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 the large-time behavior of solutions to a Cauchy problem for a quasilinear reaction-diffusion equation arising in combustion theory, with step-like initial data and nonlinear source terms that may be nonpositive near one equilibrium and positive on part of the interval. Under spec…
This paper applies the contour integral method to a mixed initial boundary value problem for second order equations with discontinuous spatial coefficients in two bounded domains separated by an interface. The argument reduces the problem to a parameter dependent spectral boundary problem, construct…
This paper constructs and studies invariant torsion-free affine connections on homogeneous spaces whose motion group contains a nonmaximal equipped stationary subgroup. Using chains of equipped subgroups and associated decompositions of the Lie algebra, it derives differential equations for geodesic…
This paper studies bounded Hilbert space operators whose spectrum is real and whose imaginary part is completely continuous, under an additional spectral cutting condition defining the class Omega. It constructs an ordered continuous family of invariant projections and analyzes the associated spectr…
The paper formulates an n-dimensional analogue of a previously studied first-order system by representing the unknowns as differential forms on a compact Riemannian manifold. It expresses the systems and their metrically adjoint counterparts using exterior differentiation and its adjoint, giving exp…
This paper studies homogeneous three-point difference schemes for one-dimensional second-order boundary-value problems with variable coefficients, focusing on canonical and conservative schemes defined through coefficient functionals. It formulates moment conditions for first- and second-order appro…
This paper studies the composition of singular kernels defined on a closed multidimensional Lyapunov surface in Euclidean space. Under stated size, continuity, and principal value conditions, it proves estimates for the composed kernel and for its increments, including simplified forms when one or b…
This paper generalizes Agmon’s results on the distribution of singularities of Dirichlet series to a broader class \(B(r,h)\) of functions represented by limits of generalized Dirichlet polynomials with clustered exponents satisfying a gap condition. Using representations by divided differences and …
This paper develops four families of integral transformations with generalized kernels in Euclidean space and in the associated space of hyperplanes. Using spaces of test functions and generalized functions, it constructs two one-parameter convolution groups, one containing the Laplace operator and …
This paper studies Green’s functions and comparison principles for self-adjoint second order elliptic operators in a domain with Dirichlet boundary conditions. Using Fredholm and Ries-Schauder integral equation arguments, it relates positivity of the Green’s function to the coefficient being below t…
This note studies perturbations of eigenvalues and eigenelements for certain non-self-adjoint operators, extending earlier methods for perturbed linear equations. For finite-dimensional non-Hermitian matrices with a zero eigenvalue, the authors describe how the structure of the Jordan chains determi…
This note develops a general theory of biorthogonal kernels in Hilbert spaces of square integrable functions with respect to nondecreasing measures, continuing earlier work on quasi-isometric mappings. It introduces complete kernels, B-kernels, Bessel, Hilbert, Riesz-Fischer, and Riesz kernels, and …
The paper studies the first boundary-value problem for a class of nonlinear elliptic systems whose coefficients depend on the unknown function. It extends the energy method used for linear strongly elliptic systems, formulating coercivity and integrability assumptions under which a generalized solut…
The paper studies how an additive category can be embedded in a larger additive category admitting direct products of finite families of objects. It constructs a matrix category over a given additive category, whose objects are finite ordered lists of objects and whose morphisms are rectangular matr…
This paper derives explicit formulas for the connection forms of a quasisymmetric affine connection space, whose curvature and torsion tensors are covariantly constant, in terms of their values at a fixed point. Using the structure equations of the associated homogeneous Lie group and canonical coor…
This paper derives interior error estimates for a grid method applied to the two-dimensional Neumann problem, particularly in cases where simple boundary approximations make local satisfaction of the boundary condition weak or low order. Using embedding theorems, a Courant, Friedrichs, and Lewy type…
The paper studies a qualitative property of solutions to a second order parabolic equation in a rectangular domain under boundedness, positivity, and smoothness assumptions on the coefficients. It considers the essential connected components of the positive and negative sets of a bounded solution, e…
