Showing 50 of 25357 papers

SOUND VELOCITIES IN CESIUM CHLORIDE AND SODIUM CHLORIDE AT PRESSURES UP TO 100 kbar

F. F. Voronov, S. B. Grigor'ev
1970 SovietRxiv: ru-197001.32796

This paper reports ultrasonic measurements of longitudinal and transverse sound velocities in polycrystalline cesium chloride and sodium chloride under quasi-hydrostatic pressures up to about 100 kbar. Using a high-pressure chamber, corrected specimen-length measurements, and transit-time data refer…

On One Variant of Averaging in Integro-Differential Equations

A. N. Filatov, L. I. Talipova
1970 SovietRxiv: ru-197001.32607

This note studies an averaging procedure for nonlinear integro-differential equations with a small parameter, in which the memory term is replaced by an integral over an infinite interval and the resulting vector field is time averaged. Under continuity, Lipschitz, boundedness, and growth assumption…

Theorem on the extraction of a basic system from a vector

È. A. Kuz'min, V. V. Ilyukhin, N. V. Belov
1970 SovietRxiv: ru-197001.32454

This crystallographic note proves a theorem on recovering an acentric basic system of points in the Fedorov group P1 from its vector system when the vector system contains a peak of multiplicity n arising from n equal point-pair vectors, under restrictions excluding higher accidental coincidences. U…

THE SCHRÖDINGER EQUATION IN HILBERT SPACE

E. A. Begovatov
1970 SovietRxiv: ru-197001.32408

The paper studies a second order Schrödinger type differential operator in a Hilbert space of Bochner integrable functions, with an operator valued potential depending on the real variable. Under assumptions on sectorial boundedness, Hölder continuity, growth of the operator family, and compactness …

A NONLINEAR ADDITION TO THE LAGRANGIAN DENSITY OF THE GRAVITATIONAL FIELD AND COSMOLOGICAL SOLUTIONS WITHOUT A SINGULARITY

V. Ts. Gurovich
1970 SovietRxiv: ru-197001.32133

This paper studies whether nonlinear curvature terms in the gravitational Lagrangian can remove cosmological singularities while preserving the usual Friedmann behavior at low curvature. Using field equations derived from an action of the form \(R + l^{-2}(l^2 R)^{4/3}\), the author constructs exact…

ON A METHOD FOR SOLVING PROBLEMS OF MATHEMATICAL PHYSICS

Ya. N. Fel'd
1970 SovietRxiv: ru-197001.32000

The paper proposes a general method for solving uniquely posed problems of mathematical physics by omitting different conditions, representing the resulting families of partial solutions as functional sets, and finding the original solution as their common element. It formulates both exact and far-z…

ON THE ZEROS OF PERIODIC DIRICHLET FUNCTIONS

A. F. Lavrik
1970 SovietRxiv: ru-197001.31932

The paper studies the location of zeros of two simple classes of periodic Dirichlet functions defined by Dirichlet series with real coefficients and functional equations relating values at s and 1 minus s. Using shortened functional equations, it derives explicit classifications of possible zero con…

ON THE \(S\)-NUMBERS OF POSITIVE OPERATORS

P. E. Sobolevskii
1970 SovietRxiv: ru-197001.31277

This paper studies estimates for the S-numbers of functions of positive linear operators in Banach spaces, including fractional powers, logarithms, iterated logarithms, and analytic semigroups. Using integral representations of fractional powers and logarithms together with standard inequalities for…

SOME SIMPLE EXAMPLES OF UNIVERSAL FUNCTIONS

Unknown
1970 SovietRxiv: ru-197001.31099

This paper gives elementary constructions of universal functions for partial recursive functions using a polynomial pairing-like map on natural numbers. It proves that any partial binary arithmetical operation satisfying three simple identities relative to this polynomial is recursively complete, an…

A PROBLEM WITH TWO FREE BOUNDARIES FOR AN ELLIPTIC EQUATION AND OPTIMAL STOPPING OF A MARKOV PROCESS

N. V. Krylov
1970 SovietRxiv: ru-197001.30948

This paper studies an elliptic boundary value problem with two free boundaries, formulated as finding a Sobolev function constrained between two obstacles and satisfying complementary sign conditions for an elliptic operator. The analysis connects this problem with a two-sided optimal stopping game …

