Mathematics › Mathematics ×

Showing 50 of 5847 papers in Mathematics

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…

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 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 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 …

EXAMPLES OF BICOMPACTA WITH NONCOINCIDING INDUCTIVE DIMENSIONS

B. A. Pasynkov, I. K. Lifanov
1970 SovietRxiv: ru-197001.70187

The paper constructs compact Hausdorff spaces whose small and large inductive dimensions do not coincide, refining earlier examples by obtaining spaces of cardinality continuum and, in one version, satisfying the first axiom of countability. The construction uses a general gluing procedure applied t…

ON ESTIMATING THE BEST APPROXIMATION OF AN INTEGRABLE FUNCTION ON THE REAL AXIS BY ENTIRE FUNCTIONS OF FINITE DEGREE

I. I. Ibragimov, F. G. Nasibov
1970 SovietRxiv: ru-197001.69349

The paper studies best approximation of functions on the real axis by entire functions of finite degree in \(L_p\) metrics, with emphasis on determining sharp or improved constants in Jackson-type estimates for \(L_2\). Using Fourier transform methods and Plancherel’s theorem, it identifies the best…

ON THE ROLE OF THE EXTREME TERMS OF A VARIATION SERIES IN THE FORMATION OF A LARGE DEVIATION OF THE SUM OF INDEPENDENT RANDOM VARIABLES

A. V. Nagaev
1970 SovietRxiv: ru-197001.69194

The paper studies how extreme order statistics contribute to large deviations of sums of independent identically distributed random variables with mean zero and finite variance. It derives conditional limiting distributions for the maximum, second maximum, and in some cases the minimum, under condit…

LIMITING DISTRIBUTIONS OF FUNCTIONALS OF A SEMI-MARKOV PROCESS DEFINED ON A FIXED SET OF STATES UP TO THE MOMENT OF FIRST EXIT

V. V. Anisimov
1970 SovietRxiv: ru-197001.69130

The paper studies limiting distributions of additive functionals of a finite semi-Markov process restricted to a set of states up to the first exit from that set. Under a group condition for the state set and attraction assumptions on the one-step functional increments, it derives weak limits for su…

On Stabilization of the Solution of the Cauchy Problem for a Parabolic Equation

A. K. Gushchin, V. P. Mikhailov
1970 SovietRxiv: ru-197001.67816

This note studies stabilization as time tends to infinity for the Cauchy problem for a parabolic equation with variable positive coefficient in the whole Euclidean space. Under boundedness, Hölder regularity, and an averaged convergence condition on the coefficient, the authors prove a necessary and…

Mappings of Families of Sets

ft(M)=t'f(M),
1970 SovietRxiv: ru-197001.67797

The paper studies one-to-one mappings between affine spaces that send every translate of a fixed bounded set onto a translate of its image, and asks when such mappings must be affine. It introduces shifts preserving a generator and the associated class of quasicylinders, then proves that every conti…

CUBATURE FORMULAS IN \(L_2^{(m)}(\Omega)\)

V. I. Polovinkin
1970 SovietRxiv: ru-197001.67650

This paper studies the asymptotic behavior of cubature error functionals in Sobolev type spaces \(L_2^{(m)}(\Omega)\), extending earlier results for the whole Euclidean space \(L_2^{(m)}(E_n)\). Using Hilbert space decompositions, extension operators, and bounded inverse arguments, it proves that a …

ASYMPTOTIC BEHAVIOR OF QUASIANALYTIC FUNCTIONS

S. P. Geisberg
1970 SovietRxiv: ru-197001.67591

The paper studies the asymptotic behavior of functions in a quasianalytic class on the real line, using the limiting rate of decrease introduced by Korenblum. It constructs an associated function and narrowing infinite strip, then proves that each quasianalytic function can be decomposed, for any re…

FUNCTIONS OF ORDERED SELECTION OF CONTINUOUS VARIABLES

Unknown
1970 SovietRxiv: ru-197001.67332

The paper introduces ordered-selection functions for continuous variables as extensions of discrete voting functions and median operations within continuous logic. It defines the function selecting the m-th value after ordering n variables, establishes its relation under increasing and decreasing or…

COERCIVE BOUNDARY-VALUE PROBLEMS

L. S. Frank
1970 SovietRxiv: ru-197001.67247

This paper develops a discrete analogue of coercive boundary conditions for elliptic difference operators on a half-space grid. It defines Sobolev-type spaces of grid functions, establishes a quasihomogeneous factorization theorem for elliptic symbols on the torus, and introduces a smoothness condit…

Multivalued mappings and some related questions

M. M. Choban
1970 SovietRxiv: ru-197001.66378

This paper studies selection problems for multivalued mappings in general topology, especially conditions under which lower or upper semicontinuous mappings admit continuous, sigma-continuous, or F-sigma-continuous sections. It establishes selection theorems for paracompact, perfectly normal, zero-d…

CONFORMAL INVARIANCE AND HUYGENS’ PRINCIPLE

N. H. Ibragimov
1970 SovietRxiv: ru-197001.65921

This paper studies second order linear hyperbolic equations in four variables for which Huygens’ principle holds, focusing on the relation between this property and conformal invariance in pseudo-Riemannian spaces of signature three minus and one plus. Using the structure of spaces with nontrivial c…

