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 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…
This paper defines fiducial distributions for the parameters of a multivariate normal population under three standard cases: known covariance with unknown mean, unknown covariance with known mean, and both mean and covariance unknown. The definitions are formulated through equalities with invariant …
This note studies the global homological structure of minimal compacta arising in a class formulation of the multidimensional Plateau problem in compact closed Riemannian manifolds. Using Čech-Aleksandrov homology, it distinguishes several admissible classes according to the boundary and realized ho…
This paper studies minimization of convex continuous nonnegative functionals on Banach spaces that are constant on a linear subspace, with special attention to Chebyshev points for systems of affine planes. It gives conditions ensuring existence of minimizers, notably quotient reflexivity of the sub…
This note studies discreteness of the spectrum for certain non-self-adjoint operators in Hilbert space by relating them to associated symmetric and self-adjoint operators. It proves criteria showing that, under semiboundedness and compactness assumptions, discreteness of the spectral kernel or of th…
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…
The paper studies separation properties of tree-like and dendroidal peripherally bicompact Hausdorff spaces, using the structure of unique ordered continua and linear hulls of closed sets. It proves that in a tree-like peripherally bicompact space any two disjoint closed sets can be separated by a d…
This paper studies boundedness criteria for singular integral and pseudodifferential operators in weighted spaces on Euclidean space. It extends earlier results of Babenko, Stein, Mikhlin, Agranovich, Plamenevskii, and others by proving weighted Lp and L2 boundedness theorems under conditions on ker…
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…
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…
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…
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 …
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…
This paper studies approximation of functions in Sobolev type classes by splines of order m on an interval and on the real line, allowing both fixed and adaptively chosen knots. It establishes error estimates in Lp and Lq metrics for functions with kth derivative in Lp, including bounds for derivati…
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…
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…
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…
This paper examines stability of convergent iterative algorithms for solving finite-dimensional, generally nonselfadjoint difference equations when computations are affected by roundoff errors. It introduces a criterion based on the number of additional guard digits required to keep the limiting err…
This note establishes Phragmén-Lindelöf type alternatives for solutions of general linear uniformly elliptic equations of arbitrary order with variable coefficients, under Hörmander’s condition excluding multiple characteristics. For cylindrical domains, it proves that bounded Cauchy data on the lat…
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…
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…
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 …
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…
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…
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…
This note establishes criteria for when the direct wreath product of two nontrivial linear groups is itself faithfully representable by matrices over a field of the same characteristic. In characteristic zero, representability holds precisely when the active group is finite, or when it is a finite e…
The paper studies differential reducibility of linear nonhomogeneous differential equations over a differential field of analytic functions, motivated by applications to algebraic independence results for values of special functions. It proves a reversible criterion: a nonhomogeneous equation is dif…
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…
This note studies boundary value problems for higher order elliptic differential operators that degenerate on a hyperplane or on the boundary of a smooth bounded domain. It introduces and analyzes B-elliptic operators involving the singular Bessel operator in weighted spaces, proving a priori estima…
This note studies sufficient conditions for the univalence of analytic and meromorphic functions arising in two inverse boundary-value problems, for functions regular in the unit disk and exterior disk. It derives criteria involving the logarithmic derivative, integral mean bounds, and Schwarzian de…
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…
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…
The paper addresses approximate solution of linear operator equations of the first kind in a Banach space when the inverse problem is ill posed and both the operator and right hand side are replaced by approximate data. It analyzes a universal iterative process for the regularized equation with boun…
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 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…
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…
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 …
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…
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…
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…
The paper studies Green’s functions for Sturm-Liouville differential expressions with operator coefficients in a separable Hilbert space, extending earlier work from the case of identity leading coefficient to variable positive operator coefficients. Under stated boundedness, differentiability, meas…
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…
The paper studies infinite nonabelian groups in which every infinite nonabelian subgroup is normal, viewed as a generalization of Schmidt groups and metahamiltonian groups. Under the assumption of local stepwise structure, it proves solvability, shows that nonperiodic examples are metahamiltonian wi…
This note studies optimal sequential estimation of a location, or shift, parameter under squared error loss within a class of invariant stopping rules and equivariant terminal decisions. It defines optimality by analogy with Wald’s criterion, comparing risks among procedures whose expected sample si…
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…
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…
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 …
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 …
