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 unique determination of a piecewise regular ovaloid of positive Gaussian curvature with boundary, allowing discontinuities of second derivatives along an internal gluing curve. The authors formulate boundary conditions on the increments of normal curvature and geodesic torsion…
The paper studies orderability for reduced free distributive multioperator groups and related algebraic structures. It gives an orderability criterion for distributive operator groups in terms of signs on finite sets of nonzero elements and semigroups generated by values of absolutely free operator …
This note gives an axiomatic characterization of the entropy of an ergodic automorphism of a Lebesgue space with invariant measure. After recalling conditional entropy, factor automorphisms, Sinai’s theorem, and Pinsker’s lemma, it introduces principal factor automorphisms and proves that such facto…
This paper studies deficiencies of meromorphic functions in Nevanlinna theory when the lower order is less than one, extending earlier results formulated in terms of the order. It gives necessary and sufficient inequalities for the possible deficiencies of two distinct values of a meromorphic functi…
This note examines absolute convergence for power series in two variables and shows that the direct analogue of Abel’s theorem for one variable is false. A counterexample is constructed in which a two-variable power series converges on selected straight lines but has no interior points of convergenc…
The paper treats a convex programming problem with a linear objective and smooth convex inequality constraints, motivated by the reduction of constrained convex Chebyshev approximation to this form. It presents two feasible direction algorithms in which each iteration determines a descent direction …
The paper studies error estimates for approximate eigenvalues and eigenvectors of an analytic compact operator pencil in a Hilbert space, with particular attention to approximations obtained by the generalized Galerkin method. It reformulates the eigenvalue problem by projecting along an approximate…
This paper studies absolutes of Hausdorff spaces and related extremally disconnected spaces mapping irreducibly onto a given space. It gives a new construction of the absolute using auxiliary extensions and introduces a companion space that maps continuously, irreducibly, bicompactly, and canonicall…
The paper studies groups in which every partial order extends to a linear order, focusing on order-independent subgroup conditions that preserve this property under quotients. It proves that for an order-extendable group, a quotient by a subgroup is order-extendable exactly when the subgroup is inva…
This paper addresses H. Neumann’s question whether the semigroup of nontrivial proper varieties of groups, with multiplication defined by extensions, is free. Using discrete and complete wreath products, the author proves embedding and identity transfer lemmas for group extensions, establishes left …
This note studies ergodic phenomena in which “time” is represented by a noncommutative discrete group, motivated by solutions of linear ordinary differential equations in the complex domain. It proves that, for two rotations of the sphere, density of the semigroup orbit implies uniform distribution,…
This paper studies nonlinear transport equations arising in nuclear reactor theory, including reactor design with prescribed spatial heat release and flux dependent material temperatures. The authors formulate the neutron flux problem as a nonlinear eigenvalue equation for a positive integral operat…
This paper studies error estimates for numerical integration of periodic multivariate functions whose absolutely convergent Fourier coefficients satisfy prescribed decay conditions. Using methods related to Korobov’s lattice constructions, it proves auxiliary counting and congruence lemmas that allo…
The paper studies stationary resonant regimes in a class of weakly perturbed nonlinear oscillatory or rotational systems with slowly varying parameters. After transforming the equations near a resonance condition between the natural and forcing frequencies, the authors develop a specialized averagin…
This note studies the homogeneous oblique derivative problem for harmonic functions in bounded three-dimensional domains when the prescribed boundary vector field is tangent to the boundary on a nonempty set, a case not covered by the standard theory. Using the maximum principle and Zaremba’s bounda…
This note studies singular non-self-adjoint differential operators of even order on the half-line with complex locally summable coefficients and general boundary conditions at the origin. Using asymptotic representations of fundamental solutions of the equation l(y) = lambda y, it characterizes squa…
