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 generalized solutions of mixed initial boundary value problems for the wave equation in exterior domains of trap type, with attention to domains that approach a closed configuration. It develops a spectral representation for the associated self-adjoint operator using heat-kernel Gr…
The paper studies birational invariants of connected linear algebraic groups over fields of characteristic zero, using Galois module structures on Picard groups of nonsingular projective models. It proves similarity invariance of the Picard module under birational equivalence, computes Picard groups…
The paper studies subspaces of dyadic compacta and the relationship between the depth of a topological space, defined via closures of discrete subspaces, and its cardinality. It develops local character invariants, proves a main theorem giving conditions under which a dyadic compactum of weight τ co…
This note studies second order linear differential equations with periodic summable coefficients, focusing on multipliers and the existence and sign of Green’s functions for quasiperiodic boundary conditions. It gives criteria in terms of zeros of solutions, auxiliary differential inequalities, and …
This note studies criteria for fundamental closed sets in Post algebras of k-valued logic, focusing on permutation groups and mixed transformation semigroups within the symmetric semigroup. It introduces notation for maximal subalgebras, imprimitive and linear subgroups, and proves that for almost a…
This paper studies equivalence transformations for systems of second order linear differential equations with matrix coefficients, focusing on the case of symmetric operators. It defines equivalence by changes of independent variables and linear transformations of the dependent vector, then derives …
The paper develops two metric approaches to defining prime ends for sequences of plane domains, not necessarily simply connected, that converge to a kernel. Using conformally invariant metrics on the domains and a metric for kernel convergence, it defines convergence of completed boundary elements a…
The note studies twice continuously differentiable Riemannian spaces homeomorphic to Euclidean space in which every body satisfies the Euclidean isoperimetric inequality. It proves a sufficient criterion for an n-dimensional space with semigeodesic coordinates: if each level hypersurface belongs to …
The paper studies a singularly perturbed nonlinear system of ordinary differential equations in which a small parameter multiplies the derivative of one variable and the initial value of that variable tends to infinity as the parameter tends to zero. Under specified growth assumptions on the right h…
This paper studies boundary value diffraction problems for quasilinear parabolic equations in cylindrical domains whose principal coefficients are discontinuous across finitely many smooth interfaces and satisfy nonlinear transmission conditions. It derives local a priori Hölder estimates for spatia…
The paper studies the convergence behavior of Hermite-Fejer interpolation processes on variants of Chebyshev node systems, especially when the endpoints are added as interpolation nodes. It proves that for the Chebyshev zeros supplemented by the points plus and minus one, the process diverges throug…
This paper studies Nemytskii superposition operators generated by Carathéodory functions on a broad class of modular spaces defined by pre-generalized and generalized functions, including weighted Lebesgue, Orlicz, Orlicz-Nakano, and Musielak-Orlicz type spaces. It gives necessary and sufficient int…
This note studies sequence properties in separable locally convex spaces that correspond to geometric properties of Banach spaces, focusing on bases, minimal systems, unconditionality, stability, and subspaces with zero inclination. It establishes criteria for basicity via equicontinuity of partial-…
This paper studies an external inverse problem for metaharmonic volume potentials with a prescribed variable density: given a body with smooth boundary and a nearby exterior metaharmonic function, it seeks a nearby body whose exterior potential coincides with that function. Under analyticity and non…
This paper studies the velocity of wave fronts for finite and semi-finite wave functions using analytic continuation of Fourier transforms into the complex plane. It proves criteria, extending Paley-Wiener type results, that relate the existence and position of wave fronts to the asymptotic behavior…
This note gives necessary and sufficient conditions for subelliptic estimates for nondegenerate pseudodifferential operators in terms of the principal symbol and its commutators. For an operator whose real and imaginary principal parts have noncollinear gradients on the characteristic set, the valid…
This note extends Dzhrbashyan’s Riemann-Liouville integro-differential generalizations of the Cauchy and Schwarz integral formulas from one complex variable to holomorphic functions on bounded convex complete circular domains in complex n-space. Using these formulas together with earlier integral re…
