authors use a Fabry Perot etalon with a time swept interference pattern, re…

ON THE SUBDIFFERENTIAL OF A COMPOSITE FUNCTIONAL

V. L. Levin
1970 SovietRxiv: ru-197001.34221

This note studies subdifferentials of composite convex functionals on Banach spaces, where a continuous convex mapping into a Banach lattice is composed with a monotone convex functional. It introduces a subdifferential for Banach lattice valued mappings and establishes conditions under which this s…

ON FINDING A MINIMAX ON A CONSTRAINED SET

V. F. Dem'yanov
1970 SovietRxiv: ru-197001.34077

The paper studies the minimization over a convex compact constrained set of a nonsmooth function defined as the maximum of finitely many continuously differentiable functions. It formulates stationarity in terms of the intersection of the convex hull of active gradients with the conjugate cone of fe…

ON CELLULAR CONVECTION IN AN INFINITELY LONG HORIZONTAL LAYER OF GAS HEATED FROM BELOW

V. I. Polezhaev, M. P. Vlasyuk
1970 SovietRxiv: ru-197001.34073

This paper studies the onset and post-critical development of cellular convection in an infinitely long horizontal gas layer heated from below, taking account of compressibility, the adiabatic temperature gradient, and gas properties beyond the Boussinesq approximation. The authors solve the two-dim…

A SET OF FEATURES DETERMINING THE PRESENCE OF A WAVEGUIDE IN THE EARTH’S CRUST OF THE GARM REGION OF CENTRAL ASIA

I. L. Nersesov, L. S. Chepkunas
1970 SovietRxiv: ru-197001.34040

This paper examines evidence for a low-velocity seismic waveguide in the crust of the Garm region of Central Asia. Using earthquakes from two localized focal zones as plunging sources, the authors construct and interpret systems of mean travel-time curves for longitudinal and transverse waves, suppl…

Sensitized photolysis on semiconductors as a principle of long-wavelength photography

A. D. SABLIN-YAVORSKII, L. M. BELYAEV, V. M. FRIDKIN
1970 SovietRxiv: ru-197001.33866

This paper proposes sensitized photolysis on semiconductor surfaces as a basis for long-wavelength photography, extending the two-stage mechanism of silver-halide latent-image formation to systems where adsorbed metal ions are reduced by photoexcited carriers. The authors examine photoreduction of s…

APPROXIMATION OF CONTINUOUS AND DIFFERENTIABLE FUNCTIONS OF MANY VARIABLES BY GENERALIZED POLYNOMIALS (FINITE LINEAR SUPERPOSITIONS OF FUNCTIONS OF A SMALLER NUMBER OF VARIABLES)

Unknown
1970 SovietRxiv: ru-197001.33795

The paper studies approximation of continuous and differentiable functions on the unit cube by generalized polynomials, defined as finite linear superpositions of functions of fewer variables with respect to prescribed one variable systems. It establishes existence and characterization results for b…

THE SPECTRUM OF UNIFORM HOMOLOGIES

E. S. Tikhomirova
1970 SovietRxiv: ru-197001.33737

The paper develops a refinement of uniform homology groups for metric spaces, motivated by the inability of earlier groups to distinguish manifolds whose bounding chains grow with different diameter orders. For each admissible order of growth, it defines subsets determined by cycles requiring chains…

ISOMETRIC IMMERSIONS OF CLASS $C^1$

S. Z. Shefel'
1970 SovietRxiv: ru-197001.33462

This note studies isometric immersions of two-dimensional Riemannian metrics into Euclidean three-space by surfaces of class C1 under an added condition of regularity with respect to affine transformations. It introduces affine regularity and proves structural results for immersions of metrics of bo…

ON SPATIALLY HOMOGENEOUS GRAVITATIONAL FIELDS

L. P. Grishchuk
1970 SovietRxiv: ru-197001.33284

This paper formulates the Einstein equations for spatially homogeneous gravitational fields in a comoving reference system, motivated by cosmological applications where the physical behavior of matter is most naturally described along the medium flow. Starting from metrics admitting a three-dimensio…

PROPERTIES OF ABSOLUTE CONVERGENCE OF MULTIDIMENSIONAL FOURIER SERIES FROM THE POINT OF VIEW OF THE GEOMETRY OF WEAK DISCONTINUITIES OF THE EXPANDED FUNCTIONS

Unknown
1970 SovietRxiv: ru-197001.33045

This paper studies how the geometry of weak discontinuities affects absolute and quasi-absolute convergence of multidimensional Fourier series and eigenfunction expansions of elliptic operators. For functions on the two-dimensional torus weakly discontinuous along a smooth curve, it introduces quasi…