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 note gives a direct proof that finite functions are dense in the homogeneous Sobolev-type space \(L_p^{(m)}(E_n)\) for \(p>1\), whose norm is defined by the \(L_p\) integral of all derivatives of order \(m\). The argument reduces the problem to smooth representatives with controlled behavior at…
The paper studies sharp norm estimates for differential operators acting on entire functions of exponential type at most ν that belong to L2 on the real axis. Using integral representations for such functions and their L2 conjugates, together with the Cauchy, Bunyakovsky inequality and Parseval iden…
This paper studies cohomological dimension functions of finite-dimensional compacta with respect to the Bockstein system of coefficient groups and their relation to Urysohn dimension. It proves a partial realization theorem for dimension functions, constructs corresponding test spaces, and shows how…
The paper studies algebraic invariants of the linear representation induced on the coefficient space of a polynomial planar differential system by rotations of the phase plane. By passing to complex coordinates and diagonalizing the representation, it gives a constructive finite integral rational ba…
This note studies characterizations of finite groups by the structure and number of classes of noninvariant solvable subgroups, especially classes defined by isoordinality or isomorphism and by restrictions on prime divisors. It introduces quasinilpotent groups through a condition on pairs of subgro…
This paper studies a boundary value problem for a linear odd order evolution equation on a finite strip, with homogeneous initial data and asymmetric boundary conditions for derivatives at the two endpoints. The argument establishes a priori estimates for finite expansions in the eigenfunctions and …
This paper extends Postnikov’s asymptotic result on the distribution of exponential rational trigonometric sums by treating denominators of the special form \(g^\tau - 1\). Using the method of moments, it removes the earlier restriction on the summation length for this case and proves that the norma…
This paper studies the first boundary-value problem for a coupled diffusion system consisting of a quasilinear parabolic equation for one unknown and an evolution equation for another, with applications suggested in reactor theory and heat processes in solidifying solutions. Under monotonicity, Lips…
This note studies finite-dimensional Lie algebras admitting regular automorphisms, with emphasis on positive characteristic, where the problem is related to degenerate simple Lie algebras. The authors prove that a Lie algebra over a field of characteristic p greater than 0 with a regular automorphis…
This paper extends the theory of normal solvability for general elliptic boundary value problems to Douglis and Nirenberg elliptic systems, including Petrovskii systems. It formulates ellipticity through the principal parts of the differential and boundary operators together with the Lopatinskii con…
This paper addresses Neuwirth’s question whether every knot group can be expressed as the free product of two free groups of equal rank with an amalgamated subgroup of rank one less than twice that rank. Using Heegaard splittings, canonical cuts on handlebody boundaries, van Kampen’s theorem, and a …
The paper studies asymptotic expansions for ordinary differential equations with a small parameter in which the limiting equation remains of the same order but degenerates at the left endpoint, causing the loss of one boundary or initial condition. It develops a method that separates the regular par…
This paper determines convergence classes for interpolation series associated with systems of linear functionals, with emphasis on the Abel-Goncharov and Gelfond interpolation problems. Using a generalized associated-function representation involving an entire function constructed from the inverse o…
This note studies spectral properties of a broad class of bounded non-self-adjoint operators in spaces with an indefinite metric, without assuming finite rank of the negative or positive part. It constructs a characteristic matrix-function for such operators, establishes its basic identities, and re…
This paper establishes criteria for the homogeneous Dirichlet problem for the polyharmonic equation in unbounded domains, considering generalized solutions for right hand sides in suitable Lebesgue spaces and the discreteness of the associated spectrum in L2. The argument develops Molchanov’s capaci…
The paper develops a variational framework for a class of degenerate elliptic boundary value problems in a weighted Sobolev setting, focusing on the half-plane as a model case. It defines anisotropic weighted spaces adapted to the operator x inverse times differentiation in x, proves trace and exten…
This paper studies embeddings of modules over associative rings, focusing on faithful primary modules, divisible modules, and modules without zero divisors. Using injective module embeddings and a construction that embeds rings from special classes into rings with identity, it proves that over an in…
This paper studies a one-dimensional two-phase Stefan problem for quasilinear heat equations with a single moving interface and Neumann boundary conditions. The authors formulate a solution concept and propose an implicit finite-difference scheme in which the time step is chosen so that the approxim…
This paper states results on analytic transformations of a boundary function and a periodic function, defined through conformal mapping, Faber polynomials, and Cauchy type integrals over domains or continua with simply connected complement. It gives conditions for the existence of sigma transforms a…
This paper studies Katetov’s maximal H-closed extension τR and its relation to the Cech compactification βR, using the notion of maximal points, defined as non-isolated points that are not points of contact of any set. It proves that every point of τR outside R is maximal, that sets of regular cardi…
The paper studies transition solutions of autonomous nonlinear differential equations of order n on the whole real axis, connecting two equilibrium values at negative and positive infinity with all derivatives tending to zero. It develops sufficient existence conditions by introducing majorizing pai…
This paper studies zeros of orthogonal systems of continuously differentiable functions on an interval, extending classical results for algebraic orthogonal polynomials. Assuming that each finite initial segment of the system is a Chebyshev system, it proves that each orthogonal function has the exp…
This note develops a method for constructing aligned-point nomograms for first-genus equations in three variables, represented with one curvilinear scale and two rectilinear scales. The problem is reduced to bringing the given relation to Massau’s determinant form by studying the differential equati…
This paper studies branching for analytic operator equations in Banach spaces under general hypotheses, with a finite dimensional branching component. It introduces the notion of an r-simple solution, meaning a zero-solution stable in a specified Laurent-series sense under small parameterized pertur…
