Showing 50 of 25357 papers

INDUCTIVELY REFLEXIVE LOCALLY CONVEX SPACES

I. A. Berezanskii
1968 SovietRxiv: ru-196801.59173

The paper studies inductively semireflexive and inductively reflexive locally convex spaces, defined through the inductive topology on the dual generated by equicontinuous sets. It establishes criteria for these properties: inductive semireflexivity is equivalent to completeness in the strongest Sch…

ON SINGLE-MODE OPEN RESONATORS

V. P. Maslov, E. M. Vorob'ev
1968 SovietRxiv: ru-196801.59165

The paper analyzes open resonators formed by equidistant conducting curves or surfaces and seeks parameter regimes in which only one transverse mode is supported. Using high-frequency asymptotics for the Helmholtz equation, the transverse-mode problem is reduced to one-dimensional Schrödinger-type e…

ON A FAMILY OF HOMOGENEOUS NETWORKS OF FORMAL NEURONS

A. L. Toom
1968 SovietRxiv: ru-196801.59134

This paper studies Markov chains modeling homogeneous networks of formal neurons with spontaneous activity, where each neuron is activated either by local persistence from neighboring states or by random self-excitation. It develops upper bounds for the probabilities of finite blocks of active neuro…

ON THE TIME REQUIRED FOR ESTABLISHING THE EQUILIBRIUM CONCENTRATION OF VACANCIES

B. S. Bokshtein, S. Z. Bokshtein, A. A. Zhukhovitskii, S. T. Kishkin, L. G. Kornelyuk, Yu. S. Nechaev
1968 SovietRxiv: ru-196801.59052

The paper investigates the time required to establish equilibrium vacancy concentrations in metals under quasi-equilibrium conditions, a parameter important for high-temperature diffusion processes. A pulse heat-capacity method is used in aluminum, lead, and an aluminum-copper alloy, varying pulse d…

ON THE RANK OF ABELIAN VARIETIES

M. I. Bashmakov
1968 SovietRxiv: ru-196801.58895

This paper studies the rank of an abelian variety over a number field by relating it to Galois cohomology groups associated with a fixed prime and a maximal ramified p-extension. Under assumptions on the fields of definition of p-power torsion, it constructs global and local exact sequences involvin…

ON THE DISTRIBUTION OF IDEAL CLASS NUMBERS \(h\) OF REAL QUADRATIC FIELDS \(K(\sqrt p)\) WITH PRIME DISCRIMINANT \(p \equiv 1 \pmod 4\) AMONG THE RESIDUE CLASSES \(\{4k+1\}\) AND \(\{4k+3\}\)

V. G. Lemmlein
1968 SovietRxiv: ru-196801.58658

This paper studies the congruence class modulo 4 of the ideal class number of real quadratic fields K(sqrt p), where p is a prime congruent to 1 modulo 4 and p is represented as a sum of two squares. Using Hasse’s formulas for the circular unit, Gauss sums, and products over quadratic residues and n…

ON A GENERAL BOUNDARY-VALUE PROBLEM

A. Dzhuraev
1968 SovietRxiv: ru-196801.58650

The paper studies a general boundary value problem for a two-function first order system of composite type in a simply connected plane domain, with one hyperbolic characteristic family and one elliptic Beltrami-type equation. Under smoothness assumptions on the coefficients and nondegeneracy conditi…

ON THE STABILITY OF DIFFERENCE SCHEMES IN A COMPLEX HILBERT SPACE

A. V. Gulin, A. A. Samarskii
1968 SovietRxiv: ru-196801.58607

This note extends operator methods for the stability analysis of difference schemes from real to complex Hilbert spaces. For two-layer schemes with constant operators, it reduces stability in weighted energy spaces to stability of an associated explicit scheme and derives necessary and sufficient, o…

PROPERTIES OF INTEGRALS OF TEMLYAKOV–BAVRIN TYPE

V. A. Gusakov
1968 SovietRxiv: ru-196801.58486

This note studies first-kind integrals of Temlyakov-Bavrin type associated with integral representations for holomorphic functions in bounded convex complete bicircular domains. For the special choice \(r_1(\tau)=\tau/a\) and \(r_2(\tau)=(1-\tau)/b\), it considers kernels defined on a product of par…

ON SOME TOPOLOGICAL PROPERTIES OF BANACH STRUCTURES AND ON CONDITIONS FOR THEIR REFLEXIVITY

G. Ya. Lozanovskii
1968 SovietRxiv: ru-196801.58168

This paper studies how Banach space topology determines order-theoretic properties in normed partially ordered structures, especially KB-lineals and KN-spaces. It compares three notions of countable type, one order-theoretic and two topological, proving their equivalence for norm-complete KN-spaces …

ON FACTORIAL \(s\)-MAPPINGS

V. V. Filippov
1968 SovietRxiv: ru-196801.57889

This note studies factorial s-mappings from spaces with a point-countable base onto Hausdorff spaces of point-countable type. It proves that such an image satisfies the first axiom of countability, by reducing to the bicompact case, establishing a sequence selection lemma, showing that the mapping i…

