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 introduces a generalized continuous interval, defined through connectedness properties of point deletions, and shows how such spaces carry natural linear orders and interval-type topologies. It characterizes ordered sets that admit suitable T1 topologies making them segments, proves a con…
This paper studies the growth of meromorphic functions of finite lower order through the quantity measuring minimal deviation from a value, defined using the maximum proximity relative to the Nevanlinna characteristic. It establishes upper bounds for this deviation in terms of the lower order, prove…
The paper gives an axiomatic characterization of categories of correspondences associated with semi-abelian categories, beginning with the more general case of beta-categories, which need not have direct sums or products. It defines beta-categories through kernel, cokernel, exactness, and intersecti…
This paper studies nonlinear equations of the form x = SF(x) and x = BF(x) in Banach spaces, where F is either a potential operator or a monotone operator and the associated linear operator may be bounded or unbounded. It formulates structural conditions linking a Banach space with an auxiliary Hilb…
The note studies upper estimates for large inductive dimension and related inductive invariants of products of bicompact spaces using cofinal approximative dimension. It proves that for finite products of bicompacta, and under a paracompactness variant, the large inductive dimension is bounded by th…
This paper studies the existence of invariant torus-like surfaces near an equilibrium of analytic systems of differential equations whose coefficients are periodic in time. Extending earlier results for special second-order systems, it applies Kolmogorov’s Newton method under nonresonance conditions…
The paper studies convergence and asymptotic rates for iterative processes used to solve finite-dimensional linear systems, allowing generally nonlinear transition operators. It introduces subordinate functionals as Lyapunov-type tools and proves a convergence criterion based on monotonic decrease, …
The paper studies continuation and branching of periodic solutions for quasilinear differential-difference equations with a small parameter. Using an auxiliary equation and analytic expansions, it derives a finite-dimensional branching equation whose small solutions are in one-to-one correspondence …
This note studies a two-player differential game in which the first player seeks to bring the state of a controlled system to a prescribed target set while the second player opposes this objective. It formulates admissible mixed strategies through set-valued dynamics and differential equations in co…
The paper gives an invariant formulation of Maslov’s canonical operator in the setting of Lagrangian geometry and the projective unitary representation associated with Schrödinger quantization. It defines a quasiclassical operator through formal WKB-type expansions, stationary phase equivalence, and…
This paper studies a boundary value problem for the mixed type equation uxx plus sgn(xy)uyy equals zero in a finite domain with two perpendicular lines of degeneration. The prescribed data are given on circular arcs and boundary segments, with allowed weak singularities of first derivatives at selec…
The paper studies heat propagation in a composite one-dimensional rod made of two materials joined by an imperfect thermal contact, with insulated lateral surface, prescribed initial temperatures, and heat exchange conditions at the ends. The boundary-value problem is decomposed into parts with homo…
The paper studies iterated Cauchy problems for singular differential operator equations involving a parameter dependent radial derivative term, a linear operator in auxiliary variables, and spectral constants. It develops basis series representations that express solutions of higher order problems t…
This paper studies Riemannian spaces admitting a generally recurrent symmetric tensor of second order, a condition encompassing recurrent tensors, tensors associated with hyperquadrics, common geodesic metrics, and projective vector fields. By analyzing the compatibility of the defining differential…
The paper studies two-person games on arbitrary convex subsets of finite-dimensional Euclidean spaces with a closed concave-convex payoff function. Using a representation of the payoff as a sum of closed concave-convex functions, it constructs conjugate functions, associated primal and dual optimiza…
This paper studies first boundary-value and Cauchy problems for higher-order strongly parabolic linear and nonlinear systems in one spatial dimension. It establishes a priori estimates in anisotropic Sobolev spaces for linear equations with merely measurable bounded coefficients, including L2 bounds…
The paper studies asymptotic estimates for incomplete trigonometric sums of the form \(\sum_{x\leq P}\exp(2\pi i ax^n/q)\), with \(q\) a high power of a prime and \(P=q^{1/r}\), extending earlier results on short sums and correcting previously misstated formulations. By separating the complete-sum c…
This note studies invariants for the action induced by conjugation of the group of upper triangular unipotent matrices on lower triangular matrices, a problem connected with Kirillov’s reduction of the classification of irreducible unitary representations. It introduces “tensor” sections determined …
This note studies decomposability and maximal decomposability of Hausdorff spaces using dispersion character, pi-bases, characteristic spaces, and relaxations of topologies by ideals. It proves that spaces with sufficiently small pi-weight, and more generally dense-in-itself pi-spaces, are maximally…
The paper studies completeness in domains of systems of analytic functions obtained by taking successive derivatives with respect to a parameter in a generating function \(F(z,u)=\sum \varphi_n(z)u^n\), evaluated at prescribed nodes. Using the Abel Goncharov interpolation formula, it derives criteri…
The paper establishes maximum principles of absolute-extremum type for solutions of certain second-order hyperbolic equations in characteristic triangular domains under sign and regularity conditions on the coefficients. These principles are applied to mixed elliptic-hyperbolic equations of Lavrent’…
The paper studies symmetric continuity and symmetric differentiability of arbitrary order for real functions on an interval when the symmetric differences are restricted to increments from a fixed set Q accumulating at zero. It classifies such sets by measure and density conditions near zero and pro…
This note studies the spectrum and Fredholm properties of singular integral operators with piecewise continuous coefficients in weighted spaces on smooth contours. Using a weighted index constructed from the jumps of the coefficient functions and the exponents of the weight, it gives necessary and s…
