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
This paper studies boundary-value problems for quasilinear systems of differential equations in divergence form whose equations in variations define strongly elliptic, positive operators. It formulates functional conditions ensuring coercivity, growth control, and compactness in suitable Sobolev-typ…
This note extends results on superconvergence and noncontinuability from lacunary power series to more general functional series whose basis functions satisfy a growth condition in domains bounded by level curves of a function u. It formulates lacunary structure for such series and proves analogues …
This paper studies the counting function for prime constellations p, p plus u1, through p plus um, including the case in which the primes are constrained to prescribed arithmetic progressions. Using Vinogradov’s method of trigonometric sums over primes, together with estimates for primes in progress…
This paper studies commutative topological groups equipped with partial order relations introduced independently of the topology, with emphasis on how convergence and order interact in iterative approximation methods. It defines almost ordered groups, semi-ordered topological groups, order-complete …
This note examines the Cauchy problem for quasilinear hyperbolic systems and the question of whether a vanishing viscosity definition of generalized solutions restores uniqueness. It constructs two parabolic regularizations of the same two-component hyperbolic system, differing only in the positive …
The note refines standard \(L^p\) norm inequalities for complex polynomials of degree \(n\) under the restriction that they have no zeros in the unit disk. Using de Bruijn’s Bernstein type inequality for the derivative on the unit circle, it proves an improved upper bound for \(\|Q_n(Re^{i\varphi})\…
This paper studies lower estimates outside exceptional sets for subharmonic functions, differences of subharmonic functions, and meromorphic functions in the unit disk. Using Riesz representation and a method of Hayman, it proves bounds in terms of an integral characteristic and an associated functi…
The paper refines estimates for the spectral function of the Laplace operator in an N-dimensional rectangular parallelepiped with homogeneous boundary conditions of the first or second kind. By expressing the eigenfunction expansion as exponential sums over lattice points and applying the Landau-Har…
The paper establishes a generalized weighted integral inequality in Euclidean space involving integration over a subspace and weights defined by distances to complementary subspaces. Using earlier Hardy, Littlewood, Sobolev, and Il’in type inequalities together with a Plessner device, the author pro…
This note studies Diophantine finiteness problems for elliptic curves over one-variable function fields with algebraically closed constant field of characteristic zero, as analogues of the Siegel-Mahler theorem and Mordell conjecture. It sketches proofs that, under a non-isotriviality assumption, on…
This paper studies a special edge-vertex graph function defined by a deletion and two contraction-type operations on an edge, with values in a ring generated by parameters subject to relations ensuring uniqueness and invariance under addition or removal of isolated vertices. It derives a system of a…
This paper studies finite groups classified by the number of conjugacy classes of noninvariant subgroups whose orders are divisible by at least one prime from a fixed set of prime divisors. It introduces the notions of pi-rank and pi-type for such groups and examines how these numerical invariants c…
This note develops a general method for deriving structural characterizations of axiomatizable classes of models, extending work of Tarski, Łoś, Chang, and Taimanov. The method is formulated through closure operations and inscribed families of defining classes, then applied to classes such as UEC an…
The paper addresses practical error estimation for grid method solutions of the interior Dirichlet problem for the Laplace and Poisson equations, where earlier estimates involved quantities depending on the unknown exact solution. It derives bounds for the difference between the exact solution and a…
This note studies spectral relations between the Hermitian components of Volterra operators, especially those obtained by perturbing self-adjoint or nonnegative operators. Using lower estimates for associated entire functions and consequences for the distribution of their zeros, it derives Schatten …
The paper presents a method for deriving Hermite interpolation formulas by passing from Lagrange interpolation to the limit as interpolation nodes coalesce, thereby obtaining coefficients for multiple nodes and derivative data. It then uses the Hermite form on a finite interval to construct quadratu…
The paper studies variability regions for finite systems of Laurent coefficients of functions represented in finitely connected circular domains as sums of Stieltjes integrals. It establishes a general convexity theorem identifying such regions with convex hulls of geometric sums of parameter arcs, …
