Showing 50 of 25357 papers

ON SUMS OF MULTIPLICATIVE FUNCTIONS

B. V. LEVIN, N. M. TIMOFEEV
1970 SovietRxiv: ru-197001.76858

The paper investigates mean values and partial sums of complex multiplicative functions under restrictions on their values at prime powers and on weighted prime sums. Building on Halász’s analytic method, the authors analyze the associated Dirichlet series near the line Re s = 1, establishing an alt…

ON THE THEORY OF \(p\)-SPACES

Unknown
1970 SovietRxiv: ru-197001.76676

This paper studies continuous mappings of p-spaces and related preservation and representation problems in general topology. It establishes conditions under which images of paracompact p-spaces under open, bicompact, regularly complete, or uniformly complete mappings are weakly paracompact or p-spac…

ON TWO PROBLEMS FROM GRAPH THEORY

V. A. Perepelitsa
1970 SovietRxiv: ru-197001.76578

The paper studies two problems in graph theory: finding minimum weight Hamiltonian circuits in directed and undirected graphs with integer edge or arc weights, and finding minimum edge coverings of graphs. It proposes a simple quadratic time algorithm that first constructs a long path and then inser…

INTEGRAL EQUATIONS WITH DEVIATING ARGUMENT

N. V. Azbelev, M. P. Berdnikova, L. F. Rakhmatullina
1970 SovietRxiv: ru-197001.76373

This paper studies systems of nonlinear integral equations with deviating arguments under measurability, continuity, and boundedness assumptions on the kernels, deviations, and prescribed outside values. It proves compactness of the associated integral operator in a space of continuous vector functi…

ON THE COMPLEXITY OF DECIDING RECURSIVELY ENUMERABLE SETS

M. I. Kanovitch
1970 SovietRxiv: ru-197001.76325

The paper studies lower bounds on the complexity of finite decision procedures for recursively enumerable sets, introducing the notion of effective nonrecursiveness in terms of unbounded recursive lower estimates. It analyzes enumerations of recursively enumerable sets, giving criteria involving reg…

ON THE APPLICATION OF THE MAXIMUM LIKELIHOOD METHOD FOR PROCESSING RANDOM GAUSSIAN PROCESSES

Yu. S. Tumashev
1970 SovietRxiv: ru-197001.76060

The paper addresses the difficulty of extending maximum likelihood estimation from discrete Gaussian measurement vectors to continuously observed Gaussian processes, where the inverse of a correlation function cannot be used directly as a matrix inverse. It approximates the correlation function by a…

DIFFERENTIAL GAMES IN MIXED STRATEGIES

È. R. Smol'yakov
1970 SovietRxiv: ru-197001.76059

This paper formulates differential games in mixed strategies for systems governed by ordinary differential equations when a value may fail to exist in pure strategies. Mixed controls are represented by time-dependent distribution functions and Lebesgue, Stieltjes measures on the players’ admissible …

ON THE INFLUENCE OF ANHARMONICITY ON THE RELAXATION TIME UNDER ADIABATIC EXCITATION AND DEACTIVATION OF MOLECULAR VIBRATIONS

S. A. LOSEV, O. P. SHATALOV, M. S. YALOVIK
1970 SovietRxiv: ru-197001.76054

This paper examines how molecular anharmonicity affects the apparent vibrational relaxation time during excitation behind shock waves and during deactivation. Using shock tube ultraviolet absorption measurements for a 10 percent oxygen and 90 percent argon mixture and for nitrogen, the authors show …

ON SINGULAR INTEGRAL OPERATORS IN A WEIGHTED HÖLDER SPACE

Unknown
1970 SovietRxiv: ru-197001.75874

The paper studies singular integral operators in weighted Hölder spaces on smooth contours, with weights having prescribed power singularities at finitely many boundary points. It establishes compactness of commutators with Hölder coefficients and gives necessary and sufficient Fredholm type conditi…

ON THE COHOMOLOGIES OF THE LIE ALGEBRA OF SMOOTH VECTOR FIELDS

I. M. Gel'fand, D. B. Fuchs
1970 SovietRxiv: ru-197001.75803

This note studies the continuous cohomology of the topological Lie algebra of smooth vector fields on a connected compact orientable smooth manifold. Building on earlier descriptions of the cohomology of formal vector fields, it introduces and analyzes filtrations of the standard cochain complex, as…

