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ON THE EXISTENCE OF MAPPINGS IN THE PLANE FOR DEGENERATING ELLIPTIC SYSTEMS OF FIRST ORDER

I. S. Ovchinnikov
1970 SovietRxiv: ru-197001.85251

The paper studies the existence of homeomorphic plane mappings between simply connected domains that solve first order elliptic systems whose ellipticity may degenerate. It develops an approximation approach, replacing the degenerate system or the domain by nondegenerate ones and passing to a limit …

ON THE PARTIAL ORDERABILITY OF RINGS AND ALGEBRAS

A. I. Veksler
1970 SovietRxiv: ru-197001.84797

The paper studies when a commutative associative ring without nonzero nilpotents and with torsion-free additive group can be equipped with partial orders compatible with multiplication, especially orders stronger than those of partially ordered rings of functions. It introduces u-cones and phi-cones…

FINDING SADDLE POINTS ON POLYHEDRA

Unknown
1970 SovietRxiv: ru-197001.84211

The paper studies the computation of saddle points for twice continuously differentiable functions that are strictly convex in one variable and strictly concave in the other, when both variables are constrained to bounded polyhedra. It characterizes saddle points by the vanishing of distances from t…

ON ANALYTIC TRANSFORMATIONS OF A NORMAL VECTOR

V. N. Logvinenko, I. V. Ostrovskii, L. I. Ronkin
1970 SovietRxiv: ru-197001.83979

The paper studies entire functions of several complex variables that are real on real vectors and transform a vector of independent standard normal variables into a standard normal variable. It strengthens a result of Linnik and Eidlin by proving that any such function is either a normalized real li…

ON SCALES OF GROWTH OF ENTIRE FUNCTIONS OF SEVERAL VARIABLES

L.S. Maergoiz
1970 SovietRxiv: ru-197001.83733

The paper studies growth scales for entire functions of several complex variables through the majorant of the function and the geometry of associated convex or quasiconvex functions. It analyzes Goldberg-type orders and shows how they correspond to scales built from homogeneous logarithmically conve…

ON THE ASYMPTOTICS OF THE SOLUTION OF A PROBLEM WITH AN INITIAL JUMP FOR A SYSTEM OF QUASILINEAR EQUATIONS WITH THE SAME PRINCIPAL PART CONTAINING A SMALL PARAMETER

K. A. Kasymov
1970 SovietRxiv: ru-197001.83443

The paper studies a singularly perturbed initial value problem for a system of quasilinear first order equations with a common principal part, where the initial condition for one component is scaled by a parameter dependent on the small parameter. Under sign and growth assumptions on the nonlinear t…

REPEATED TWO-PERSON GAMES OVER LARGE TIME INTERVALS

A. Yu. Levin
1970 SovietRxiv: ru-197001.82856

This paper studies repeated two-person zero-sum matrix games in which each pair of pure strategies has both a payoff and a mean duration, and the total encounter time is large but finite or random. It argues that ordinary optimal strategies for the payoff matrix, and generally also those for payoff …

A PRIORI ESTIMATES FOR EQUATIONS WITH A PARAMETER

A. S. Bratus'
1970 SovietRxiv: ru-197001.82769

This note studies differential operators with smooth coefficients depending on a complex parameter on a ray, focusing on cases where the usual nonvanishing condition for the principal symbol fails. It derives necessary conditions for weighted a priori estimates in terms of the imaginary part of a Po…

PARAMETRIC REPRESENTATION OF UNIVALENT FUNCTIONS

V. Ya. Gutlyanskii
1970 SovietRxiv: ru-197001.81837

This paper gives a parametric characterization of the class of normalized univalent holomorphic functions in the unit disk. It introduces a compact class of nondecreasing two variable functions and uses Stieltjes integrals to formulate a Löwner type differential equation whose solutions yield exactl…

ON INTEGRAL OPERATORS

V. B. Korotkov
1970 SovietRxiv: ru-197001.81655

The paper studies when linear operators from normed spaces into spaces of measurable functions can be represented by scalar products with strongly measurable dual-valued kernels, extending earlier integral-operator representation results beyond separable settings. It introduces C-operators and chara…

LIMIT THEOREMS FOR FUNCTIONALS OF THE PROCESS OF STEP SUMS OF RANDOM VARIABLES DEFINED ON A SEMI-MARKOV PROCESS WITH A FINITE SET OF STATES

