SovietRxiv · Open Access in English
Rediscovering the Soviet scientific archive, in English
25357 full-text translations 14926 English PDFs 22539 abstracts
Showing 50 of 5847 papers in Mathematics
The paper develops a variant of the chord method in which interpolation nodes are chosen as the zeros of the quadratic Chebyshev polynomial, aiming to reduce interpolation remainders and improve convergence estimates. It first proves an error estimate for multivariable functions with bounded second …
This paper presents a method for solving a mixed boundary value problem for a coupled system of two Fourier type equations arising in thermodiffusion. Using Fourier and Laplace transforms, the solution with prescribed initial data and provisional boundary values is represented through integrals invo…
This paper constructs and studies a sixth degree line complex generated by a tetrahedral quadratic complex. Starting from properties of the cones of the quadratic complex and their intersections with opposite principal planes, it defines a set of lines for which a naturally associated two-valued inv…
This paper gives structural characterizations of several classes of models and algebraic systems, building on earlier work on quasivarieties. It characterizes categories structurally equivalent to universally axiomatizable classes of models, analyzes quasifree and free closures via substructures, di…
This paper studies solutions of second order uniformly elliptic linear equations in a spherical layer, with bounded sufficiently smooth coefficients and nonpositive zeroth order term. It defines the number of sign changes as the number of essential connected components of the positive and negative s…
This paper studies a nonlinear boundary value problem for the equation \(u_{xy}=f(x,y,u,u_x,u_y)\) in a bounded domain with a curvilinear boundary, with data prescribed on \(y=g(x)\) and on \(x=0\). The authors construct a method of lines approximation by replacing the solution on vertical lines wit…
The paper proves undecidability results for recognizing homeomorphism and homotopy equivalence among polyhedra and manifolds. It defines the homeomorphy problem in algorithmic terms using combinatorial triangulations, then constructs 4-dimensional manifolds associated with finite group presentations…
This paper studies the asymptotic behavior as a small positive parameter tends to zero for solutions of linear parabolic differential equations whose limiting first order problem has discontinuities or derivative discontinuities along characteristics. By transforming to characteristic coordinates an…
This note proves a criterion for an irreducible cubic polynomial with rational coefficients to occur as the characteristic polynomial of a rational symmetric matrix: it is necessary and sufficient that all roots be real. The argument reduces the problem, following earlier work, to the rational equiv…
This paper studies a boundary value problem for pairs of holomorphic functions in a multiply connected plane domain, with boundary condition involving complex conjugation and a Hölder continuous coefficient of unit modulus. Using an adjoint homogeneous problem and singular integral equations with re…
This note studies linear dynamical systems on Banach spaces and their relation to autonomous linear differential equations with bounded linear operator. It proves that such a system corresponds to an equation dp/dt = Ap exactly when the associated one-parameter operator group is uniformly continuous…
This paper establishes sufficient criteria for the absence of closed trajectories in planar dynamical systems with continuous and differentiable right-hand sides. Using quantities derived from the vector field, especially curvature-related expressions along trajectories, it formulates algebraic and …
The paper develops uniqueness criteria for initial value problems for ordinary differential equations formulated in a real Banach space, including nonsingular and singular cases where the equation is required only for positive time. It introduces a general comparison framework based on an auxiliary …
This paper studies perturbations of the continuous spectrum for operators of the form \(L=L_0+K\), where \(L_0\) is multiplication by the spectral parameter and \(K\) is an integral operator with a Hölder continuous, compact kernel satisfying symmetry and decay conditions. Extending Friedrichs’ appr…
This note formulates integral representation theorems for functions analytic in an angular domain, extending earlier results on entire functions and related Paley-Wiener type representations. Using special integral transforms with Mittag-Leffler kernels, it gives representations for functions of pre…
The paper proves completeness results for eigenvectors and associated vectors of non-self-adjoint operators with discrete spectrum in a separable Hilbert space. Its main theorem treats compact Hilbert-Schmidt operators whose real and imaginary self-adjoint parts are sign-definite, showing that the r…