The paper studies general boundary value problems for elliptic differential equations of arbitrary order whose coefficients may be discontinuous across an interior interface. It formulates boundary and conjugation conditions using general differential operators, proves a relation between covering co…
The paper studies the joint distribution of prime elements in two imaginary quadratic fields, specifically the Gaussian field and the field generated by the square root of minus three, under the condition that the two primes have equal norm. It relates this counting problem to the analytic continuat…
The note studies Lie algebras and Lie rings admitting regular automorphisms of finite period, where no nonzero element is fixed. It proves that any Lie algebra over a field of arbitrary characteristic with such an automorphism of period n is solvable, with derived length bounded by 2 to the power n …
This paper relates the stability of one-layer finite difference schemes for linear parabolic-type Cauchy problems to convergence of measures on spaces of continuous paths. Starting from a fundamental solution satisfying positivity, boundedness, and localization assumptions, it constructs path-space …
The paper studies Volterra type integral equations with delayed arguments under monotonicity and continuity assumptions, motivated by applications such as delayed feedback systems. It first records the resolvent kernel representation for a linear delayed Volterra equation and then establishes compar…
The paper studies fixed point phenomena in constructive metric spaces, focusing on mappings of the square into itself and their relation to constructive analogues of Brouwer’s theorem. It constructs continuous and uniformly continuous operators on the constructive square, including a continuous retr…
This paper studies asymptotic solutions of linear differential systems with a small parameter when the leading matrix has multiple roots with several elementary divisors, including a resonant forcing term. After reducing the leading matrix to Jordan form, the author constructs formal expansions in f…
The paper studies least square trigonometric approximation of continuous two variable periodic functions on prescribed equidistant grids. It defines the polynomial of best quadratic approximation at these nodes, represents it through products of Dirichlet kernels, and relates special limiting cases …
This paper studies exact operations on the class of all groups, understood as product constructions with fixed embeddings of factors, and organizes their known and proposed properties into systems of internal, external, and associativity postulates. It analyzes implications and equivalences among th…
This paper studies boundary value problems for general Petrovsky parabolic systems with variable coefficients in domains of broad geometric form, including nonconvex cylindrical domains, noncylindrical bounded domains, and certain exterior unbounded domains. Using half space fundamental matrices and…
This paper constructs fundamental matrices of solutions for Petrovskii parabolic systems and related elliptic systems under integral Hölder, or Dini type, continuity assumptions on the coefficients, weakening the usual Hölder hypotheses. Using Levi’s parametrix method, Green matrix estimates, and co…
This note constructs the partition of the set of all Poisson-stable motions induced by the standard invariant classes: stationary, periodic, almost periodic, uniformly Poisson-stable, recurrent, almost recurrent, and pseudo-recurrent motions. It identifies eleven invariant component classes and prov…
This paper studies a Wiener-Hopf equation of the first kind and argues that restrictive solvability conditions can be avoided by enlarging the solution class to include generalized functions consisting of an square integrable part together with Dirac delta functions and their derivatives. The method…
The paper develops a general sieve-theoretic framework for quasi-prime numbers, defined as integers whose prime divisors exceed a prescribed threshold depending on the interval length. Its main theorem estimates, for broad integer sequences satisfying average distribution in arithmetic progressions,…
The paper studies Fourier coefficients of Poincaré series of dimension negative two for the principal congruence group, reducing the problem to estimates for sums involving Kloosterman sums and the Bessel function. It proves bounds for the sum S(A,N,l,nu) under coprimality conditions, including an e…
The paper develops an axiomatic theory of random normed spaces, linear spaces in which each vector is assigned a distribution function interpreted as the probability law of its norm. The proposed triangle operation includes the Menger and Wald approaches as special cases and leads to results on mini…
This paper develops asymptotic representations for solutions of a two-dimensional renewal-type equation arising in boundary-value problems for random walks with one lattice-valued component and a nonnegative second component. The authors formulate the problem through first-passage and overshoot prob…
The paper introduces mixed norm spaces for functions on bounded domains decomposed into groups of variables and studies singular integral potentials over finite dimensional domains or smooth manifolds. It proves boundedness estimates for potentials with kernel r to a negative power from appropriate …
The paper characterizes semigroups whose lattice of subsemigroups, including the empty subsemigroup, is Dedekind. Using structural lemmas on periodic semigroups, idempotent classes, and strong semilattices, it shows that such a semigroup decomposes as a strong semilattice of components each containi…
The paper studies periodic subgroups of linear algebraic groups over algebraically closed fields, with emphasis on conjugacy questions for Sylow subgroups and maximal periodic subgroups. Using structural results on maximal tori, normalizers, and solvable algebraic groups, it proves that Sylow p-subg…
This note studies Fourier series in the Haar system and contrasts their behavior with trigonometric Fourier series. It establishes sharp estimates for Haar Fourier coefficients of functions in Lp and of bounded variation, including summability consequences and examples showing optimality. The paper …
The paper studies the location of singularities of analytic functions on the boundary of polycylinders and applies this property to entire functions of several complex variables. It proves, by using plurisubharmonicity of the distance to the nearest singularity, that if a boundary point of a polycyl…
The paper studies first order linear elliptic systems with real constant coefficients in Euclidean spaces and the restrictions imposed by Petrovsky ellipticity on the number of equations. It proves an existence criterion in terms of the Hurwitz, Radon, Eckmann function, showing that such systems of …
The paper gives a solvability criterion for the Dirichlet problem for a class of quasilinear elliptic equations, avoiding the usual global monotonicity restriction on the zeroth order term. The argument uses a comparison lemma for associated parabolic equations, constructs sub- and supersolutions, a…
This paper studies the spectral zeta function associated with the Laplace-Beltrami operator on the group of n-dimensional unitary matrices, equipped with its standard invariant metric. Using the radial part of the Laplacian, the author derives an explicit fundamental solution of the heat equation in…
