Showing 50 of 25357 papers

A NON-SELF-ADJOINT ONE-DIMENSIONAL PERTURBATION OF THE OPERATOR OF MULTIPLICATION BY THE INDEPENDENT VARIABLE

V. È. Lyantse
1968 SovietRxiv: ru-196801.46830

The paper studies a rank-one non-self-adjoint perturbation of the operator of multiplication by the independent variable in L2 on the real line, assuming analytic continuation and strip-type square-integrability conditions on the perturbing vectors. It characterizes nonreal eigenvalues as zeros of a…

ON THE STABILITY OF BODIES OF REVOLUTION WITH RESPECT TO RADIAL PERTURBATIONS

G. S. Bisnovatyi-Kogan, Ya. B. Zel'dovich, A. M. Fridman
1968 SovietRxiv: ru-196801.46711

This paper examines the stability of rotating self-gravitating bodies of revolution under radial perturbations, including perturbations that cause crossing of mass layers. Using an energy method for systems of spherical and cylindrical layers with conserved angular momenta, the authors show that rad…

ON THE ORIENTING ACTION OF MICA ON THE GROWTH OF THIN Bi FILMS

R. N. Sheftal', Yu. F. Ogrin, V. N. Lutskii, M. I. Elinson
1968 SovietRxiv: ru-196801.46641

This study examines how strongly mica substrates orient the growth of thin bismuth films when the mica surface is separated from the deposited metal by an intermediate organic layer. Bismuth was vacuum deposited on mica coated with celluloid layers of varying thickness, on coated glass, and in a sec…

ANALOGS OF STIRLING’S FORMULA

V. M. Kalinin
1968 SovietRxiv: ru-196801.46631

The paper develops several parameterized analogs of Stirling’s formula for the gamma function, motivated by applications requiring expansions in variables other than the argument itself. It derives asymptotic expansions for the gamma function and its reciprocal using a shift parameter, with coeffici…

THE STRUCTURE OF A GROUP AND THE STRUCTURE OF ITS SUBGROUPS

Unknown
1968 SovietRxiv: ru-196801.46548

This note studies how restrictions on subgroups of finite groups determine the structure of the whole group, with particular attention to solvability, maximal subgroups, and classes of finite p-groups. It introduces several auxiliary classes, including generalized Schmidt and Frobenius groups, E-gro…

ON DUALITY IN PROBLEMS OF THE CALCULUS OF VARIATIONS

A. D. Ioffe, V. M. Tikhomirov
1968 SovietRxiv: ru-196801.46488

The paper develops duality formulas for variational problems in which an integral functional is minimized subject to an integral constraint. Using Young transforms and convexity, it proves that the value function of a basic calculus of variations problem can be represented as a maximum over a scalar…

ON A GENERALIZED FORMULA OF M. RIESZ

D. L. Berman
1968 SovietRxiv: ru-196801.46456

The paper extends a quadrature identity for trigonometric polynomials, previously shown to include M. Riesz’s formula as a special case, to analytic functions associated with a finite plane domain and to half-integer trigonometric polynomials. Using Faber polynomials and a shift operator defined thr…

ON FINDING THE EXTREMUM OF A LINEAR FUNCTION ON A CONVEX SET

A. A. Kaplan
1968 SovietRxiv: ru-196801.46302

The paper considers the problem of maximizing a linear function over a closed bounded convex body in finite-dimensional Euclidean space. It proposes a cutting-plane procedure that starts from an enclosing polyhedron and an interior point, repeatedly solves a linear programming relaxation, and, when …

INVARIANT SUBSPACES OF DISSIPATIVE VOLTERRA OPERATORS

G. È. KISILEVSKII
1968 SovietRxiv: ru-196801.46289

This paper studies invariant subspaces of simple dissipative Volterra operators whose imaginary components are nuclear, with emphasis on the nonunicellular case. Using characteristic operator functions, their divisors, and relations between type and weight, it develops lattice operations for invaria…

ON MINIMA OF THE NORM FUNCTION IN IMAGINARY QUADRATIC FIELDS

E. A. Anfert'eva, N. G. Chudakov
1968 SovietRxiv: ru-196801.45964

This note studies the maximal minimum norm among ideal classes in imaginary quadratic fields, focusing on effective lower bounds for the quantity defined by the least norm in each class. Building on analytic identities for Epstein zeta type sums attached to reduced binary quadratic forms, the author…

