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 studies \(k\)-decomposable topological spaces, especially spaces that fail to be \((k+1)\)-decomposable or maximally decomposable, within the class of dense-in-itself \(T_0\) and \(T_1\) spaces. Using ends, filters, ultrafilters, and refinements or relaxations of topologies, it gives chara…
This paper addresses the independence of infinite systems of group identities and gives an effective construction for a known problem on varieties of groups. For every odd integer n at least 4381, it proves that the identities of the form (x^{rn}y^{rn}x^{-rn}y^{-rn})^n = 1, with r ranging over prime…
This note studies the almost sure asymptotic behavior of the maximum of a separable homogeneous isotropic Gaussian random field in Euclidean space, extending earlier one-dimensional results for stationary Gaussian processes. Under assumptions on the existence of continuous first and second derivativ…
This paper studies when a value of the Markov spectrum in a specified interval also belongs to, or lies in the closure of, the Lagrange spectrum. Building on methods of Freiman, it formulates conditions in terms of two-sided sequences of continued-fraction partial quotients, convergence of such sequ…
This note states several estimates for families of homeomorphic, quasiconformal, and Sobolev-type mappings of plane and spatial domains under integral bounds on derivatives or inverse derivatives. Using a previously established inequality, it derives lower bounds for the distance of image continua f…
The paper proves existence theorems for nonlinear operator equations in scales of Banach spaces under energy type inequalities and multiplicative norm estimates. Using the Leray Schauder principle, it gives conditions under which equations of the form Au + Ku = h have solutions, including versions b…
The paper applies model theory and nonstandard analysis to questions of topological equivalence for Banach spaces, revisiting the theorem that all infinite-dimensional separable Banach spaces are homeomorphic. It constructs nonstandard Banach spaces through internal function spaces and ultrapowers, …
The paper introduces a generalized construction of Steenrod homology groups for compact metric spaces. It starts with a category of locally finite simplicial complexes and closed simplicial embeddings satisfying union and gluing axioms, together with specified chain classes over a coefficient group …
The paper studies when the eigenvectors of model contractions, realized as restrictions of the adjoint shift on invariant subspaces of vector-valued Hardy space, form a Riesz basis. Using the Sz.-Nagy and Foias characteristic function, it gives criteria for the basis property in terms of inner opera…
This paper studies the local behavior of homogeneous Gaussian random fields near high regular glints, or high-level points with prescribed gradient structure. It first establishes an ergodic theorem for measurable homogeneous fields and applies it to Gaussian fields with continuous sample functions …
This paper studies the Cauchy problem for the linearized hyperbolic system describing a rotating compressible fluid in three dimensions, with smooth rapidly decreasing initial data and, in the general representation, smooth forcing terms. It derives explicit integral formulas for the velocity and pr…
The paper studies a modified localization principle for Fourier series with respect to fundamental systems of Laplace operator eigenfunctions in an arbitrary N-dimensional domain. Instead of requiring convergence at a fixed point where the expanded function vanishes locally, it considers almost ever…
The paper characterizes functionally separable and Tikhonov topological spaces in terms of the behavior of divergent nets under bounded continuous real-valued functions. It proves that, within T1 spaces, functional separability is equivalent to the property that every divergent net with two limit po…
The paper introduces multilevel dynamic games as a formal framework for complex hierarchical systems composed of relatively autonomous subsystems. It defines a finite tree of positions, local games at each position, probabilistic transitions between states across levels, and several important subcla…
The paper studies elliptic boundary value problems for properly elliptic operators with boundary operators that cover the equation, without assuming that the boundary operator system is normal. It constructs a Green vector function for problems with finite dimensional solvability conditions, proves …
This paper studies the structure of the set of positive deviations of a meromorphic function, defined through the growth of the maximum reciprocal distance from a value relative to the Nevanlinna characteristic. It compares this set with the sets of defective values in the senses of Nevanlinna and V…
The paper studies perturbations of the continuous spectrum for the multiplication operator in \(L_2(-\infty,\infty)\) under a class of infinite-dimensional completely regular perturbations represented as \(V=A^*B\). Using an operator-valued function \(K(\zeta)=1+BS_\zeta A^*\), it characterizes nonr…
The paper introduces pseudodevelopable spaces, defined by the existence of a sigma-biconservative pairbase, and studies their role in problems concerning symmetrizability. It gives equivalent characterizations of this class, establishes preservation under hereditary operations, countable products, c…
This note studies spaces of topological embeddings of manifolds, especially locally flat and locally simply connected embeddings in codimension other than two. It proves a local isotopy theorem implying local p-connectedness of the space of locally flat embeddings, using reductions to local cube emb…
This paper studies estimation of a shift parameter for distributions supported on a bounded interval, with emphasis on equivariant Pitman estimates and their sequential analogues. It proves an upper bound for the mean squared error of the fixed-sample Pitman estimate in terms of the sample size and …
This paper studies a boundary value problem in an infinite layer for systems of linear differential difference equations with constant coefficients, where some components are prescribed at the initial hyperplane and the remaining components at the terminal hyperplane. Using a determinant associated …
The paper studies constructive characterizations of functions in L2 on the unit sphere in terms of their best approximation by finite spherical harmonic sums and the behavior of spherical Fourier coefficients. It establishes necessary and sufficient conditions, under Lozinskii type assumptions on a …
This note extends Glicksberg’s generalization of Kakutani’s fixed point theorem in locally convex Hausdorff linear topological spaces to a broader class of set-valued mappings. After recalling closed multifunctions, it introduces a weaker notion of partial closedness, defined by a limiting condition…
This paper studies the asymptotic decay of the error in finite-past linear prediction for multidimensional stationary sequences of full rank, measured through the difference between finite and infinite prediction accuracy. It establishes necessary and sufficient conditions linking polynomial decay o…