This note extends earlier undecidability results in group theory to algorithmic recognition problems for effectively complete classes of finitely presented groups. It first supplies details and strengthened auxiliary lemmas for the construction of groups associated with a word, showing that such a g…
The paper evaluates the definite integral of sin^m x divided by p plus q cos x over the interval from 0 to pi, for integer m at least 2 and parameters satisfying q not equal to zero and p squared minus q squared nonnegative. By transforming the integral to a beta type integral, analyzing convergence…
The paper studies meromorphic functions whose zeros, poles, or specified value-points of derivatives lie on, or sufficiently near, a finite system of rays, in connection with deficient values in Nevanlinna theory. It introduces a quantitative notion of closeness to the rays and a generalized deficie…
The paper studies a matrix Riemann, Privalov boundary value problem on a Lyapunov contour, with boundary condition involving a bounded measurable coefficient matrix and Cauchy type integrals. It shows that when the coefficient matrix is nonsingular and continuous, it admits a canonical matrix factor…
This paper studies Fourier type expansions associated with a mixed boundary value problem for the equation uxx minus K(x)utt equals 0 in a strip, where K(x) may vanish or become singular at the endpoints. Assuming K(x) has prescribed power behavior near 0 and 1, the analysis uses the corresponding s…
This paper develops a Lie-theoretic framework for computing the principal transformation group of a system of partial differential equations and for using that group to construct special solutions. It reduces general systems to quasilinear first-order form, derives determining equations for infinite…
This note studies holomorphic functions of a complex parameter whose values are closed linear operators between Banach spaces, under the assumption that all values are semi-Fredholm operators of one of the two types. It introduces an invariant defined by vectors in the kernel that admit arbitrarily …
This note studies Chebyshev sets, subsets of a metric space for which every point has a unique nearest point in the set, in the setting of Banach spaces. It introduces envelope constructions for subsets and proves several supporting-ball lemmas, then uses finite-dimensional approximations by planes …
This paper studies matrix elements of irreducible unitary representations of the motion group of Lobachevsky space and their connection with generalized Fock-Mehler transforms. Using representation-theoretic integral formulas, it derives expressions for associated and zonal spherical functions in te…
The paper extends Livshits’ triangular reduction theory from bounded non-self-adjoint operators to a class of closed unbounded quasi-Hermitian operators with finite rank. It defines characteristic functions for rank-one operators, proves that simple operators are unitarily equivalent exactly when th…
The paper studies stability of solutions to Cauchy and mixed problems for linear and quasilinear hyperbolic equations, as well as first order hyperbolic systems, in unbounded and half-space domains. Using Sobolev generalized solutions, energy inequalities, integrability conditions on time-dependent …
This paper studies the stability of characteristic exponents for nonlinear perturbations of diagonal linear systems of ordinary differential equations with bounded time-dependent coefficients. It argues that an integral separation condition on the diagonal coefficients is sufficient, without assumin…
This paper studies zeros and oscillation of solutions of the higher order differential equation y^(n) + p(x)y = 0 with continuous coefficient on an interval or half-line. It proves comparison theorems showing that oscillatory behavior satisfying a stated condition is preserved under larger positive …
This paper develops a small-parameter method for solving operator equations in a Banach-type space by means of majorant power series. A preliminary scalar lemma gives existence, uniqueness, positivity, and convergence radius estimates for an analytic root of a majorizing equation, including converge…
The paper studies mapping properties of fractional negative powers of strongly invertible self-adjoint positive differential operators on bounded domains star-shaped with respect to a ball. Using Sobolev embedding results, refinements of fractional-order operator theorems, and inequalities for weigh…
This note studies the spectral multiplicity of dynamical systems generated by stationary Gaussian processes with continuous spectral measure. Using Itô’s decomposition of the Hilbert space of trajectory functionals into symmetric multiple integral components, it constructs examples of processes with…
This note studies an infinite system of nonlinear functional equations in the real Hilbert space l2, presented as a functional analogue of Lichtenstein’s nonlinear integral equation. A multilinear-type functional on the unit ball is defined by an infinite series with symmetric square-summable coeffi…