This paper studies the global realization in three-dimensional Euclidean space of two-dimensional metrics of class C2 with negative curvature of class C1, weakening earlier regularity assumptions for such problems. The argument treats metrics written in strip coordinates as ds2 = dx2 + B2dy2, with c…
This paper studies the asymptotic distribution of eigenvalues of positive self-adjoint operators generated by general elliptic boundary-value problems in unbounded domains. Using a parametrix construction for the associated parabolic problem, it first establishes estimates for the Green matrix under…
This paper studies finite-dimensional subspaces of Banach spaces with the e-property, meaning that any norm-one linear extension of the identity on the subspace must be the identity on the whole space. It gives criteria for saturated subspaces, which imply the e-property, in the spaces l_p^n, distin…
The paper considers a class of discrete programming problems with separable additive or multiplicative objective components, an additional function bounded below by separable terms, integer resource constraints, finite variable domains, and supplementary feasibility conditions. It proposes a solutio…
The note constructs a compact Hausdorff space satisfying the first axiom of countability for which the small inductive dimension and covering dimension differ. Starting from the lexicographically ordered square and Cantor set quotients, the author defines two bicompacta of dimension 1 and glues them…
The paper develops a theory of elliptic problems of S. L. Sobolev type in which boundary conditions are imposed on submanifolds with finitely many conical point singularities rather than on the boundary of the ambient manifold. It introduces weighted functional spaces adapted to such singularities a…
This note studies polynomials orthogonal over the area of a simply connected Jordan domain, with unit, analytic, and more general nonanalytic weights, under smoothness assumptions on the boundary and weight. It establishes asymptotic formulas for the orthonormal polynomials in the exterior domain, e…
The paper addresses a question of F. Hall concerning when irreducible representations of polycyclic groups over absolutely algebraic fields of prime characteristic must be finite-dimensional. It develops module-theoretic lemmas for cyclic representations, using servile submodules over polynomial and…
The paper extends approximation theorems of A. F. Timan, I. E. Gopengauz, and S. A. Telyakovskii from functions with continuous integer-order derivatives to functions on an interval possessing a continuous derivative of arbitrary fractional order. It proves that, for \(r=r' + \alpha\) with \(0<\alph…
This paper studies the asymptotic distribution of the first time at which a cumulative process exceeds a high level, extending a known limit theorem for sums of independent identically distributed random variables to sums governed by a regular semi-Markov process. The construction uses an embedded e…
The paper applies a continuous-parameter stabilization method to the Dirichlet problem for a second-order nonlinear elliptic equation of the form Δz + f(x, y, z) = 0 in a bounded domain with zero boundary values. Working in Hölder spaces, the authors formulate conditions under which the associated l…
This paper studies higher order Bogolyubov and Krylov averaging approximations for ordinary differential equations on the whole time axis, with attention to solutions that remain bounded for all time. Using a theorem of Zabreiko, Kolesov, and Krasnoselskii on small bounded solutions, it establishes …
This paper develops consequences of a previously established local criterion for the existence of wave operators for pairs of self-adjoint operators. It formulates sufficient trace-class conditions ensuring subnormality and normality, including unitary equivalence of absolutely continuous parts, and…
This paper studies the local topological structure near an isolated singular point of a two-dimensional autonomous system whose leading terms are homogeneous of degree m, with special attention to analytic systems and to systems of class C_m. Using branch counts for curves defined by the vector-fiel…
This paper studies the propositional logic of finite problems developed by Yu. T. Medvedev as a refinement of Kolmogorov’s interpretation of intuitionistic logic as a calculus of problems. It introduces notions of alpha-logics, weakly constructive logics, finite rank of formulas, and finite logics, …
This note studies the structure of optimal and equivalent mixed strategies in finite matrix games. Using an entropy-type maximization argument and the Kuhn-Tucker theorem, it proves that an optimal strategy, as well as strategies equivalent or approximately equivalent to arbitrary mixed strategies, …