ON THE THEORY OF THE GEYSER PROCESS

A. G. Merzhanov, A. S. Steinberg, H. S. Shteinberg
1970 SovietRxiv: ru-197001.30631

This paper develops a quantitative physical model for the geyser process, treating eruptions as explosive releases of superheating energy accumulated in an underground water chamber under hydrostatic pressure. The authors analyze the induction interval between eruptions using a simplified system in …

On Oscillations of Systems Close to Essentially Nonlinear Ones

NGUYEN VAN DAO
1970 SovietRxiv: ru-197001.30617

This paper studies periodic oscillations of systems that are close to essentially nonlinear differential systems with a small parameter, focusing on the special case in which the first solvability conditions for the principal amplitudes are identically satisfied for part of the arbitrary constants. …

Effect of Hindered Molecular Rotation in Molecular Crystals on the Magnetic Relaxation Rate Due to Intramolecular Dipole-Dipole Interactions

R. Sh. LOTFULLIN, G. K. SEMIN
1970 SovietRxiv: ru-197001.30365

This paper develops a theoretical treatment of nuclear magnetic relaxation in molecular crystals arising from intramolecular dipole dipole interactions when molecules undergo hindered reorientation about a fixed axis. Using the distribution of molecular orientations for random rotational jumps in a …

ON THE CLASSIFICATION OF TRISYMMETRIC SPACES

L. V. Sabinin
1970 SovietRxiv: ru-197001.30246

The note classifies nontrivial trisymmetric homogeneous Riemannian spaces with simple compact Lie groups of motions. It reformulates trisymmetry in terms of invoproducts and corresponding involutive sums of Lie algebras, proves auxiliary restrictions on the mirrors and isotropy subgroups, and reduce…

ON A SEQUENCE OF LINEAR POSITIVE OPERATORS

I. I. Ibragimov, A. D. Gadzhiev
1970 SovietRxiv: ru-197001.30214

This paper constructs a broad sequence of linear positive operators defined through analytic kernels and parameter sequences, encompassing classical Bernstein, Bernstein Chlodovsky, Mirakyan, and Baskakov operators as special cases. Using Korovkin type arguments, it establishes uniform convergence o…

CAMOUFLET EXPLOSION IN LIQUID AND ELASTOPLASTIC MEDIA

L. V. Al'tshuler, A. V. Balabanov, V. A. Batalov, N. A. Gerashchenko, V. A. Rodionov, V. A. Svidinskii, D. M. Tarasov
1970 SovietRxiv: ru-197001.30010

This paper investigates camouflet cavity formation produced by spherical explosive charges in liquids and elastoplastic media, including water, zinc chloride solution, wet clay, aluminum, cement and sand mortar, and rock salt. The authors combine pulsed radiographic measurements of cavity expansion …

ON THE UNIQUENESS OF THE SOLUTION OF THE CAUCHY PROBLEM FOR LINEAR EVOLUTION SYSTEMS WITH VARIABLE COEFFICIENTS

V. A. Kondratiev, S. D. Èidel'man
1970 SovietRxiv: ru-197001.29827

The paper studies uniqueness for the Cauchy problem for linear evolution systems with variable coefficients, including systems of arbitrary type solved with respect to time and systems whose spatial part is elliptic or parabolic in the sense of Petrovsky. It develops a weighted L1 estimate in a thin…

ON THE RELATION OF THE DEFORMATION FORCE

I. V. Maksimov, È. I. Sarukhanyan, N. P. Smirnov
1970 SovietRxiv: ru-197001.29736

This paper examines how the deformation force associated with motion of the Earth’s rotational pole may affect atmospheric circulation, especially the positions of the Icelandic low and Azores high. The authors derive the vertical and horizontal components of the force, argue that the vertical compo…

Differential pursuit games with constrained phase coordinates

A. B. Kurzhanskii
1970 SovietRxiv: ru-197001.29264

This paper studies differential games of approach for linear controlled systems with convex control constraints, constraints on selected phase coordinates, and terminal payoffs measuring distance to a target set. It formulates a programmed approach problem and an adjoint optimization problem in dist…