The paper studies local energy decay for the exterior Dirichlet problem for the wave equation in odd-dimensional Euclidean space outside a bounded obstacle. It introduces the class of almost star-shaped domains, defined by the existence of a family of strictly convex level surfaces satisfying a geom…
This note studies Kolmogorov’s weak dependence condition for the past and future of Gaussian stationary processes, expressed through the coefficient beta. For discrete time, it gives a necessary and sufficient spectral characterization: the spectral density must factor as the squared modulus of a po…
The paper studies embedding theorems for weighted function spaces of fractional order with mixed norms on a half-space, addressing the case where both the source and target are mixed-norm type spaces. It defines the relevant weighted fractional spaces through first-order finite differences and estab…
This paper studies the asymptotic distribution of extreme order statistics \(x_{kn}\) when \(k\to\infty\) and \(k/n\to 0\), emphasizing conditions for both integral and local asymptotic normality. It introduces a class of locally regular distributions, formulated through the behavior of \(p_F(\lambd…
This paper establishes Phragmén-Lindelöf type estimates for solutions of second order evolution equations with constant complex coefficients in an infinite slab, under two-point boundary conditions in the time variable. For equations previously characterized as well posed, it shows that suitably str…
This paper establishes a priori estimates up to the boundary for solutions of elliptic boundary value problems in norms adapted to functions analytic in tangential variables. Using Schauder-type estimates and commutator bounds, it proves an estimate for uniformly elliptic operators in a layer with b…
The paper studies complex K-theory with coefficients for an odd prime p, relating Adams-Toda homotopy operations to differentials in the Atiyah-Hirzebruch spectral sequence. It constructs cellular spaces representing mod p K-theory with prescribed homotopy groups and uses them to define 2(p-1)-perio…
This note derives necessary optimality conditions for an optimal control problem with fixed endpoints, differential dynamics, mixed equality constraints, and set constraints of inequality type, considering variations that are small in absolute value. Under stated smoothness, cone, and nondegeneracy …
This paper studies a generalized Carleman boundary value problem for analytic functions in a simply connected domain with a Lyapunov boundary, where the boundary transformation may preserve or reverse orientation and the condition includes both the function and its complex conjugate. The authors red…
This paper studies pseudodifferential operators on a smooth compact manifold that are elliptic away from a hypersurface but degenerate on it in a prescribed quasihomogeneous manner. It introduces adapted Sobolev-type spaces and analyzes boundary and coboundary conditions imposed on the degeneracy su…
The paper develops a probabilistic framework for branching systems described by ordinary differential equations whose right-hand sides may change across prescribed time intervals according to probability measures depending on prior states. It defines state spaces, branching solution processes, reali…
The paper studies systems of second-order partial differential equations of composite type in two variables, represented by a complex equation whose characteristics include one double real family and two imaginary families. It shows that a general equation of this type can be reduced, under suitable…
This paper studies when the sample mean is an admissible estimator of a one-dimensional location parameter under loss functions other than the quadratic loss. For Laplace loss, and for samples from a distribution with a continuously differentiable unimodal density, the authors derive an integral con…
This paper studies complete solvability and reducibility for linear multidimensional differential equations in finite-dimensional Banach spaces with continuous, and later almost periodic, operator coefficients. It gives necessary and sufficient conditions for complete solvability in terms of a rotor…
This note refines a limit theorem for the number of classes of purely radical quadratic forms of negative determinant. Using a generalized Esseen inequality, estimates for averages of complex powers of Dirichlet L-functions, Bombieri’s density theorem as applied by Barban, and Rogozin’s concentratio…
The paper introduces and analyzes a boundary value problem for the degenerating hyperbolic equation y^m u_xx minus u_yy equals zero in a characteristic domain, with data prescribed on the line of degeneracy and a fractional derivative relation imposed on the characteristic boundary. Using the Darbou…
This note addresses several questions on perfectly normal bicompact spaces, especially nonmetrizable examples and mapping properties. It constructs a nonmetrizable perfectly normal bicompact admitting an open countably multiple map onto the Cantor set, and, assuming the continuum hypothesis, a conne…
This paper studies the flow of entry times of a stationary time-homogeneous Markov process into a measurable subset of the phase space from its complement. It introduces a basic conditional mean measure for entries and proves, under convergence and regularity assumptions, an asymptotic formula for t…
This note studies maximal resolvability of products of topological spaces, addressing a question about whether known product theorems for maximally resolvable spaces extend to other natural product topologies. Using dense families of subsets, dispersion character, and cardinal estimates for products…
This paper studies estimation of regression coefficients in a discrete-time Gaussian process with a deterministic linear regression component and stationary noise. It introduces and analyzes “pseudobest” unbiased estimates, defined as maximum-likelihood estimates computed using a chosen pseudospectr…
This paper presents a qualitative method for analyzing second-order nonlinear dynamical systems by transforming the governing equations to a canonical form involving characteristic functions determined from a functional characteristic equation. The approach relates the real parts of these characteri…
This note studies boundary value problems for higher order singular elliptic equations with constant and variable coefficients involving the Bessel operator in a quarter-space. Using explicit fundamental solutions, generalized shift operators, Poisson kernels, and the Lopatinskii complementing condi…
This note studies finite separability in semigroups, distinguishing semigroups whose arbitrary subsets can be separated from exterior points by homomorphisms onto finite semigroups from those where only subsemigroups are required. It gives a general necessary and sufficient criterion in terms of fin…
This paper studies summability and boundedness properties of solutions to a class of hypoelliptic constant coefficient equations in unbounded domains, under quasi-homogeneity assumptions on the characteristic polynomial and absence of nonzero real characteristic zeros. It introduces function spaces …