This note generalizes the structural formula for convex univalent functions from the disk and annulus to a multiply connected circular domain bounded by one exterior and finitely many interior circles. It introduces an auxiliary class of regular functions represented by boundary measures and constru…
This paper develops a nomographic representation for equations of the form f1 plus f2 plus f3 plus f4 plus f5 plus f6 equals zero using an oriented transparent overlay shaped as a ruler. The method transforms the six-variable relation by introducing auxiliary variables, arbitrary functions, and scal…
This note studies random walks on finitely generated groups, focusing on Martin boundaries and positive harmonic functions. It proves that for an irreducible Markov chain invariant under a transitive nilpotent group of transformations, every bounded harmonic function is constant, while showing by ex…
This note gives sufficient conditions under which solutions of a multidimensional singular integral equation in Euclidean space satisfy a Lipschitz condition after stereographic compactification. Assuming nonvanishing of the symbol, Sobolev type regularity and continuity conditions on the coefficien…
This note studies bounded generalized solutions of multidimensional quasilinear elliptic equations in divergence form under natural growth, coercivity, and differentiability assumptions. Using Hölder continuity estimates, weighted integral inequalities, and difference quotient arguments, it proves l…
This note establishes uniform estimates for derivatives of arbitrary order, including Hölder coefficients, for solutions of Dirichlet and eigenfunction problems associated with the elliptic operator div(p(x) grad u) plus q(x)u when the coefficients are discontinuous across an internal surface. For a…
This paper studies conditions for the absolute convergence of multiple Fourier series of periodic functions, focusing on properties measured separately in each variable. It shows that one variable criteria applied independently are insufficient, and formulates sufficient conditions in terms of parti…
This paper develops a weak topological framework for studying differential equations in Banach spaces and applies fixed point and rotation methods to the existence of periodic solutions. After formulating properties of an N-weak topology and fixed point results for weakly continuous mappings, it def…
The paper studies when a homeomorphism between connected completely regular spaces extends to homeomorphisms of their bicompact extensions with punctiform remainders. Using a previously proved extension theorem, it shows that if the extensions are acyclic in dimension one, then such an extension is …
This paper develops conditions for smoothness of functions of several variables and estimates for convolution operators in translation-invariant norms. The method is based on elementary algebraic identities that yield operator inequalities for finite differences with different steps and orders, lead…
This note studies projections in a Hilbert space relative to a continuous bilinear metric defined by a bounded Gram operator, allowing the form to be non-Hermitian. It derives an operator formula for the generally multivalued projector onto a linear manifold in terms of an operator whose range is th…
This note studies how the spectrum of a semibounded singular elliptic operator is affected by changes in the boundary, boundary conditions, and, locally, the coefficients of the differential expression. Using extension theory for semibounded operators, it proves compactness of differences of inverse…
The paper studies analytic solutions of the partial differential equation \(\partial^r u/\partial x^r = a y^m \partial^n u/\partial y^n\), where \(m<n\), and derives a series representation in terms of prescribed derivatives at \(y=0\). This representation yields necessary and sufficient growth cond…
This paper proves existence results for the first, second, and third boundary value problems for one dimensional linear parabolic equations with discontinuous coefficients. The discontinuities occur across moving lines whose regularity is assumed only to be Hölder with exponent greater than one half…
This paper studies divergence and non-summability phenomena for Fourier series in \(L^p\) classes under rearrangement, in relation to longstanding questions about trigonometric series, Walsh series, Haar series, and general orthonormal systems. Building on Kolmogorov, Menshov, and Zagorskii, and usi…
This note addresses the problem of describing almost homogeneous, almost additive functionals of a multidimensional Wiener process, focusing on functionals with zero mathematical expectation. It proves that, under a square integrability and small time continuity condition in the presented proof, eve…