ON THE APPROXIMATION OF POLYNOMIALS OF TWO VARIABLES BY FUNCTIONS OF THE FORM \(\varphi(x)+\psi(y)\)

M.-B. A. Babaev
1970 SovietRxiv: ru-197001.29212

The paper studies uniform approximation on a rectangle of continuous functions of two variables by sums of one-variable functions, \(\varphi(x)+\psi(y)\). It identifies a class of supermodular-type functions for which the best approximation error is given explicitly by one quarter of the alternating…

The Cauchy Problem for Weakly Hyperbolic Equations

V. N. Shuhman
1970 SovietRxiv: ru-197001.29026

This paper studies the Cauchy problem for nonstrictly hyperbolic linear partial differential equations with variable coefficients in Gevrey-type classes. It formulates conditions on the real characteristic roots and uses pseudodifferential factorization, Gårding estimates, and induction on the order…

HELIUM IN GROUNDWATER ON A DEEP SEISMIC SOUNDING PROFILE IN THE TRANS-URALS

B. P. Bulashevich, V. N. Bashorin
1970 SovietRxiv: ru-197001.28761

This study examines whether helium concentrations in groundwater can indicate deep tectonic faults along a deep seismic sounding profile in the Trans-Urals. Water samples, mainly from pumped wells 80 to 100 m deep, were degassed by vacuum extraction and analyzed for helium, then compared with seismi…

On the Rhythmic Nature of New Phase Growth in Potassium Nitrate

Yu. G. Asadov, V. I. Nasirov
1970 SovietRxiv: ru-197001.28454

This study examines the morphology of polymorphic transformations in potassium nitrate, with emphasis on the growth of the high-temperature beta phase from single-crystalline alpha-phase specimens. Using purified, well-faceted crystals and microscopic observation on a thermostated heating stage, the…

UNSTABLE EXTREMAL PROBLEMS

V. F. Sholohovich
1970 SovietRxiv: ru-197001.28327

This paper studies regularization of solvable but unstable extremal problems over closed convex subsets of real Banach spaces, for quasiconvex lower semicontinuous functionals. The proposed method replaces the original minimization by the search for the least norm element in approximate level sets, …

ON THE STABILITY OF SELF-OSCILLATIONS OF A FLUID

V. I. Yudovich
1970 SovietRxiv: ru-197001.28271

This paper develops a linearization principle for the stability of periodic self-oscillations in infinite-dimensional dynamical systems, formulated as nonlinear partial semigroups on a Banach space. It proves an analogue of the Andronov-Witt theorem: a smooth cycle is asymptotically stable with asym…

JUSTIFICATION OF THE AVERAGING METHOD

I. B. Simonenko
1970 SovietRxiv: ru-197001.28147

The paper justifies Bogolyubov’s averaging method for abstract parabolic equations in a Banach space, considering evolution equations with a rapidly varying nonlinear term and an unbounded linear operator generating an analytic semigroup. Under assumptions on fractional power spaces, compactness, di…

CONSTRUCTION OF SEPARATRIX SURFACES AND REGIONS OF STABILITY IN THE PHASE SPACES OF NONLINEAR SYSTEMS

B. N. Petrov, R. A. Nelepin, B. M. Shamrikov
1970 SovietRxiv: ru-197001.27622

The paper develops a method for constructing separatrix surfaces and stability regions in the phase spaces of nonlinear systems of the form consisting of a linear part plus a scalar nonlinearity. By transforming the system to diagonal coordinates and introducing two-dimensional revealing sections in…

On bicompact spaces with noncoinciding dimensions

Unknown
1970 SovietRxiv: ru-197001.27600

The paper develops quotient and decomposition constructions for bicompact spaces designed to separate covering dimension, small inductive dimension, and large inductive dimension. After formulating a general scheme, it constructs families of bicompacta built from ordered compacta, Cantor sets, and m…