COMPUTATIONAL FORMULAS FOR STRUCTURE FACTORS AND THEIR DERIVATIVES IN THE CASE OF ANISOTROPIC THERMAL VIBRATIONS

V. I. Burdina
1968 SovietRxiv: ru-196801.57727

This paper derives computational formulas for crystallographic structure factors and their coordinate derivatives when anisotropic thermal vibrations are included, a case in which standard tabulated formulas for space groups are no longer directly applicable. Using a symmetry-based treatment, the au…

On a Differential Game of Pursuit

N. N. Krasovskii
1968 SovietRxiv: ru-196801.57495

This paper studies a fixed-terminal-time differential game of approach between pursuing and pursued controlled motions with bounded convex control sets, where the payoff is the terminal distance between selected components of the two phase vectors. Under a specified “rough case” involving convex att…

ON THE THEORY OF HEATING IN HYPERSONIC FLOW

L. M. Biberman, S. Ya. Bronin
1968 SovietRxiv: ru-196801.56897

This paper examines aerodynamic heating of blunt bodies in hypersonic air flow when radiation transfer is coupled to the gas dynamics rather than treated as a separate postprocessing correction. The authors formulate and solve equations near the stagnation line including viscosity, thermal conductiv…

THEOREMS ON HOMEOMORPHISMS IMPLEMENTED BY ELLIPTIC OPERATORS

Ya. A. Roitberg
1968 SovietRxiv: ru-196801.56750

The paper studies homeomorphism theorems for elliptic boundary value operators in Sobolev type spaces, including spaces with boundary trace components and quotient or graph norm constructions. Starting from a known homeomorphism theorem for a properly elliptic operator with normal covering boundary …

APPROXIMATION OF DISCONTINUOUS FUNCTIONS BY FOURIER SUMS

G. I. Natanson
1968 SovietRxiv: ru-196801.56732

This note studies the approximation of nonperiodic continuous functions on a finite interval by partial sums of their trigonometric Fourier series, focusing on the effect of a jump in the periodic continuation at an endpoint. Using estimates based on moduli of continuity and extremal constructions f…

ON A CLASS OF GAMES ON THE UNIT SQUARE

Unknown
1968 SovietRxiv: ru-196801.56275

This paper studies zero-sum games on the unit square whose continuous payoff kernels have a prescribed simple form on connected components outside a closed set. It introduces families of multivalued mappings associated with this closed set and proves a sufficient condition under which both players p…

FEATURES OF THE SPECTRA OF SOURCES OF COSMIC RADIO EMISSION IN THE DECAMETER WAVELENGTH RANGE

S. Ya. Braude, I. N. Zhuk, S. M. Lebedeva, A. V. Men', B. P. Ryabov
1968 SovietRxiv: ru-196801.55989

Measurements of the spectra of 55 discrete cosmic radio sources were made in the decameter range from 25 to 12.6 MHz, using a broadband radio telescope with electrical beam steering, with reliable tabulated flux densities for 38 sources. The results show that many low-frequency spectra deviate subst…

A SIMILARITY CRITERION IN THE OPTICS OF TURBID MEDIA

V. A. Timofeeva
1968 SovietRxiv: ru-196801.55899

This paper examines similarity criteria for optical fields in turbid media, focusing first on the established use of specific scattering as a criterion when scattering indicatrices are identical. Laboratory experiments measured relative brightness at varying optical depths and directions in media wi…

SUPERSONIC FLUTTER OF THREE-LAYER PLATES

A. I. Smirnov
1968 SovietRxiv: ru-196801.55859

This paper analyzes the supersonic flutter of finite three-layer plates using previously derived elastic equilibrium equations that account for bending stiffness of the load-bearing layers, shear stiffness of the core, inertia, in-plane loads, and aerodynamic loading. Assuming piston-theory aerodyna…

On Quasilinear Equations in Banach Space

P. E. Sobolevskii
1968 SovietRxiv: ru-196801.55406

The paper studies local solvability of quasilinear evolution equations in Banach spaces of the form v'(t)=A(t)v(t)+f(t,v(t)), where A(t) generates contraction semigroups with a common domain and the nonlinear term may be unbounded on the base space. It extends earlier existence and uniqueness result…

On Some Linear Polynomial Operations in the Complex Domain

Unknown
1968 SovietRxiv: ru-196801.55324

This paper extends earlier results on linear polynomial operations from periodic real functions to analytic functions in a finite complex domain with rectifiable boundary and simply connected complement. Using Faber polynomials and conformal mapping, it introduces shift and even shift operations and…

Oscillations of the Solar Irradiation of the Earth Caused by Secular Changes in the Elements of the Earth’s Orbit

