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 addresses the failure of the Noether property for the homogeneous Dirichlet problem for multidimensional elliptic systems of second order. It constructs, in Euclidean spaces of arbitrary even dimension, a class of elliptic second order systems obtained as the product of two first order mat…
The paper studies multiple Hecke series for the full linear group over a central division algebra over a p-adic field and related zeta-functions defined by zonal spherical functions. It proves that the multiple Hecke series is a rational function in its several variables with coefficients in the int…
The paper studies integral norm estimates for Laplace eigenfunctions with Dirichlet boundary conditions, motivated by convergence questions for Fourier expansions in eigenfunction systems and by the c-property for orthogonal systems. Using explicit eigenfunctions in a product of a disk and a cube, a…
This paper studies the asymptotic structure of solutions of periodic dissipative differential equations in Banach spaces, including equations generated by unbounded operators and evolutionary boundary value problems. It develops fixed point principles for monotone dissipative operators on regularly …
The paper studies first order canonical differential operators in a separable Hilbert space on the half-line, with a skew unitary operator defining the canonical structure and an operator-valued summable potential satisfying an anticommutation condition. Using fundamental solutions and integral repr…
The paper studies a class of free-boundary problems for the heat-conduction equation on a time-dependent interval, motivated by the impact of a viscoplastic rod against a rigid obstacle. It formulates boundary conditions in which the moving endpoint is constrained by an operator acting on the unknow…
The paper addresses a problem posed by Erdős concerning infinite sequences over a finite alphabet in which no two adjacent segments have the same multiset of symbols. It constructs a specific block of length 20 on five symbols with several parity and asymmetry properties, then uses cyclically shifte…
This paper studies small nonzero solutions of nonlinear operator equations of the form Ax = (1 + μ)x in a Banach space, where A is decomposed into linear, quadratic, and higher order terms and the eigenvalue 1 of the linear part has a two-dimensional eigenspace. Using cone methods and the eigendirec…
This paper studies a Tricomi-type boundary-value problem for a second-order equation of mixed parabolic-hyperbolic type in a domain separated by the line of degeneracy. Under sign and regularity assumptions on the coefficients, the authors establish an extremum principle for regular solutions, which…
This paper studies solvable varieties of groups contained in products of nilpotent and abelian varieties, with particular attention to varieties that do not contain the variety of all metabelian groups. Using module-theoretic arguments over integral group rings, annihilator ideals, and several lemma…
This paper studies nuclear structures in locally convex spaces through the decrease properties of equicontinuous subsets of dual spaces. It defines the nuclear topology associated with a given topology, characterizes it as the topology of uniform convergence on nuclear subsets of the dual, and relat…
This note addresses whether the multiplicity of a base is preserved under mappings in general topology, giving a positive answer to a question of P. S. Aleksandrov. It proves directly that if a perfect mapping sends a space with a base of multiplicity at most a cardinal \(\tau\) onto another space, …
This paper states a series of results on mappings associated with topological groups, continuing work on free topological groups by Markov and Graev. It introduces classes of spaces such as amoebic, D-bicompact, and standard spaces, and shows that broad classes of topological groups can be represent…
This paper formulates a planar model for stationary electrochemical machining as a Cauchy problem for the Laplace equation, in which the workpiece boundary supplies both potential and normal derivative data and the tool is sought as a level curve of the resulting potential. Assuming analytic boundar…
The paper addresses the construction of invariant equipment and a canonical frame for an m-parameter manifold in projective space, consisting of m-dimensional surfaces through whose points pass m distinguished lines in general position. Using moving frames, Pfaffian differential forms, and successiv…
The paper studies well-posedness, in the sense of Tikhonov, for unconditional minimization problems for functionals on Banach spaces, with emphasis on convergence of minimizing sequences. It establishes sufficient conditions involving monotone nonlinear operators, positivity or quasi-negativity of a…