The paper develops energy inequalities for boundary-value problems for a broader class of second-order equations of mixed elliptic-hyperbolic type, extending earlier work related to Chaplygin’s equation. It specifies domains with elliptic and hyperbolic parts, characteristic boundary arcs, and coeff…
The paper introduces reduced free products of nonassociative algebras defined by systems of multilinear identities over a field of characteristic zero, with special attention to commutative and anticommutative free products. It gives equivalent constructions by ideals in ordinary nonassociative free…
This paper studies solutions of an infinite order differential equation formed from iterates of a finite order linear differential operator with entire coefficients, where the characteristic function has minimal growth of class [1/s, 0]. It proves that, when the right hand side is entire, the domain…
This paper computes the Plancherel measure for the Riemannian symmetric space \(SL(n,\mathbb R)/SO(n,\mathbb R)\). It first gives an integral representation of the positive definite zonal spherical functions in terms of lower triangular unipotent matrices and Gram determinants, normalized by an expl…
This paper derives trace formulas for a singular Sturm-Liouville operator on the half-line with Dirichlet boundary condition and an integrable potential satisfying a first moment condition. Using the denominator of the resolvent, expressed through the scattering function and its phase, the authors r…
This note generalizes the classical uniqueness theorem for bounded holomorphic functions in the unit disk. It considers sequences approaching a boundary point within a fixed chordal sector, satisfying both the usual divergence condition and a separation condition after conformal mapping to the upper…
The paper addresses the Hardy and Littlewood problem of representing sufficiently large integers in the form of a prime plus two squares. It states an asymptotic formula for the number of such representations, with a specified remainder term, and explains its reduction to equations involving product…
This paper studies a class of singular integro-differential equations on a smooth closed contour in the complex plane, under Hölder-type smoothness assumptions on the coefficients and kernels. The equation is reduced to a differential boundary-value problem for a piecewise holomorphic Cauchy-type in…
This paper develops fixed point criteria for operators that leave invariant a cone in a real Banach space, focusing on completely continuous operators that either compress or stretch the cone in prescribed norm regions. Using topological methods, it proves existence of fixed points and nonzero fixed…
The paper presents a numerical method for solving generalized homogeneous linear systems of the form (A minus lambda B)X equals 0, with particular attention to cases in which one or both matrices are singular. The method combines computation of one characteristic root and vector with successive redu…
This paper studies ill-posed Cauchy problems for evolution equations generated by closed unbounded operators in Banach spaces, focusing on when restricting to bounded solutions restores well-posedness. Using analytic continuation of strongly continuous semigroups and estimates based on logarithmic s…
This note extends results of Dixmier on special unitary irreducible representations of nilpotent Lie groups to arbitrary unitary irreducible representations of connected nilpotent Lie groups. It shows first that, once a representation is realized so that the enveloping algebra acts as all differenti…
This note studies the asymptotic growth and stability of solutions of weakly nonlinear ordinary differential systems by comparing them with linear systems obtained by freezing the coefficient matrix. It derives an integral estimate, based on an identity for parameter-dependent matrix exponentials an…
The paper studies the Dirichlet problem for second order linear elliptic systems with constant real coefficients in two variables, without assuming strong ellipticity. Focusing on the case of two unknowns in the unit disk when the characteristic equation has a double complex root, it uses the repres…
This paper studies geodesic flows on manifolds of constant negative curvature through the framework of Kolmogorov dynamical systems. It constructs suitable measurable partitions, using horocycles and properties of fundamental domains, to prove that geodesic flows on two-dimensional finite-area manif…
This paper studies the Cauchy transform for functions and generalized functions of several complex variables on products of smooth closed contours. It establishes boundary estimates and differentiation properties for multidimensional Cauchy-type integrals, extends singular Cauchy operators and their…