Sh. G. Sharaf, N. A. Budnikova
1968 SovietRxiv: ru-196801.55028

This paper extends astronomical calculations of climatic insolation variations caused by secular changes in the Earth’s orbital eccentricity, longitude of perihelion, and obliquity. Building on Milanković’s formulation and later recalculations, the authors revise trigonometric precession formulas, d…

ON THE THEORY OF TRANSPORT PHENOMENA IN DENSE MEDIA

Unknown
1968 SovietRxiv: ru-196801.54317

This paper examines the theoretical justification of transport laws and kinetic coefficients for isotropic dense multicomponent media within nonequilibrium statistical mechanics. Using Zubarev’s nonequilibrium ensemble method, it expands the distribution function about a local equilibrium form and d…

HOLOGRAPHY WITHOUT A REFERENCE BEAM IN THE CASE OF THREE-DIMENSIONAL HOLOGRAMS

V. V. Aristov, V. G. Lysenko, V. B. Timofeev, V. Sh. Shechtman
1968 SovietRxiv: ru-196801.53960

This paper analyzes reference-beam-free holography for three-dimensional holograms, extending earlier results for two-dimensional recording media where reconstruction yields the Patterson function of the object. Using a Fourier representation of the recorded interference intensity and applying the W…

DETERMINATION OF THE BOND ENERGY IN TWO-DIMENSIONAL CRYSTALS OF ZIRCONIUM ADSORBED ON TUNGSTEN AND NIOBIUM

Unknown
1968 SovietRxiv: ru-196801.53413

This paper examines the growth and disappearance of two-dimensional zirconium crystals adsorbed on crystallographically distinct regions of tungsten and niobium single-crystal surfaces. Using field-emission microscopy and Arrhenius analysis of temperature-dependent growth and two-dimensional sublima…

SURFACE IONIZATION OF THE RADICAL $\mathrm{C_4H_{10}N}$

È. Ya. Zandberg, U. Kh. Rasulev
1968 SovietRxiv: ru-196801.52996

This study examines the surface ionization of the radical C4H10N formed when diethylamine interacts with heated tungsten and oxidized tungsten in weak electric fields. Using retarding-potential measurements in a mass spectrometer, the authors compare the velocity distribution of C4H10N positive ions…

ON THE QUESTION OF DIAMOND ETCHING

M. I. KARKLINA, Yu. P. MASLAKOVETS
1968 SovietRxiv: ru-196801.52936

This paper investigates the etching of Yakut diamond octahedra in molten hydroxides, nitrates, and peroxide-containing mixtures of potassium and sodium compounds in air at 560 to 700°C. Etching rates were determined from weight loss and surface area estimates, while etched surface morphology was exa…

DECIPHERING THE PATTERSON FUNCTION FROM ITS MULTIPLE PEAKS

È. A. Kuz'min, V. V. Ilyukhin, N. V. Belov
1968 SovietRxiv: ru-196801.52935

The paper presents a method for deciphering a Patterson function by exploiting multiple peaks in the vector system, using two selected peaks to generate quadrilaterals and then successively enlarged polygons that isolate shifted copies of the basic atomic system. The authors argue that comparison an…

ON THE ABSOLUTE AND UNIFORM CONVERGENCE OF FOURIER SERIES IN EIGENFUNCTIONS OF A SELF-ADJOINT ELLIPTIC OPERATOR OF ORDER \(2m\)

I. K. Kendzhaev
1968 SovietRxiv: ru-196801.52904

The paper studies absolute and uniform convergence of Fourier series with respect to eigenfunctions of a self-adjoint elliptic operator of arbitrary order 2m in an N-dimensional domain, under general boundary conditions. Extending earlier results for second order operators, it gives sufficient Sobol…

INTERNAL INVERSE PROBLEMS OF POTENTIAL THEORY

A. I. Prilepko
1968 SovietRxiv: ru-196801.52901

This paper studies internal inverse problems in potential theory, concerned with determining the domain and density of a body from equality of its potential on an interior intersection. For generalized potentials associated with uniformly elliptic second order operators, it gives a lemma reducing eq…

INTEGRAL THEOREMS TAKING LARGE DEVIATIONS INTO ACCOUNT WHEN CRAMÉR’S CONDITION IS VIOLATED

A. V. Nagaev
1968 SovietRxiv: ru-196801.52675

This note studies large deviation probabilities for sums of independent identically distributed centered random variables with unit variance when Cramér’s condition is violated, assuming a density with tails asymptotic to exp of minus a subexponential power. It gives asymptotic formulas for the tail…

CONDITIONS FOR STRUCTURAL STABILITY AND CLASSIFICATION OF CELLS OF A THREE-DIMENSIONAL DYNAMICAL SYSTEM WITHOUT CLOSED TRAJECTORIES

K. Eshmuradov
1968 SovietRxiv: ru-196801.52515

This paper studies third order dynamical systems in a bounded domain with a smooth contact free boundary, under the restriction that closed trajectories are absent. It formulates necessary and sufficient conditions for structural stability under small perturbations of the right hand sides and their …