The paper develops and justifies an operational method for mixed initial boundary value problems for systems of linear parabolic differential equations on adjacent intervals with discontinuous coefficients and boundary conditions that may contain time derivatives. The problem is reduced to homogeneo…
The paper studies Sobolev-type plane mappings with generalized derivatives and the behavior of such mappings on level sets of Sobolev functions. It proves that if a mapping belongs to an appropriate class and the level function has conjugate integrability, then almost every level set has rectifiable…
This paper studies zeta functions with non-abelian characters associated with an arbitrary central simple algebra over a number field, motivated by their relation to Hecke operators and automorphic functions. After defining local and global spherical functions, automorphic functions on the idele gro…
The paper studies representations of the group SU(2,1) induced from finite-dimensional irreducible representations of the subgroup MN in an Iwasawa decomposition, with N acting trivially. It realizes these representations on spaces of square-integrable functions on a subgroup isomorphic to U(2), dec…
This paper studies four-dimensional Einstein spaces satisfying the Einstein condition with nonzero constant proportionality and belonging to the second class of embedding in a higher-dimensional flat space. Using the algebraic Gauss, Codazzi, and Ricci embedding equations for two second fundamental …
This paper studies generalized symmetric gamma correlations for nonnegative random variables whose joint density is expanded in products of normalized Laguerre polynomials with gamma marginal densities. It proves a necessary and sufficient condition for such an expansion to define a nonnegative join…
This note studies absolutes of homogeneous spaces, especially topological groups and their factor spaces, in the category of completely regular spaces. Using inverse spectra of compacta, irreducible perfect mappings, and structural results on locally bicompact groups, it proves that the absolute of …
This note formulates a series of results on the structure and position of normal subgroups in finite groups, with particular emphasis on finite p-groups and on groups expressible as products of permutable or structurally restricted subgroups. It describes p-groups with cyclic Frattini subgroup, refi…
The paper studies the extension and construction of normal Hausdorff linear topologies on partially ordered linear structures called K-lineals. It gives conditions under which a normal topology on a sublineal, a structurally complete normal subset, or the bounded part of a function representation ex…
Chernavskii outlines a proof of local contractibility for groups of homeomorphisms of metrizable manifolds under the compact-open, uniform, and majorant topologies, with special attention to compact manifolds and to open manifolds that are interiors of compact manifolds. The argument reduces the glo…
The paper generalizes the Radon-Nikodym theorem to vector measures with values in Banach spaces, weakening earlier restrictions by introducing a more general integral for bilinear operator valued integration. It defines this tau integral, proves its countable additivity, and uses it to represent vec…
This paper studies smooth embeddings of spheres in smooth compact manifolds having the homotopy type of a sphere, comparing smooth isotopy, combinatorial isotopy, and the action of local knots under codimension and connectivity restrictions. It proves that quotienting smooth isotopy classes by local…
This paper establishes an a priori estimate for solutions of the Dirichlet problem for a class of hypoelliptic differential equations in a bounded domain with continuously differentiable boundary. Under conditions on the operator’s constant strength, the behavior of its symbol in selected orthogonal…
This note extends Gårding’s inequality to a class of degenerate elliptic operators in a bounded domain of a half-space adjacent to the boundary where degeneracy occurs. Using weighted Sobolev type spaces and mixed Fourier, Bessel transform methods, it formulates Dirichlet integrals associated both w…
This paper studies trace formulas for a self-adjoint operator with discrete spectrum under bounded self-adjoint perturbations. It strengthens a result of Halberg and Kramer by giving conditions under which convergence of the spectral shift sum is equivalent to convergence of the corresponding diagon…
This paper studies structural properties of feathered paracompact, or paracompact p, spaces under closed mappings and in relation to bases. It proves that the closed image of such a space can be decomposed into a countable union in which all exceptional sets are discrete and the remaining fibers are…
The paper proves a fixed point theorem for generalized condensing operators on closed convex subsets of locally convex linear topological spaces. It introduces a definition based on the bicompactness of sets invariant under the operator and relates this framework to earlier fixed point principles fo…