The paper studies perturbed differential systems whose unperturbed motions contain both oscillatory variables and rotational variables, with periodic dependence on the rotational coordinates. Using variation of constants and the averaging method, it derives asymptotic equations for the slowly varyin…
The paper studies transformation operators for singular Goursat problems associated with a hyperbolic equation whose characteristic line is singular, and with a related parabolic-type equation. It derives integral connection formulas and asymptotic or series expansions relating solutions with differ…
This paper studies generalized continuity and differentiability of measurable real functions when increments are restricted to a fixed measurable set near zero, called a congruent set. It introduces three density conditions on the increment set and proves necessary and sufficient criteria under whic…
The paper studies singularly perturbed boundary value problems for elliptic partial differential equations of the form involving a small biharmonic term, with homogeneous boundary conditions on the function and its Laplacian. Using the Vishik and Lyusternik boundary layer method, it constructs an as…
This paper proves Sobolev-type embedding theorems for domains whose boundaries may contain angular points of zero angle, where the usual cone condition fails. Using estimates on functions in generalized conical bodies with cusp parameter, it derives pointwise and integral norm inequalities for funct…
This paper proposes an acceleration of Mayants’ iterative method for refining roots of secular equations and their associated homogeneous linear systems. It shows that, at any iteration step, the vector solution can be expanded as a power series in the spectral parameter, with coefficients generated…
This paper studies a class of invariant first order systems that become hyperbolic for a Lorentz signature metric, focusing on their structure after separating a distinguished time coordinate. The system is rewritten in terms of spatial exterior differentiation and its adjoint, and it is shown that …
This paper addresses the inverse scattering problem on the half-line for second-order differential equations whose coefficients include an inverse-square singularity, under weighted integrability assumptions on the real potential. Using a method related to the Agranovich and Marchenko approach, it g…
This paper computes the centers of all connected simply connected noncompact simple real Lie groups, extending a method used by Dynkin and Onishchik for compact and complex simple groups. The argument realizes each real form through an involutive automorphism of a compact simple Lie algebra, proves …
This paper gives a sufficient operator-theoretic condition for solvability of the multidimensional moment problem. It considers tensor products of linear spaces with involution and commuting symmetric real operators, proving that if one operator is self-adjoint in each induced one-dimensional comple…
The paper studies transient phenomena in continuous-time branching processes with finitely many particle types when the dominant characteristic root of the mean matrix tends to zero. For a compact class of indecomposable processes with uniformly bounded second and third factorial moments, it derives…
This note studies a singularly perturbed boundary value problem for the second order equation with a small parameter multiplying the highest derivative, in the case where the right hand side depends only on the unknown function and the independent variable. Under smoothness assumptions near the limi…
This paper studies laws of large numbers for random variables associated with non-homogeneous Markov chains, allowing each variable to depend on a fixed finite number of consecutive time instants. Using Dobrushin-type coefficients of ergodicity, it derives variance bounds for sums of such variables …
This note extends a modification of the Lobachevsky-Graeffe method for numerical solution of algebraic equations to cases in which roots have equal moduli and may be multiple, avoiding a preliminary separation of multiple roots. It derives how repeated Graeffe transformations and a small shift of th…
This note studies metrically complete, sufficiently smooth Riemannian spaces possessing a pole, under the assumption of positive curvature, or more specifically positivity in two-dimensional directions tangent to geodesic rays from the pole. Using Fermi coordinates, associated two-dimensional surfac…
The paper studies when a symmetric operator in a Hilbert space completion of a topological vector space has a self-adjoint extension commuting with the self-adjoint closure of another commuting symmetric operator. It proves an extension criterion based on strong self-adjointness and a reality condit…
The paper studies entire analytic solutions of a class of partial differential equations that includes the heat equation and a mixed type equation, characterizing such solutions through series expansions and growth restrictions on an associated entire function. It formulates and solves a Cauchy prob…