TEMPERATURE DEPENDENCE OF STIMULATED AND UNSTIMULATED CURRENT IN POLYCRYSTALLINE CdSe AT 77–273° K

A. G. Gol'dman, M. M. Pyshnyi
1970 SovietRxiv: ru-197001.75779

The study investigates the temperature dependence of stimulated and unstimulated currents in polycrystalline cadmium selenide powder photoresistors between 77 and 273 K. Using sandwich-type cells measured in a cryostat after thermal resetting, the authors recorded current-voltage characteristics bef…

THE HILBERT SPACE OF S. L. SOBOLEV AS A VARIATIONAL STRUCTURE

A. L. Kalashnikov, S. N. Slugin
1970 SovietRxiv: ru-197001.75701

The paper introduces the notion of a variational structure, a partially ordered Hilbert space in which every finite set has a unique upper bound minimizing a natural quadratic functional over all its upper bounds. It develops basic properties of these variational upper and lower bounds, showing that…

ON AN ECONOMICAL CONSTRUCTION OF THE TRANSITIVE CLOSURE OF A DIRECTED GRAPH

V. L. ARLAZAROV, E. A. DINITS, M. A. KRONROD, I. A. FARADZHEV
1970 SovietRxiv: ru-197001.75216

The paper addresses the problem of constructing the transitive closure of a directed graph more economically than the standard cubic bound, focusing on the acyclic case as a component of a broader reduction for general graphs. It partitions the vertices of an acyclic graph into ranks and expresses t…

THEOREMS ON THREE CYLINDERS FOR SOLUTIONS OF LINEAR EVOLUTION QUASI-ELLIPTIC EQUATIONS

T. G. Pletneva, S. D. Eidelman
1970 SovietRxiv: ru-197001.74993

The paper establishes three-cylinder type estimates for weak solutions of linear evolution quasi-elliptic equations of arbitrary order, including parabolic equations and models for transverse vibrations of elastic plates and rods. Using algebraic ellipticity and sectoriality conditions on the princi…

On Spaces Close to Normal and Their Bicompact Extensions

E. Shchepin
1970 SovietRxiv: ru-197001.74987

The paper studies when the Wallman compactification of a space coincides with the Ponomarev, Zaitsev compact extension defined via finite intersections of canonically closed sets. It introduces the notion of a seminormal space, a T1 space in which any two disjoint closed sets can be contained in dis…

ON THE INDEX OF CERTAIN CLASSES OF INTEGRAL OPERATORS

N. K. Karapetyants, S. G. Samko
1970 SovietRxiv: ru-197001.74938

This paper studies Noether properties and index formulas for integral operators on the real line whose kernels combine convolution terms with essentially bounded measurable coefficients having prescribed limiting values at infinity. A class of admissible coefficient functions is defined, and the mai…

EXACT CONDITIONS FOR LOCALIZATION AND CONVERGENCE OF FOURIER SERIES WITH RESPECT TO FUNDAMENTAL SYSTEMS OF FUNCTIONS OF THE BELTRAMI OPERATOR

V. A. Il'in
1970 SovietRxiv: ru-197001.74937

This paper establishes conditions for localization and uniform convergence of Fourier series associated with arbitrary fundamental systems of functions of the Beltrami operator on multidimensional domains or suitable Riemannian submanifolds. Using previously developed properties of such fundamental …

ON THE CARDINALITY OF EXTREMALLY DISCONNECTED SPACES AND COMPLETE BOOLEAN ALGEBRAS

D. A. Vladimirov, B. A. Efimov
1970 SovietRxiv: ru-197001.74609

The paper studies restrictions on the cardinalities of infinite extremally disconnected bicompact spaces and complete Boolean algebras, using Stone duality and cardinal invariants such as type, weight, Suslin number, and algebraic weight. It develops embedding and generation arguments for complete B…

DETECTION OF LINEAR POLARIZATION OF THE PULSAR MP 0628 AND SOME CHARACTERISTICS OF ITS RADIO EMISSION IN THE METER-WAVE RANGE\

V. V. Vitkevich, Yu. P. Shitov
1970 SovietRxiv: ru-197001.74344

Observations of the pulsar MP 0628 were carried out at 86 and 105 MHz with a 12-channel receiving system on the Pushchino East-West radio telescope arm to study its meter-wave radio emission. The measurements show a dispersion measure of 34.36 pc cm-3, substantially larger than an earlier reported v…