On Finitely Axiomatizable Superintuitionistic Logics

Unknown
1970 SovietRxiv: ru-197001.65830

The paper studies finitely axiomatizable superintuitionistic propositional logics through the deductive ordering of short formulas and the associated structure of formulas modulo deductive equivalence. It classifies all formulas of length at most five up to deductive equivalence into twenty represen…

EXISTENCE OF LACUNARY SYSTEMS IN BANACH SPACES

B. E. Veits
1970 SovietRxiv: ru-197001.65626

This paper studies lacunary systems in separable Banach spaces densely embedded in Hilbert spaces, with emphasis on spaces whose norm is twice continuously Fréchet differentiable and has bounded second derivative on the unit sphere. Using Taylor estimates for the squared norm and weak convergence ar…

THE GAMMA-CORRELATION PROCESS AND ITS PROPERTIES

I. O. Sarmanov
1970 SovietRxiv: ru-197001.65576

The paper constructs a class of nonnegative Markov processes with gamma marginal distributions, defined through a bilinear expansion in normalized Laguerre polynomials. It proves that the proposed two-dimensional density satisfies the Markov equation, converges in mean, and is nonnegative by identif…

ANALOGUES OF THE CAUCHY KERNEL AND THE RIEMANN BOUNDARY-VALUE PROBLEM ON A HYPERELLIPTIC SURFACE

E. I. Zverovich
1970 SovietRxiv: ru-197001.65396

The paper constructs explicit analogues of the Cauchy kernel on the genus 2 hyperelliptic Riemann surface defined by a six branch point algebraic equation. It computes normalized Abelian differentials and period data, then develops several Cauchy-type kernels, including discontinuous and meromorphic…

ON THE THEORY OF THE SECOND VARIATION OF FUNCTIONALS ON THE CLASS \(S\) OF UNIVALENT FUNCTIONS

K. I. Babenko
1970 SovietRxiv: ru-197001.65215

The paper develops second variation methods for extremal problems in the class of normalized univalent functions in the unit disk. Using Goluzin and Schiffer type variations generated by complex measures, it derives first variation formulas for Taylor coefficients, recovers the Schiffer equation as …

ON THE THEORY OF SOLUTIONS OF NONLINEAR OPERATOR EQUATIONS

Ya. D. Mamedov, V. M. Musaev
1970 SovietRxiv: ru-197001.65203

The paper studies nonlinear operator equations in a Banach space in which the operator has both an ordinary nonlinear dependence on the current value and a Volterra dependence on the past function. It establishes existence and uniqueness theorems under continuity, boundedness, and generalized Lipsch…

APPLICATION OF THE DISPERSION METHOD IN ADDITIVE PROBLEMS WITH A RESTRICTED SET OF PRIME NUMBERS

T. M. Fedulova
1970 SovietRxiv: ru-197001.64703

This note studies binary additive equations in which one summand is a product of a fixed number of distinct primes and the other is represented by forms such as xy, x squared plus y squared, or a positive definite binary quadratic form. Using Linnik’s dispersion method, together with sieve reduction…

ON SUMS OF CHARACTERS WITH PRIME NUMBERS

Unknown
1970 SovietRxiv: ru-197001.64648

This paper studies character sums over shifted primes, specifically sums of nonprincipal characters modulo a large prime q evaluated at p + k for primes p up to N. Combining I. M. Vinogradov’s method for estimating trigonometric sums with earlier ideas of the author, it proves an estimate that is no…

ON LOCAL CONJUGACY OF DIFFEOMORPHISMS

G. R. Belitskii
1970 SovietRxiv: ru-197001.64135

This note studies local conjugacy of smooth local diffeomorphisms of Euclidean space fixing the origin, revisiting results of Sternberg by replacing iterative constructions with a fixed-point approach. For infinitely differentiable diffeomorphisms, it proves that when the derivative at the fixed poi…

A PRIORI ESTIMATES FOR THREE-LEVEL DIFFERENCE SCHEMES

A. V. Gulin
1970 SovietRxiv: ru-197001.63114

The paper derives a priori estimates and sufficient conditions for stability with respect to the right-hand side for three-level operator difference schemes in a Hilbert space. The approach reduces the three-level scheme to an equivalent two-level scheme and applies separation of stationary inhomoge…

ERGODIC THEOREMS FOR MULTICHANNEL SERVICE SYSTEMS

A. A. Borovkov
1970 SovietRxiv: ru-197001.62393

This paper studies ergodic limiting behavior in multichannel loss service systems governed by stationary sequences of interarrival and service times, using occupancy processes that record residual numbers in service after future time shifts. It proves convergence, in a strong coupling sense, to stat…

Exterior Problems for the Polyharmonic Equation

V. I. Polovinkin
1970 SovietRxiv: ru-197001.62118

The paper studies exterior boundary-value problems for the polyharmonic equation in unbounded domains of Euclidean space whose complements are bounded. It formulates families of problems with standard Dirichlet-type boundary data on a simple boundary, distinguished by prescribed asymptotic behavior …

INVESTIGATION OF THE BIFURCATION OF SMALL EIGENFUNCTIONS IN THE CASE OF MULTIDIMENSIONAL DEGENERACY

M. A. Krasnosel'skii
1970 SovietRxiv: ru-197001.62049

This paper studies bifurcation of small eigenfunctions for nonlinear operator equations in a real Banach space when the eigenspace corresponding to an isolated Fredholm spectral point has arbitrary finite dimension. It justifies reducing the problem by projection to a finite-dimensional homogeneous …