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 first boundary-value problem for a degenerate nonlinear parabolic equation arising in one-dimensional nonstationary filtration, \(u_t=(\varphi(u))_{xx}\), with nonnegative initial and boundary data. A generalized solution is defined through an integral identity, and existence …
This paper studies the completeness in L2 of eigenfunctions and associated functions for Dirichlet problems generated by strongly elliptic systems of differential equations with matrix coefficients and a small skew term depending on a parameter. The argument reduces the differential problem to opera…
This note refines earlier results relating the variation of a set in Euclidean space to metric properties of its complement, using notions of variations of different orders and entropy or metric dimension of projections. It proves lemmas showing that, when a set of dimension parameter p approximates…
The paper develops a line-geometric analogue of triorthogonal systems of surfaces, building on Lie’s and Klein’s correspondence between line geometry and conformal geometry. Using a canonical moving tetrahedron and exterior differential equations, it studies complexes of lines that decompose into on…
This paper studies uniform convergence of Fourier expansions in eigenfunctions of the Helmholtz equation on arbitrary odd-dimensional domains, under homogeneous boundary conditions of the first, second, or third type and summation by increasing eigenvalues. It proves that convergence to the expanded…
This note studies the local analytic Goursat problem for a first order system of differential equations in two variables, with each unknown prescribed on a line, and also indicates the analogous formulation for analytic curves through the origin. The system is reduced to integral equations along cha…
This note extends Kuhn’s theorem on the equivalence of mixed and behavior strategies in games in generalized form to a broader class of recall structures. It introduces auxiliary notions describing relevant preceding information sets, proves two general results about possible positions and relevance…
This paper studies the asymptotic behavior of eigenvalues and eigenfunctions for a class of second order elliptic systems with matrix coefficients in a bounded domain with Lyapunov boundary, under Dirichlet boundary conditions and positivity assumptions. Using Carleman’s method together with Lopatin…
The paper studies the one-dimensional non-self-adjoint differential operator Ly equals minus y double prime plus p(x)y in L2 on the real line, where p has real and imaginary parts satisfying local boundedness and summability assumptions. It gives sufficient conditions for the resolvent to be complet…
This paper studies coefficient bounds for the subclass of normalized typically real functions in the unit disk that remain typically real under rotation by a factor of i, a class consisting of odd functions with real coefficients. Using an associated Carathéodory function with positive real part, de…
This note studies decompositions of infinitely divisible probability laws into independent components, focusing on laws with positive finite or countable Poisson spectrum and a Gaussian component. It characterizes, in the rational bounded-spectrum case, when such a law belongs to the class of laws w…
The paper establishes an a priori \(L_p\) estimate for generalized solutions of elliptic systems of order \(2m\) in a smooth bounded domain, subject to homogeneous boundary conditions up to order \(m-1\). The argument extends interior estimates to the boundary by proving a local constant coefficient…
This paper studies projective differential geometry of n-dimensional surfaces in projective N-space that possess p-dimensional plane generators along which the tangent plane remains constant, a class generalizing developable surfaces and related to bending problems. Using moving projective frames an…
This note studies regularity conditions for discrete-time probability processes on an abstract state space, formulated through sigma-fields generated by past, present, and future observations and through the associated Hilbert space of square-integrable functions. Using a projection lemma for decrea…
This paper derives asymptotic formulas for generalized Legendre functions and Gegenbauer functions for large degree and fixed order, with attention to ranges of the argument where existing expansions are less accurate, especially near zero. The method represents solutions of the generalized Legendre…
This paper studies a special three-dimensional nonlinear differential system of Aizerman type, reducible to equations involving a scalar nonlinearity satisfying generalized Hurwitz conditions. It develops qualitative results on trajectories, intersections with the plane x = 0, boundedness, limit set…
This note studies convergence of solutions of difference equations to solutions of corresponding differential equations in spaces of entire functions and in associated spaces of generalized functions. It develops an operator framework for constant shift-commuting operators, using characteristic func…