ESTIMATES OF THE NUMBER OF STATES OF FINITE AUTOMATA

A. N. Maslov
1970 SovietRxiv: ru-197001.27387

This paper studies the state complexity of operations on regular sets of words represented by finite automata, taking the number of states in a minimal representing automaton as the complexity measure. It gives binary alphabet examples showing that known upper bounds for union, product, and iteratio…

On the Temperature of the Exospheres of the Earth, Mercury, Venus, Mars, Jupiter, and of the Solar Corona

I. M. Matora
1970 SovietRxiv: ru-197001.26527

This paper examines whether the temperatures of planetary exospheres and the solar corona are constrained by the gravitational potentials of their parent bodies. By comparing the Earth’s upper exosphere and the upper solar corona, it notes that the ratio of hydrogen particle thermal energy to gravit…

ON A METHOD FOR SOLVING THE CAUCHY PROBLEM FOR THE LINEARIZED BOLTZMANN EQUATION AND FOR COMPUTING SPACE-TIME CORRELATION FUNCTIONS

A. D. Khon'kin
1970 SovietRxiv: ru-197001.26512

The paper develops a method for solving the Cauchy problem for the linearized Boltzmann equation and for computing space-time correlation functions of a classical one-component gas in the Boltzmann limit. Treating the collision term as an operator in a Hilbert space, it uses semiboundedness to invok…

ON LINEAR ESTIMATES OF REGRESSION

A. A. Tempel'man
1970 SovietRxiv: ru-197001.26483

This note studies estimation of unknown finite-dimensional regression functions in the mean of a random function with known correlation kernel. Using reproducing-kernel Hilbert spaces and extended kernels, it characterizes canonical isometries associated with the random function and derives uniforml…

CALCULATION OF THE MAGNITUDE OF STABLE ROUGHNESS AFTER RUNNING-IN (ELASTIC CONTACT)

I. V. KRAGELSKII, V. S. KOMBALOV
1970 SovietRxiv: ru-197001.26436

This paper develops a calculation method for the stable roughness that forms after running-in during sliding elastic contact. Using the molecular-mechanical theory of friction together with a fatigue interpretation of wear, the authors argue that the stable surface state corresponds to the roughness…

Calculation of luminescence depolarization with changes in temperature and concentration of the fluorescent substance

Academician of the Academy of Sciences of the BSSR A. N. SEVCHENKO, V. I. POPECHITS, A. M. SARZHEVSKII
1970 SovietRxiv: ru-197001.26172

This paper extends S. I. Vavilov’s theory of concentration depolarization of fluorescence by incorporating temperature and viscosity as variables affecting resonance migration of excitation energy in viscous solutions. Treating fluorescent molecules as Brownian particles, the authors derive collisio…

ON INTERFERENCE MEASUREMENTS IN GAS DYNAMICS

È. P. Kazandjan, V. S. Sukhorukikh
1970 SovietRxiv: ru-197001.26105

The paper addresses the difficulty of interpreting gas-dynamic interferograms in monochromatic light when fringe breaks, crowding, or discontinuities prevent direct fringe tracking, a problem often resolved by also recording achromatic fringes. It proposes a method for determining the integer optica…

FACTORIZATION OF SYMMETRIC MATRIX POLYNOMIALS

V. A. Yakubovich
1970 SovietRxiv: ru-197001.25870

The paper studies factorization of complex matrix polynomials satisfying the symmetry condition A(lambda) equals A*(-conjugate lambda), motivated by applications in stability, optimal control, and differential games. It gives necessary and sufficient conditions for representing such a polynomial as …

Rocket Measurements of Temperature and Wind in the Upper Atmosphere of the Polar Region by the Artificial Luminous Clouds Method

Y. E. Blamont, M. L. Shanen, M. Maillard, L. A. Andreeva, L. A. Katasev, S. M. Poloskov, G. F. Tulinov, D. B. Uvarov
1970 SovietRxiv: ru-197001.25631

Joint Franco-Soviet rocket experiments on Hayes Island in 1967 and 1968 measured temperature, winds, and diffusion in the polar upper atmosphere using artificial luminous sodium and aluminum oxide clouds released at about 120 to 174 km. Temperatures were derived from Doppler broadening of sodium res…