This paper studies boundary value problems for the Euler, Poisson, Darboux equation with data prescribed on the singular line. Three Cauchy-type problems are formulated for different ranges of the parameter, using analytic representations of solutions and conjugate solutions. The paper gives existen…
The paper studies geometric properties of mappings generated by regular solutions of first order elliptic systems and related second order elliptic equations with analytic coefficients. Using Vekua’s representation of solutions after analytic continuation to two complex variables, it constructs a fa…
This note studies the Cauchy problem for Sobolev type operator differential equations in a Hilbert space, allowing the inverse of the principal operator to be unbounded. It proves existence, uniqueness, and a stability estimate under boundedness and continuity assumptions on the products involving t…
This paper studies stability of solutions for several partial differential boundary value problems in a complex Banach space that are not covered by earlier Volterra operator reduction methods. It considers first order, parabolic, and damped hyperbolic type equations on a half-plane with a continuou…
The paper proposes a unified iterative method for solving Fredholm integral equations of the first and second kind by treating them as a single parameter-dependent equation involving a kernel, an unknown function, and a spectral parameter. For real or complex symmetric kernels, it gives substitution…
The paper studies an oblique derivative boundary-value problem for a first-order elliptic system in a multiply connected plane domain, formulated for a complex function satisfying a generalized Beltrami-type equation. It reduces the problem to an equivalent Riemann-Hilbert problem for a system of th…
This note proves P. S. Alexandrov’s conjecture that every bicompact topological group is a dyadic compactum. The argument represents a bicompact group of weight τ as the limit group of a transfinite Pontryagin Li series and constructs compatible special mappings from an inverse spectrum of products …
The paper studies classes of integro-differential equations of convolution type, including paired equations on positive and negative half-lines, with kernels, right-hand sides, and solutions specified by weighted integrability conditions. Using Fourier transform methods and the theory of Riemann bou…
This note studies harmonic approximation for almost-periodic functions whose Fourier exponents have no finite limit points, relating the deviation of Fourier partial sums to best approximation by entire functions of finite degree. It proves a general inequality bounding the remainder of a Fourier su…
The paper studies several classes of infinite systems of linear algebraic equations with difference-index convolution terms and finite exceptional rows, including systems modified by finite rotation-group factors. Using Laurent transforms, convolution properties for weighted sequence spaces, and Rie…
This note studies linear summability of sequences by Toeplitz matrices, focusing on relative strength, coverability of countable families and nested chains, and prescribed summation behavior. It proves that zeros can be inserted into certain divergent functional series so that the resulting series i…
This paper studies uniform distribution for multidimensional systems of functions built from linear finite difference equations with integer coefficients and dominant characteristic roots greater than one, including Pisot-type cases. Using a method based on exponential sum estimates, it establishes …
Vinogradov announces a new bound for the Riemann zeta function on the line Re s = 1, namely ζ(1+it) = O((log t log log t)^{2/3}) for sufficiently large t. The estimate is derived from a new bound for exponential sums of the form ∑ e^{2πif(x)} with f(x) = −t log x/(2π), under specified size and smoot…
This note establishes a quantitative relation between oscillation and growth for solutions of a uniformly parabolic linear equation in a bounded cylindrical domain. Under boundedness, smoothness, and ellipticity assumptions on the coefficients, it defines the number of sign changes as the number of …
This note studies global stability of the zero solution for a three-dimensional autonomous system with constants satisfying positivity and Hurwitz-type inequalities and a continuous nonlinearity obeying a generalized sign condition. Building on earlier sufficient criteria by Tuzov, it proves a neces…
This note develops a cubical analogue of Postnikov’s theory of homotopy resolvents, intended for use in questions concerning fiber spaces. It defines cubical complexes with face and degeneracy operators, introduces cochains, nonabelian one-dimensional cocycles, and cohomology with local coefficients…
This note applies a multidimensional local theorem for large deviations to Pearson’s chi-square statistic for multinomial trials with fixed positive cell probabilities. It derives asymptotic formulas for the tail probability P{chi-square greater than tau squared} as both the number of observations a…