ELECTRICAL CONDUCTIVITY OF ARTIFICIAL SEMICONDUCTING DIAMOND

L. F. Vereshchagin, O. G. Revin, V. N. Slesarev, I. N. Seifi-Khusainov, A. S. Chmykhov
1970 SovietRxiv: ru-197001.74290

This paper reports measurements of the electrical conductivity of synthetic diamond single crystals doped with aluminum and compares them with undoped crystals synthesized under similar conditions. Using a specially designed temperature-controlled contact apparatus and point-contact rectification te…

REPRESENTATION OF STATISTICS OF DISCRIMINANT ANALYSIS AND ASYMPTOTIC EXPANSIONS WHEN THE DIMENSIONS OF THE SPACE ARE COMPARABLE WITH THE SAMPLE SIZES

A. D. Deev
1970 SovietRxiv: ru-197001.74132

The paper studies error distributions in linear discriminant analysis for two multivariate normal populations with common covariance when the dimension is comparable to the training sample sizes. It represents the Anderson classification statistic and the associated conditional error probabilities t…

ON BICOMPACTA WITH NONCOINCIDING INDUCTIVE DIMENSIONS

V. V. Filippov
1970 SovietRxiv: ru-197001.74115

The paper constructs compact Hausdorff spaces, bicompacta, whose covering dimension and small and large inductive dimensions do not coincide. Using lexicographically ordered zero-dimensional compacta, decompositions and gluings over marked subsets of the square and the Sierpiński carpet, it gives ex…

Topological Structure of Normally Solvable Elliptic Operators with Constant Coefficients in the Plane

P. A. Frolov
1970 SovietRxiv: ru-197001.74045

The paper studies the topology of classes of elliptic constant coefficient matrix differential operators in the plane, focusing on the connected components of operators satisfying a positivity condition for the associated matrix pencil. It gives a necessary and sufficient criterion, expressed throug…

ON SECOND SOLUTIONS OF BOUNDARY-VALUE PROBLEMS

V. S. Klimov
1970 SovietRxiv: ru-197001.73429

This paper studies the existence of nontrivial positive solutions for nonlinear boundary value problems using cone methods in Banach spaces. It develops an abstract fixed point principle for a positive completely continuous operator satisfying a cone contraction condition and a Bernstein type a prio…

The Influence of Forbush Effects on the State of the Cosmic Layer in the Lower Ionosphere

P. VELINOV, L. I. DORMAN, G. NESTOROV
1970 SovietRxiv: ru-197001.73230

This paper investigates how Forbush decreases in galactic cosmic rays affect the cosmic-ray-produced layer of the lower ionosphere at altitudes of about 50 to 80 km. Using nighttime long-wave radio absorption observations on the Brașov to Sofia path for 25 April to 12 May 1960, together with cosmic-…

ON THE PROBLEM OF OBSERVING NONLINEAR SYSTEMS

P. D. Krut'ko
1970 SovietRxiv: ru-197001.72978

The paper addresses the observation problem for nonlinear dynamical systems, specifically the determination of unmeasured phase coordinates or initial state values from measured output signals. It proposes embedding the nonlinear system in a parameter-dependent family whose zero-parameter member is …

A NEW MODIFICATION OF THE SCHEELITE STRUCTURAL TYPE—THE CRYSTAL STRUCTURE OF $\mathrm{Nd}_2\mathrm{WO}_6$

T. M. Polyanskaya, S. V. Borisov, N. V. Belov
1970 SovietRxiv: ru-197001.72892

The paper reports the crystal structure determination of a new scheelite-related modification, Nd2WO6, using x-ray diffraction data from twinned plate crystals synthesized hydrothermally and from chloride melts. The structure is described mainly in space group I2/c, with a cell related to scheelite …

APATITE-LIKE PHASES IN THE SYSTEMS MeO—Nd₂O₃—SiO₂

A. M. Shevyakov, I. F. Andreev, T. A. Tunik, V. V. Shurukhin
1970 SovietRxiv: ru-197001.72679

This paper examines apatite-like phases formed in the MeO, Nd2O3, SiO2 systems, where Me is Mg, Ca, or Ba, through heterovalent substitution of Nd3+ by divalent cations. Samples with nominal compositions of the type Me x Nd5-x(SiO4)3Oy were synthesized by prolonged firing at 1450 degrees C and analy…

CRYSTAL STRUCTURE OF PARAOXYACETOPHENONE

G. M. Lobanova, I. M. Gel'fand, S. L. Ginzburg, M. G. Neigauz, L. A. Novakovskaya, G. V. Gurskaya
1970 SovietRxiv: ru-197001.72635