D. S. Sil'vestrov
1970 SovietRxiv: ru-197001.81218

The paper studies step-sum processes formed from random rewards attached to the states of a finite semi-Markov process, with holding times and increments depending on the current state. Under ergodicity of the embedded Markov chain and finite second-moment assumptions, it establishes convergence of …

ASYMPTOTIC PROPERTIES OF SOLUTIONS OF ONE CLASS OF INTEGRAL EQUATIONS OF THE THEORY OF ELASTICITY AND MATHEMATICAL PHYSICS

V. A. Babeshko
1970 SovietRxiv: ru-197001.80941

This note studies a class of Bessel-kernel integral equations arising in mixed boundary-value problems of elasticity and mathematical physics for a layer with a circular change of boundary conditions, with emphasis on the large-radius limit. Under analyticity, factorization, and asymptotic assumptio…

THE CENTER AND SPREAD OF A PROBABILITY DISTRIBUTION

V. M. Zolotarev
1970 SovietRxiv: ru-197001.80282

The paper introduces two characteristics of probability distributions, called the r-center and r-spread, defined through integrals of the imaginary and real parts of the logarithm of the characteristic function. It develops their basic properties, including behavior under scaling and reflection, add…

NONABELIAN \(CL\)-GROUPS

D. I. ZAĬTSEV, L. M. KLYATSKAYA
1970 SovietRxiv: ru-197001.80026

This paper extends the theory of abelian groups in which all L-closed subgroups are complemented to a nonabelian setting. It defines a nonabelian CL-group as a group satisfying a complement condition for L-closed subgroups of maximal abelian subgroups and possessing an invariant maximal abelian subg…

GROUPS OF TYPE \(CS\)

E. I. Shatylo
1970 SovietRxiv: ru-197001.79322

This paper studies finite groups that are not decomposable into a uniform product of their Sylow subgroups while all proper subgroups are so decomposable, termed groups of type CS. Using skew products of cyclic groups with finite fields and presentations by generators and relations, it develops stru…

On the structure of differential games

Academician N. N. KRASOVSKII, A. I. SUBBOTIN
1970 SovietRxiv: ru-197001.78384

This paper studies minimax time-to-encounter differential games for systems with additive controls of two players, using approximation strategies defined through set-valued contingent dynamics. It introduces stability and absorption notions for families of closed sets and constructs extremal strateg…

On a Necessary Condition for Tikhonov Regularizability

V. A. Vinokurov
1970 SovietRxiv: ru-197001.77859

The paper studies a necessary topological condition for Tikhonov regularizability of approximate solutions to injective equations between metric spaces. It proves that if such a problem is regularizable, then the images under the regularizing operators of any dense subset of the data space form a de…

UNIFORM ESTIMATE FOR THE NUMBER OF REPRESENTATIONS OF UNITY BY A BINARY FORM OF DEGREE \(n \ge 3\)

V. A. Tartakovskii
1970 SovietRxiv: ru-197001.77758

The paper studies the number of integral solutions to the Thue equation defined by a binary form of degree at least three representing unity. Building on earlier finiteness results of Thue and uniform bounds known mainly for cubic forms, it addresses whether a bound depending only on the degree can …

ON THE QUESTION OF AN ASYMPTOTIC FORMULA

B. G. Kotsarev
1970 SovietRxiv: ru-197001.77714

The paper studies asymptotic formulas for the number of solutions of Waring-type congruences modulo prime powers, especially in cases where such formulas may fail when the number of variables equals the exponent. It replaces the fixed right-hand side by a variable ranging over a short interval and i…

INTEGRABILITY OF THE MAJORANT OF PARTIAL SUMS OF A TRIGONOMETRIC SERIES WITH QUASICONVEX COEFFICIENTS

S. A. Telyakovskii
1970 SovietRxiv: ru-197001.77275

This paper studies maximal functions formed from the partial sums of cosine and sine trigonometric series whose coefficients tend to zero and form a quasiconvex sequence. It proves asymptotic estimates for the integrals, away from the origin, of the majorants of these partial sums in terms of tail m…

ON POLYHEDRAL REPRESENTATIONS OF METRIC SPACES

I. M. Kozlovskii
1970 SovietRxiv: ru-197001.77245

This note studies inverse polyhedral representations of metric spaces, with emphasis on irreducibility, standardness, and behavior on systems of closed subsets. It extends results of Freudenthal, Isbell, and Pasynkov by proving that every sigma-locally finite system of closed subsets of a complete m…

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…

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 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…

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…

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…

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…