This paper studies the large-parameter Cartwright-Littlewood type equation with periodic forcing and nonlinear damping under symmetry, monotonicity, and nondegeneracy assumptions, focusing on the parameter range previously conjectured to yield convergence of all solutions. The argument uses asymptot…
The paper addresses a problem of P. S. Alexandrov asking whether every n-dimensional cyclic compactum contains an n-dimensional closed Cantor manifold, equivalently an irreducibly cyclic subcompactum. It constructs a two-dimensional quotient compactum from a disk by identifying vertices of regular p…
The paper formulates a boundary-value problem for plane motion in a barotropic atmosphere in a bounded simply connected domain, addressing the difficulty of specifying lateral boundary conditions for primitive-equation models. It prescribes the normal velocity on the boundary and, on inflow portions…
This note studies a nonlinear boundary value problem for a piecewise analytic function satisfying a power relation on a contour, with nonvanishing coefficient of index kappa and exponents that are boundary values of analytic functions. Using the argument principle, it derives necessary restrictions …
This note studies continuous triangular summation methods for Fourier series in eigenfunctions of the Laplace operator with Dirichlet boundary conditions on a bounded normal domain. Using kernel estimates and a comparison with the kernel for the ordinary multidimensional Fourier integral, it establi…
The paper studies the asymptotic optimality of cubature formulas with a boundary layer regular in the sense of S. L. Sobolev in Sobolev-type spaces, focusing on the case of the weight function given by a power of the Fourier variable. It develops properties of discrete functions associated with a re…
The note studies structural descriptions of solution sets for systems of equations with one unknown in a free group, building on earlier work of Lyndon and the author on finite parametric representations. It proves that any soluble such system has its solution set representable by finitely many word…
This note studies simple graded Lie algebras over the complex numbers whose negative part is generated by the degree minus one component. It constructs a universal infinite-dimensional graded Lie algebra using a free Lie algebra in negative degrees and multilinear operator spaces in nonnegative degr…
The paper studies analytic properties of the resolvent kernel for a self-adjoint fourth-order ordinary differential operator on the half-line with a compactly supported smooth real potential. It relates this problem in L2(0, infinity) to a parameter-dependent boundary-value problem on a finite inter…
This paper studies linear differential systems with bounded uniformly continuous recurrent coefficients and asks when their probable spectrum is stable. It introduces absolute regularity, states that almost every system in the associated dynamical hull has this property, and derives a stability crit…
The paper studies algorithmic and definability properties of algebras of one-place primitive recursive, general recursive, and partial recursive functions under addition, multiplication, and inverse-type operations. It proves a general nonrecursiveness criterion for subsets of these function classes…
The paper proposes a method for accelerating two-sided iterative approximations to fixed points of operators in partially ordered Banach spaces with cones. For linear positive operators of the form x equals Ax plus f, it constructs smaller invariant cone segments by replacing each pair of lower and …
This note studies harmonic analysis on the hyperboloid associated with a real pseudo-orthogonal group, where noncompact stabilizers make the decomposition of the natural unitary representation in L2 difficult. Using representations connected with the isotropic cone and invariant generalized spherica…
The paper studies cubature formulas for weighted integration over an n-dimensional domain that are exact for all polynomials of even degree 2l and use the minimal possible number of nodes. It reformulates the exactness conditions as a matrix equation involving the node matrix, weights, and Gram matr…
This paper studies the Green matrix for homogeneous parabolic boundary value problems for systems whose coefficients may be discontinuous across a smooth interior hypersurface. The authors formulate the transmission problem, relate the constant coefficient model problem in the whole space to a stand…
This paper studies estimates for neighboring coefficients of normalized univalent functions in the unit disk, focusing on bounds for the difference between the moduli of consecutive coefficients. Using coefficient systems associated with meromorphic univalent functions outside the unit disk and a le…