The paper studies complex canonical systems with periodic Hermitian coefficients and a fixed nonsingular skew-Hermitian matrix, viewed as a Banach space mapped to the group of J-unitary monodromy matrices and then to spectra with Krein type distinguished. It introduces argument functions and integer…
The paper studies dimension inequalities for normal spaces and closed mappings in the setting of generalized paracompactness. It extends the sum theorem for covering dimension to point-finite open covers and proves a Hurewicz type dimension-lowering theorem in Morita’s form, giving an inequality for…
This note addresses a problem posed by P. S. Aleksandrov, whether every n-dimensional bicompactum contains a continuum of type Vn, a strengthened form of an n-dimensional Cantor manifold. Using Aleksandrov, Cech cohomology, the paper introduces local notions of n-dimensional obstacles and basic poin…
This paper classifies nonsymmetric homogeneous Riemannian spaces with irreducible rotation group in the case where the transitive motion group is simple of type A, locally isomorphic to SU(N). The argument reduces the geometric problem to a representation-theoretic condition on embeddings of compact…
This note studies nonlinear integral equations of the form in which an unknown function equals an integral whose kernel depends on the unknown function. Using approximation by stepwise kernels and compactness ideas related to the Leray-Schauder method, it establishes sufficient conditions for M-solv…
This note studies inconsistent finite systems of linear inequalities by approximating them with consistent perturbed systems and introduces the defect as the minimal uniform relaxation needed for consistency. It derives formulas for the defect of rank r subsystems consisting of r+1 inequalities usin…
This note studies the fundamental equations for surfaces of negative Gaussian curvature in asymptotic parameters, extending the classical sine-Gordon type equation for constant negative curvature to the case of variable curvature. Using the Peterson-Codazzi equations, formulas for geodesic curvature…
This paper studies convex domains homogeneous under affine transformations, with projectively homogeneous bounded convex domains reformulated through associated homogeneous cones. It establishes structural results for the automorphism group, including maximal compact stabilizers, embedding in an alg…
This note proves that the horocycle flow on a compact surface of constant negative curvature has zero entropy, in contrast with the known positive entropy of the corresponding geodesic flow. The argument constructs a finite measurable partition of the space of line elements such that, for sufficient…
The paper studies the immersion of torsion-free symmetric spaces of affine connection of the first class into an affine space of minimal dimension, under the assumptions that the Ricci tensor is nondegenerate and, for dimension greater than two, that the curvature matrix has rank greater than two. U…
This paper proves a lattice-theoretic analogue of a principal consequence of Grushko’s theorem for finitely generated groups. Although the direct Grushko-type statement fails for lattices, the author shows that if a finitely generated lattice is expressed as a free product of finitely many sublattic…
The paper studies when a Riemann surface obtained by conformally gluing the two boundary lines of an infinite strip by a continuously differentiable increasing function has parabolic type. It constructs piecewise linear approximations to the gluing function, decomposes the strip into quadrilaterals,…
This paper characterizes pairs of subsets of the real line that can occur as the points where a sequence of continuous real functions tends respectively to positive and negative infinity. It recalls that each such set must be of class \(F_{\sigma\delta}\), and observes that the two sets must also be…
This paper studies continuous self-maps of the real line through reducible invariant sets and the structure of fixed points of their iteration processes. It establishes relations among periodic points of different orders, including restrictions when periods that are powers of two are absent and the …
The paper studies singular integral equations on bounded smooth surfaces with edges, where the kernels have a Calderon-Zygmund type principal singularity and the unknown is sought in weighted Lebesgue spaces determined by distance to the edge. It establishes boundedness and interchange properties fo…
This paper studies diffusion processes with a small diffusion coefficient and derives local asymptotic results for their transition densities as the small parameter tends to zero. Starting from an asymptotic expansion of the stochastic process around the deterministic solution, it gives conditions u…
This paper addresses the determination of the accessory constants in the Christoffel-Schwarz integral for mapping a simply connected polygon onto a half-plane. It develops a computational method based on expanding the integrand factors into binomial power series, leading to systems of equations for …