THE EFFECT OF HEATING AND PRESSURE ON SOME PHYSICAL PROPERTIES OF DIAMONDS

A. V. NIKITIN, M. I. SAMOILOVICH, G. N. BEZRUKOV,
1968 SovietRxiv: ru-196801.45963

This paper examines how heating under high pressure affects defect-related physical properties of natural and synthetic diamonds, with emphasis on nitrogen impurities and associated optical and paramagnetic centers. Natural Yakut diamonds and several synthetic diamond specimens were treated for seve…

ANGULAR AND ENERGY DISTRIBUTION OF SECONDARY IONS DURING BOMBARDMENT OF A TARGET BY IONS AT GLANCING ANGLES

U. A. Arifov, A. A. Aliev
1968 SovietRxiv: ru-196801.45917

This paper investigates the angular and energy distributions of secondary ions emitted when heated tungsten and molybdenum targets are bombarded at glancing incidence by alkali ions with energies of 1 to 3 keV. Using movable-probe angular measurements and electrostatic analysis of energy spectra, th…

High-Rank Moments in a Weakly Rarefied Gas

R. G. Barantsev, I. B. Lutanskaya
1968 SovietRxiv: ru-196801.45703

This paper analyzes high-rank moments of the molecular distribution function in a weakly rarefied gas near local equilibrium. Using a Hermite polynomial expansion and the 56-moment system of equations for small Knudsen numbers, it solves the linearized relations for second, third, fourth, and fifth …

COEFFICIENTS OF EXTREMAL POLYNOMIALS

L. G. Lozner
1968 SovietRxiv: ru-196801.45283

The paper studies relations between the coefficients of extremal polynomials on the interval [0,1] and the number of their Chebyshev alternants. Using Voronovskaya’s functional method together with convex geometric arguments, it characterizes projections of the unit ball of polynomials with bounded …

SOME EXTREMAL PROBLEMS

S. L. Krushkal'
1968 SovietRxiv: ru-196801.45168

This note studies extremal problems for univalent analytic functions and related classes of quasiconformal mappings. Using variational methods, it characterizes extremal slit mappings in the unit disk, relates them to quasiconformal extension problems with prescribed interpolation data, and proves c…

ON THE STABILITY OF INVERSE PROBLEMS OF GEOMETRICAL SEISMOLOGY

V. M. Markushevich
1968 SovietRxiv: ru-196801.44719

This paper studies the stability of inverse problems in geometrical seismology for a spherically symmetric Earth, where seismic velocity is to be inferred from hodographs. It treats separately the cases of a surface source and a deep source, formulating the corresponding integral equations and using…

A SPHERICAL CUT IN AN ELASTIC SPACE

L. T. Boiko, V. A. Zyuzin, V. I. Mossakovskii
1968 SovietRxiv: ru-196801.44237

This paper treats an axially symmetric elasticity problem for an infinite elastic space cut along part of a spherical surface. Using Trefftz displacement potentials and analytic functions of a complex variable, the authors derive integral representations for displacements and stresses and reduce the…

EXPERIMENTAL DETERMINATION OF THE NUMBER OF FAST NEUTRONS IN THE FISSION SPECTRUM

F. Nasyrov, B. D. Stsiborskii
1968 SovietRxiv: ru-196801.44217

This paper reports an experimental determination of the fast neutron spectrum in the core of a highly enriched uranium fast reactor, with emphasis on estimating the fraction of neutrons at energies up to 24 MeV. The authors use threshold indicators, fission chambers, and activation measurements to o…

ON PRODUCTS, POWERS, AND CONTRACTIONS OF HOMOMORPHISMS

M. A. Gol'dman, S. N. Krachkovskii
1968 SovietRxiv: ru-196801.44120

This paper studies linear homomorphisms between linear topological spaces, with emphasis on closedness, products, powers, and restrictions of such operators. It proves that a homomorphism with closed kernel and closed range is a closed operator, establishes conditions under which products of homomor…