The paper studies functional relations between operators of the form B equals a function of A, focusing on concave and related functions of a positive self-adjoint operator beyond the Hilbert space setting. Using Lorentz spaces and a generalized moment inequality for Phi-functions, it establishes bo…
This paper studies linear isometries between spaces of summable analytic and harmonic functions on bounded planar domains, focusing on the cases \(L_a^p(D)\), \(L_h^p(D)\), and Smirnov spaces \(E^p(D)\) for \(p \ne 2\). It develops a general representation theorem for isometric operators on subalgeb…
The paper develops a method for realizing spaces of regular functionals on K-spaces by embedding their maximal extensions into a common extended K-space of continuous extended-valued functions. It defines a notion of disjointness for functionals on different normal subspaces and proves the existence…
This paper studies finite p-groups through enumeration of subgroups, normal subgroups, and epimorphic images, with emphasis on deriving existence results from congruences for subgroup counts. It proves divisibility and congruence theorems for subgroups of prescribed order, exponent, and structure, i…
The paper studies the Green matrix for an inhomogeneous boundary-value problem for general parabolic systems in the sense of Petrovskii, with zero initial condition and prescribed boundary data. Using methods developed for elliptic Green functions and parabolic potential kernels, it defines a princi…
This paper studies spectra associated with uniformly bounded families of finite-dimensional operators acting in normed spaces, introducing several notions of spectral kernels defined through asymptotic approximate eigenvalues. It establishes basic topological and inclusion properties of these kernel…
This note studies relations among absolutely summing, semi-integral, quasi-nuclear, and generalized p- and q-quasi-nuclear mappings between locally convex and Banach spaces. Using tensor product formulations and nuclearity criteria, it characterizes absolutely summing operators via continuity of ind…
This paper introduces and studies multistage matrix games with inertia, in which each player’s admissible mixed strategies at a given step are constrained by the pure strategies realized in several preceding steps. The authors formalize inertia of finite depth, define limiting expected average payof…
The paper studies a class of nonlinear differential systems formed by a finite-dimensional linear part in feedback with a possibly history-dependent nonlinearity, under controllability, spectral, and quadratic inequality assumptions. Using a frequency-domain negativity condition for an associated He…
This note studies eigenvector systems of completely nonunitary contractions modeled as restrictions of the adjoint shift to invariant subspaces determined by inner operator functions. Under assumptions of isolated eigenvalues, complete eigenfunctions, and uniform minimality, it gives equivalent crit…
This paper studies extremal cases in compact simply connected Riemannian spaces with sectional curvature bounded above by a positive constant and with closed geodesics bounded below in length by the corresponding spherical value. It proves that equality in the length of a closed geodesic, in the per…
This paper studies cones in affine space whose associated family of parallel translated cones is invariant under a group acting transitively on nonvertex points, with attention to when such symmetry forces the cone to be elliptic. It proves several classification theorems: under closedness, sharpnes…
The paper studies a binary additive problem for representations of an integer N as N = n1 + n2, where all prime divisors of n1 are small and all prime divisors of n2 are large, relative to powers of N. It defines the counting function L(N, N1/alpha, N1/beta) and proves an asymptotic estimate for all…
This note gives necessary and sufficient conditions for subelliptic estimates for pseudodifferential operators in a domain, expressed through the principal symbol and the leading symbols of iterated commutators of the operator with its formal adjoint. The argument introduces an integer invariant mea…
This note studies how holomorphic quadratic differentials on closed Riemann surfaces of genus greater than one depend on the moduli of the surface. Using the Bers-Teichmüller realization of moduli by normalized quasiconformal mappings and a variational formula for solutions of the Beltrami equation,…
This note studies two-level iterative schemes for solving linear operator equations with a self-adjoint positive operator in a Hilbert space. Implicit schemes are reduced to equivalent explicit schemes, allowing convergence estimates to be expressed through norms of resolving or transition operators…
This note formulates existence results for elliptic boundary value problems in bounded plane domains with corners and with internal curves of coefficient or boundary condition discontinuity reaching the boundary. Using weighted Sobolev spaces, the argument reduces local model problems near corners a…
This paper proves the consistency of the fragment NF3 of Quine’s New Foundations, consisting of those axioms whose stratification uses at most three type levels. Using Specker’s criterion, the argument reduces consistency to the construction of a model of three-type theory admitting an epsilon-isomo…
This note studies a singular Nicoletti boundary value problem for a system of first order ordinary differential equations with conditions imposed at prescribed points, allowing the right hand sides to have nonintegrable singularities at those points. Using Carathéodory type assumptions, comparison f…
This paper studies non-uniqueness phenomena in the coefficient problem for normalized univalent functions in the unit disk, focusing on solutions of the differential-functional equations that give necessary extremality conditions for the coefficient functional. Using subclasses with p-fold rotationa…
Vinogradov develops a variant of Morse theory for incomplete spaces of the form M setminus K, where M is complete and K is a closed subset, by introducing responsible and noncritical points and proving a fundamental homotopy invariance lemma under admissibility conditions. The method is applied to t…
The paper develops a generalized implicit function theorem for operators in Banach spaces under weakened differentiability assumptions, requiring only control of the deviation from the derivative at the origin and uniform boundedness of inverse linearizations. This result is applied to bounded solut…
This paper studies local analytic quasigroups defined by analytic mappings between equal-dimensional manifolds and develops canonical power-series decompositions for their defining equations. Using isotopic coordinate transformations and an induction on homogeneous degree, it proves the existence an…
This note studies necessary first order conditions for a class of nonsmooth minimization problems with equality constraints, convex inequality constraints, and an additional constraint requiring one variable to be selected by an operator depending on the other. Using a feasible directions framework,…