The crystal structure of paraoxyacetophenone was investigated by X-ray diffraction in connection with comparisons to benzophenone, which has the same space group but different piezoelectric behavior. Unit-cell parameters, density measurements, and Weissenberg intensity data showed that the orthorhom…

VISUAL ESTIMATES OF THE COLOR OF THE TWILIGHT SKY FROM OBSERVATIONS ABOARD THE “SOYUZ-5” SPACECRAFT

K. Ya. Kondrat'ev, A. P. Galtsev, O. I. Smoktiy, E. V. Khrunov
1970 SovietRxiv: ru-197001.72440

This paper reports visual observations of the color and brightness structure of the twilight aureole near the Earth’s horizon made from the Soyuz-5 spacecraft in January 1969. The authors describe the vertical sequence of colors under cloudless, continuous cloud, and broken cloud conditions, noting …

ASYMPTOTIC BEHAVIOR OF THE EIGENVALUES OF INTEGRAL CONVOLUTION OPERATORS ON A FINITE INTERVAL WITH KERNELS WHOSE FOURIER TRANSFORMS ARE RATIONAL

B. V. Pal'tsev
1970 SovietRxiv: ru-197001.72031

The paper studies the large-index asymptotic behavior of eigenvalues of convolution integral operators on a finite interval when the Fourier transform of the kernel is a rational function, with particular attention to non-self-adjoint cases where the transform may be complex-valued. Using an analyti…

ON THE ORIGIN OF THE [OI] LINES IN THE SPECTRA OF SUPERNOVAE

V. G. Gorbatskii
1970 SovietRxiv: ru-197001.71934

This paper examines the origin of the forbidden neutral oxygen lines at 6300 and 6364 Å in type I supernova spectra, focusing on the supernova in IC 4182. It argues that the observed emission can be explained by fluorescence in an expanding, initially highly ionized hydrogen envelope, analogous to t…

ON STONE’S THEOREM

Unknown
1970 SovietRxiv: ru-197001.71367

This paper extends Stone duality to Hausdorff zero-dimensional spaces by introducing topological Boolean algebras whose topology is generated by specified ultrafilters and their complements. It defines closed topological algebras through a condition on nonprincipal algebraic components, proves conti…

ON ISOMETRIC OPERATORS ON SUBSPACES OF \(L^p\)

A. I. Plotkin
1970 SovietRxiv: ru-197001.71358

This note studies linear isometries defined on subspaces of complex and real \(L^p\) spaces, with emphasis on the case \(p \ne 2\). It proves distributional lemmas showing that, except for even integer cases requiring an additional algebraic condition, an \(L^p\)-norm preserving operator on a subspa…

ON THE CHOICE OF STEP IN COMPUTING DERIVATIVES

A. S. Kronrod, V. A. Kronrod, I. A. Faradzhev
1970 SovietRxiv: ru-197001.70790

This paper studies the selection of a finite-difference step for numerical computation of derivatives on a uniform grid. It proves an asymptotic expansion for the central kth difference operator, showing that its leading discretization error is proportional to k times the square of the step and to t…

ON AUTO-REDUCIBILITY

B. A. Trakhtenbrot
1970 SovietRxiv: ru-197001.70779

This paper introduces and studies auto-reducibility for mass problems, formalized as membership problems for sets of natural numbers, using oracle machines that compute each value without querying that value itself. It relates non-auto-reducibility to Kolmogorov and Loveland selection-based randomne…

ON SOME OSCILLATIONS IN RESONATORS WITH ROUND MIRRORS

V. P. Bykov
1970 SovietRxiv: ru-197001.70704

This paper analyzes ray oscillations in a two-dimensional open resonator formed by a circular mirror and a plane mirror. A finite-difference mapping for successive reflected rays is derived and linearized near the axial solution, then numerical calculations are used to identify nonresonant zones ass…

ON THE UNIQUENESS OF THE SOLUTION OF THE CAUCHY PROBLEM FOR A SECOND-ORDER EQUATION WITH VARIABLE COEFFICIENTS

N. N. Chaus
1970 SovietRxiv: ru-197001.70695

This note studies uniqueness for the Cauchy problem for second-order parabolic equations with complex parameter and variable coefficients, allowing unbounded lower-order terms and solutions on a finite time interval. The argument reduces the variable-coefficient problem to a uniqueness question for …