ON THE THEORY OF GROUPED SAMPLES

N. A. Bodin
1968 SovietRxiv: ru-196801.43920

This note refines and extends results on estimation from grouped samples to multidimensional distributions depending on a vector parameter. It formulates maximum likelihood estimation after partitioning the observation space into finitely many cells, gives conditions for existence and uniqueness of …

THE REALITY OF THE WESTWARD DRIFT OF THE GEOMAGNETIC FIELD ACCORDING TO ARCHAEO-MAGNETIC DATA

S. P. Burlatskaya, T. B. Nechaeva, G. N. Petrova
1968 SovietRxiv: ru-196801.43912

This paper examines whether the westward drift of the geomagnetic field is a real geophysical phenomenon and what its existence implies for interpretations of dipole and non-dipole components of the main field. Using archaeomagnetic secular variation curves, especially inclination data from regions …

ON THE STABILITY OF SOLUTIONS OF A SYSTEM OF DIFFERENTIAL EQUATIONS IN THE PROBLEM OF AUTONOMOUS DETERMINATION OF THE COORDINATES OF A MOVING OBJECT

V. N. Koshlyakov, Yu. B. Lyusin, V. A. Storozhenko, M. E. Temchenko, I. Sh. Shulman
1968 SovietRxiv: ru-196801.43760

This paper studies Lyapunov stability in the autonomous determination of the coordinates of a moving object by an inertial navigation system with a horizon-stabilized platform. The nonlinear equations for latitude, longitude, and platform orientation are transformed using Rodrigues-Hamilton paramete…

NONLINEAR EQUATIONS WITH POTENTIAL AND MONOTONE OPERATORS

Unknown
1968 SovietRxiv: ru-196801.43535

This paper studies nonlinear equations of the form x = BF(x) in separable locally convex spaces embedded in a Hilbert space, where F maps into the strong dual and B is a bounded linear operator whose Hilbert-space restriction has positivity or quasi-positivity properties. By reducing the equation to…

ON A CLASS OF PSEUDODIFFERENTIAL OPERATORS

Yu. V. Egorov
1968 SovietRxiv: ru-196801.42978

This paper studies a class of pseudodifferential operators of principal type characterized by a priori Sobolev estimates with loss parameter δ. It gives necessary and sufficient algebraic conditions on the principal symbol at characteristic points for the estimate with δ = 2/3, using auxiliary nonex…

ON THE APPROXIMATION VISCOSITY OF DIFFERENCE SCHEMES

N. N. Yanenko, Yu. I. Shokin
1968 SovietRxiv: ru-196801.42795

This paper studies approximation viscosity in finite-difference schemes for linear hyperbolic systems, focusing on whether numerical dissipation preserves contact discontinuities. Using the first differential approximation of a general difference scheme, the authors define property K and a stronger …

THE INFLUENCE OF HEAVY ATOMS ON INTERCOMBINATION TRANSITIONS IN PORPHYRIN MOLECULES

A. T. Gradyushko, V. A. Mashenkov, A. N. Sevchenko, K. N. Solov'ev, M. P. Tsvirko
1968 SovietRxiv: ru-196801.42369

This study examines the external heavy atom effect on intercombination transitions in porphyrins and metalloporphyrins, using etioporphyrin I and related complexes in alkyl iodide solvents. Fluorescence quenching, lifetime measurements, low-temperature phosphorescence spectra, and pulse spectroscopi…

Mappings of type $s$ of locally convex spaces

B. S. Brudovskii
1968 SovietRxiv: ru-196801.42329

The paper extends the notion of mappings of type s, previously studied for normed spaces, to separated locally convex spaces by defining them through images of neighborhoods as strongly nuclear sets. It establishes several equivalent characterizations, including representation by rapidly decreasing …

QUASISTATIONARY STATES IN A CONICAL POTENTIAL WELL

E. E. Nikitin
1968 SovietRxiv: ru-196801.42230

This paper analyzes quasistationary nuclear states in an upper conical adiabatic potential well arising near intersections of electronic terms of the same symmetry, with emphasis on triatomic systems near an equilateral configuration. By separating angular variables and imposing single-valuedness of…

Stability of Nonlinear Impulsive Systems

A. Kh. GELIG
1968 SovietRxiv: ru-196801.42198

This paper studies stability and dissipativity of nonlinear impulsive control systems with pulse-width, frequency-pulse, amplitude, time, and phase modulation, including systems whose linear parts may contain distributed-parameter elements. It formulates sufficient frequency-domain conditions, expre…