The paper extends Sobolev’s theory of cubature formulas for periodic functions to formulas that incorporate prescribed derivatives, viewed as multidimensional analogues of Hermite quadrature. It formulates the error functional on an n-dimensional torus with a general period matrix and derives an exp…
The paper studies the limiting behavior, as noise tends to zero, of the unique invariant measure of a nondegenerate Markov diffusion that is a small perturbation of a dynamical system on a compact manifold. Using an action functional and the associated quantities V(x,y), the authors define equivalen…
The paper studies equivalence and singularity of probability measures generated by Hilbert space valued Gaussian functions. Using reproducing kernel Hilbert spaces associated with operator valued covariance kernels, it gives necessary and sufficient conditions for equivalence of two such Gaussian me…
This paper studies how classes of topological spaces can be characterized as images of metric spaces under mappings with prescribed separation and quotient properties. It introduces quasi-refining and weakly refining sequences of covers and proves representation theorems: spaces with quasi-refining …
This paper extends Sinai’s construction of invariant measures for two-dimensional toral Y-diffeomorphisms to Y-flows on compact three-dimensional manifolds with everywhere dense contracting and expanding foliations. It first establishes the existence of arbitrarily fine Markov partitions by regular …
This note extends a cohomology construction for associative commutative unital algebras over a commutative unital ring by using the prime spectrum with the Zariski topology. For a subset of the spectrum, it defines subcomplexes of tensor powers consisting of elements that vanish near the subset, for…
The paper studies classes of transfinite index functions on the space J to the power omega_nu and formulates comparison principles determining when sets defined by relations between indices belong to specified Borel-type or projective classes. Using Lyapunov’s lemma on regular index classes, it deri…
The paper studies non-self-adjoint operator functions in a Hilbert space that depend rationally on a spectral parameter, with emphasis on resolvent growth and completeness of eigen and associated elements. It establishes sufficient conditions, formulated through approximation numbers and local princ…
This paper studies singular integral equations on a Lyapunov contour in the space Lp with bounded measurable coefficients, using the projectors associated with the Cauchy singular operator. It proves a perturbation theorem for operators of the form aP plus Q, giving Fredholm stability under multipli…
The paper studies a class of nonlinear stochastic programming problems, including nonconvex cases, in which a measurable decision function is constrained by probabilities of membership in random sets and by an expected linear operator inequality. For the case of two probabilistic constraints, the au…
This paper studies the structure of nonlinear tensor functions in Minkowski space through their symmetry groups. It argues that once the symmetry group of a tensor function is known, the function can be represented as a linear combination of invariant basis tensors, with scalar coefficients dependin…
The paper studies a multidimensional multifront Stefan problem for parabolic heat equations with several moving internal and external phase fronts, formulated in two spatial variables with extension to higher dimensions indicated. It defines a regular classical solution and reduces the free boundary…
This paper studies semiformal completions of constructive arithmetic, motivated by Gödel incompleteness for recursively axiomatized extensions of intuitionistic arithmetic. It compares two completion procedures: Feferman-style transfinite progressions obtained by iterating reflection principles over…
This note studies how diffusion processes obtained by small random perturbations of a dynamical system with a stable equilibrium leave a bounded domain whose deterministic trajectories are attracted to the equilibrium. Using a variational functional and the associated quasipotential, it establishes …
The paper studies independence for subsemigroups of a semigroup as an analogue of free decomposition in group theory, emphasizing that the semigroup notions obtained from group-theoretic analogies are not equivalent. It introduces unit-ideal subsemigroups, records their elementary closure properties…
The paper studies projective transformations of complete analytic Riemannian spaces of dimension at least three, comparing the connected identity components of the projective and affine transformation groups. Using local normal forms for metrics admitting a non-affine projective one-parameter group,…
This paper derives boundary growth estimates for solutions and derivatives of homogeneous elliptic boundary value problems for properly elliptic operators with covering boundary operators. Using previously established derivative estimates for Green functions, the author represents solutions by princ…