This note studies the distribution of completely critical cyclic fields of degree l^h, where l is a prime and h is positive, ordered by the size of their discriminants. Using group theoretic considerations, the Kronecker-Weber theorem, and properties of Dirichlet L-functions, it first describes the …
The paper formulates a generalized geometric extremal problem for determining the extreme intersection point of an axis with a convex polyhedron represented as a Minkowski sum of convex hulls of finite point sets. It argues that this formulation preserves the structure of applied problems better tha…
This note gives a description of the irreducible unitary representations appearing in the decomposition of the regular representation of the group of unimodular third order complex matrices preserving a Hermitian form of signature two, one. It realizes representations through operators on functions …
The paper studies best uniform approximation on the real axis of almost-periodic functions by entire functions of finite exponential degree. For functions whose Fourier exponents are lacunary with ratios bounded below by a number greater than one, it proves that the remainder after truncating the Fo…
The paper studies eigenfunction expansions arising from boundary value problems for the hyperbolic equation with variable coefficient \(\psi_{\sigma\sigma}-K(\sigma)\psi_{\theta\theta}=0\), reduced by a change of variables to a Klein-Gordon type equation on a finite interval with separated boundary …
The paper studies best uniform approximation of continuous Hilbert space valued functions by families of linear operator values \(A(q)x\), motivated by approximate solutions of systems of differential equations with boundary conditions. It extends earlier results from bounded operator functions to c…
This paper extends Pólya’s theorem to entire functions of exponential type defined on isotropic vectors in three complex variables and associated with harmonic functions in three-dimensional space. Using integral inversion formulas relating the entire function to its corresponding harmonic function,…
This paper proves a completeness theorem for the eigen and associated elements of a completely continuous operator in a Hilbert space, written as T = A + iB with self-adjoint semidefinite real and imaginary parts. Assuming that B has finite trace, the argument shows that the root elements correspond…
This note studies a finite-difference analogue of a linear incompressible system involving velocity, pressure, and a bounded matrix operator, with Cauchy and mixed boundary conditions. It develops discrete gradient, curl, and divergence operators on staggered lattice subsets and proves finite-differ…
The paper studies local and global properties of completely continuous vector fields on real Banach spaces, using local degree, regular points, regular differentiability, openness, and local topological behavior. It establishes criteria under which regular points imply openness, describes local prei…
The paper develops a general framework for classes of generalized functions, starting from the Mikusinski and Korevaar approach and parameterizing the construction by a class of growth estimates. It defines fundamental sequences, equivalence classes, differentiation, strong and weak convergence, and…
The paper studies operator functions on a Hilbert space equipped with an indefinite metric defined by a fundamental symmetry, focusing on two-sided J-nonexpansive operators and their analytic dependence in the unit disk. Using transformations that relate such operators to contractions, together with…
This paper studies the arithmetic complexity of solving the finite difference approximation to the Poisson equation on a square with Dirichlet boundary conditions. Assuming precomputed discrete Green functions for dyadic subsquares, it constructs a multilevel decomposition of the right hand side and…
This note studies the Cauchy problem for a second-order parabolic equation in which a small positive parameter multiplies the highest derivative, with initial data that may have a jump discontinuity at the origin. As the parameter tends to zero, the limiting first-order equation loses smoothness alo…
This note studies upper bounds for the sum of two Nevanlinna defects of a meromorphic function in the finite plane whose order is less than one. Reducing the question to the defects at zero and infinity, it estimates the characteristic function through canonical products and proves an auxiliary inte…
The paper studies the existence of absolute minimizers for two-dimensional parametric variational problems on differentiable manifolds, extending earlier results for Euclidean space and for the Plateau problem in Riemannian manifolds. It defines admissible surfaces of Tonelli type and considers posi…