SOME LIMIT THEOREMS FOR LARGE DEVIATIONS

Werner Wolf
1968 SovietRxiv: ru-196801.41890

The paper studies large deviation limit theorems for normalized sums of independent, not necessarily identically distributed random variables, in settings where the classical Cramér exponential moment condition may fail. It derives integral and local asymptotic formulas comparing tail probabilities …

THE VELOCITY FIELD EXCITED BY A SHOCK WAVE IMPINGING ON A STATIONARY THIN SYMMETRIC BODY

E. A. Krasil'shchikova
1968 SovietRxiv: ru-196801.41839

This paper analyzes the velocity field generated when a finite-amplitude plane shock wave strikes a stationary thin body symmetric about a plane in an unbounded compressible medium. Under small perturbation and irrotational-flow assumptions, the problem is linearized and formulated for the velocity …

ON ONE DEFINITION OF DIMENSION

V. Egorov, Yu. Podstavkin
1968 SovietRxiv: ru-196801.41748

The paper studies a dimension invariant, denoted Dind, proposed by A. V. Arkhangel’skii, which combines covering and inductive approaches to topological dimension. It proves that for normal spaces the large inductive dimension satisfies Ind X ≤ Dind X, and that for perfectly normal spaces the two di…

A POSSIBLE MECHANISM FOR THE FORMATION OF COMPLEX RADIATION DEFECTS IN SILICON INTRODUCED BY ELECTRON IRRADIATION

S. M. Gorodetskii, L. B. Kreinin
1968 SovietRxiv: ru-196801.41715

The paper examines possible mechanisms by which electron irradiation produces complex radiation defects in silicon, focusing on secondary associations formed from vacancies and interstitial atoms rather than on unstable primary defects. Using the McKinley-Feshbach scattering cross section and a Kinc…

The Occurrence of Discontinuities in the Continuation of Solutions of Nonlinear Mixed Problems for Hyperbolic Equations in the Plane

V. N. Gol'dberg
1968 SovietRxiv: ru-196801.41621

The paper studies continuation of solutions to nonlinear mixed boundary value problems for second order hyperbolic equations in a plane strip when a boundary nondegeneracy condition fails at a finite time. It analyzes the resulting loss of classical continuation, proves blowup behavior of first deri…

A PERIODIC BOUNDARY-VALUE PROBLEM FOR AN ORDINARY DIFFERENTIAL EQUATION OF SECOND ORDER

Yu. V. KOMLENKO, E. L. TONKOV
1968 SovietRxiv: ru-196801.41580

The paper studies periodic boundary value problems for second order ordinary differential equations with summable periodic coefficients, focusing on existence of the Green function, its sign, and related differential inequality methods. Using the distribution of zeros of solutions of the associated …

ON AN ESTIMATE OF THE SOLUTION OF THE FIRST BOUNDARY-VALUE PROBLEM FOR A PARABOLIC EQUATION OF SECOND ORDER

Yu. N. Cheremnykh
1968 SovietRxiv: ru-196801.41442

This paper derives an upper estimate for the modulus of a classical solution of the first boundary-value problem with zero lateral boundary data for a second-order linear parabolic equation in an expanding space-time domain. Under uniform ellipticity and a sign condition on the divergence of the low…

EMBEDDING OF CERTAIN CLASSES OF FUNCTIONS OF ONE VARIABLE

P. L. Ul'yanov
1968 SovietRxiv: ru-196801.41342

This paper studies embedding theorems for classes of one-variable functions whose first moduli of continuity in Lp are controlled by a given modulus. It establishes sufficient conditions, expressed as weighted series involving the modulus of continuity, for membership in Orlicz-type spaces such as L…

RINGS WITHOUT NILPOTENT ELEMENTS AND COMPLETELY PRIME IDEALS

V. A. Andrunakievich, Yu. M. Ryabukhin
1968 SovietRxiv: ru-196801.41326

This note studies associative rings without nonzero nilpotent elements through completely prime and completely semiprime ideals. Using m-systems and a Zorn lemma argument, it proves the existence of completely prime ideals over a completely semiprime ideal and shows that every completely semiprime i…