The paper introduces a generalized notion of concavity for positive monotone operators acting on cones in a real Banach space, using two nested cones and a distinguished positive element. It proves, by topological methods, that completely continuous operators in this class have a continuous branch o…
This note studies uniqueness for a mixed initial boundary value problem for certain systems of linear partial differential equations on a half line, where the spatial operator is a polynomial in an nth derivative and the boundary conditions prescribe selected derivative traces at the origin. Extendi…
This note studies the first boundary value problem for a general fourth order elliptic equation in two variables whose principal part degenerates on a portion of the boundary lying on the x-axis. It formulates weighted function spaces and boundary conditions appropriate to different rates of degener…
This paper studies polynomials orthogonal on the boundary of a bounded plane domain with a differentiable positive weight, relating their behavior to the smoothness of the contour and the differential properties of the weight. Using conformal mapping of the exterior domain, Szego-type factorization,…
The paper studies geometric properties of differentiable solutions to nonlinear first-order systems of partial differential equations under a strong ellipticity condition formulated in terms of the local affine geometry of the associated mapping. Using methods from quasiconformal mapping theory and …
This note studies upper bounds for the number of limit cycles of the differential equation dy/dx = P(x,y)/Q(x,y), where P and Q are real polynomials of degree n. The authors reduce the problem to counting nontrivial, nonhomologous cycles on integral curves of the corresponding complex projective equ…
This paper applies F. Riesz’s representation theorem to functional equations defined by linear operators on Hilbert and Banach function spaces. It argues that when the equation has a unique solution and the value of the solution at a point is bounded by the norm of the data, this point value can be …
The paper studies non-self-adjoint mixed problems for first-order hyperbolic systems in the plane with boundary conditions containing time derivatives at both endpoints. Using separation of variables and asymptotic analysis of the associated parameter-dependent boundary problem, it defines regular b…
This letter clarifies the relation between the author’s earlier note on differential equations with pure mixed derivatives and prior work by Bianchi and Nicoletti. It acknowledges that several results in the note, including existence and uniqueness for characteristic boundary data and the Cauchy pro…
This paper studies the first boundary value problem with zero boundary data for a class of quasilinear elliptic equations in a bounded domain of arbitrary dimension. Under ellipticity, boundedness, differentiability, and monotonicity assumptions on the coefficients, it proves existence of solutions …
This paper develops estimates for eigenvalues of self-adjoint operators with discrete spectrum in a Hilbert space, using moments generated by a chosen vector and its iterates under the operator. A lemma on weighted norms of functions of the spectrum is applied to polynomials to obtain computable int…
This paper develops a statistical kinetic description of steps on a growing crystal surface, motivated by the coagulation of layers of different heights during crystal growth from vapor, solution, or melt. For a one-dimensional echelon of parallel steps with random heights, it formulates a nonlinear…
This paper studies self-adjoint systems of higher order differential equations with symmetric matrix coefficients and develops Sturm-type results for their conjugate points. It proves separation of distinct systems of conjugate points, comparison theorems under ordering of the coefficients, and spec…
The paper develops a continuous analogue of Christoffel’s formula for orthogonal polynomials in the setting of one-dimensional Sturm-Liouville systems. It defines transformations of the potential and eigenfunctions by Wronskian-type determinants associated with a polynomial nonnegative on the spectr…
This paper develops an operational calculus for functions defined on the whole real line under local integrability and two-sided Laplace convergence assumptions. It constructs a quotient space from pairs of right and left Laplace transforms and proves that this space is linearly isomorphic to the or…
The paper studies uniform approximation of classes of continuous periodic functions, defined by Weyl derivatives and moduli of smoothness, by partial Fourier sums and Fejér sums. It formulates two related problems: determining principal terms of approximation errors uniformly over a function class, …
The paper studies the uniform asymptotic behavior of the maximal deviation between functions in Hölder classes on a finite interval and truncated arithmetic means of their Chebyshev series partial sums. Extending earlier results for ordinary partial sums, it analyzes the quantity obtained by taking …