This paper gives an inversion and Plancherel formula for the group of second order unimodular matrices over a nondiscrete locally compact field, focusing on the case of a totally disconnected field with residue characteristic not equal to 2. Using the previously described irreducible unitary represe…
This note establishes a priori estimates in Sobolev norms \(L_p\), for \(p>1\), for solutions of elliptic equations with discontinuous complex coefficients across an interface, subject to general boundary and conjugation conditions. The argument reduces the problem to local estimates near the surfac…
This note studies the decidability of systems of equations with one unknown in free groups. Building on Lyndon’s work on single equations, it shows that any solution of such a system must occur among values of finitely many parametric group elements of the form \(A S^m B T^n C\), with bounded word l…
The paper studies trace type formulas for pairs of singular Sturm-Liouville operators on the half-line whose spectra are discrete and which differ in the boundary condition at the origin, and later also by a finite perturbation of the potential. Using finite interval approximations, interlacing of e…
This paper studies irreducible unitary representations of the group SL(2,K), where K is an arbitrary locally compact nondiscrete field. It constructs the principal continuous series from multiplicative characters of K, realizes these representations through Fourier transforms and generalized kernels…
The paper introduces and studies vector ordered analogues of Hausdorff eta sets, called eta lineals, under set theoretic hypotheses including the generalized continuum hypothesis and, in applications, the continuum hypothesis. It proves isomorphism theorems for eta lineals of prescribed cardinality,…
The paper studies exact best uniform trigonometric approximations and Kolmogorov widths for periodic function classes whose derivatives have a prescribed modulus of continuity. Extending earlier results for zeroth and first derivatives, it develops estimates by comparison with Lipschitz-type classes…
This note studies boundary limit behavior of pseudoanalytic functions in the unit disk, focusing on the set of cluster values at a boundary point after excluding values forced by prescribed approach curves ending at nearby boundary points outside a closed exceptional set. Under the assumption that t…
This note studies general elliptic boundary value problems for systems in a bounded domain whose differential and boundary operators depend polynomially on a complex parameter lying in an angle. It formulates algebraic semi-boundedness conditions, extending the ellipticity and Lopatinskii conditions…
The note addresses a problem of Hua Loo-keng concerning whether a two-dimensional affine lattice point set can contain infinitely many pairs of prime coordinates. For the case in which the determinant of the two linear forms in the variables is nonzero, the author introduces a weighted prime-countin…
The paper studies stability of systems of Volterra integral equations by reducing nonlinear or complex systems to majorant linear systems with nonnegative kernels and applying integral inequalities and generalized norming. It gives necessary and sufficient stability criteria for linear Volterra syst…
The paper studies the equivalence between rectifiability of webs and nomographic representability of functions of several variables by nomograms of aligned points. It formulates a web through an equation z equals phi of n variables and gives necessary and sufficient conditions for rectifiability in …
This paper extends the notion of Rozet nets from three-dimensional projective space to generalized conjugate nets in projective N-space and studies the Laplace sequences generated by them. Using a moving projective frame, Pfaffian systems, exterior differentiation, and prolongation, it derives the c…
This paper studies infinite antagonistic games on the unit square with payoff kernels that may be unbounded, addressing conditions under which the upper and lower values over distribution strategies coincide. It introduces quasi-invariance of a kernel with respect to families of transformations of t…
Rashevskii introduces the associative superenvelope of a complex Lie algebra as a completion of its universal associative envelope with respect to a countable system of norms on symmetrized formal series. The paper establishes multiplication estimates ensuring that this completion is a countably nor…
The paper studies nonlinear differential and functional equations using variational methods in Banach spaces, focusing on convex functionals, potential monotone operators, and associated minimization principles. It proves that an increasing potential operator yields uniqueness of solutions to P(u) =…
The paper studies convergence criteria for sequences of linear operators that map continuous functions on [-1,1] to algebraic polynomials of bounded degree, focusing on alternatives to the usual uniform boundedness of operator norms. Using the correspondence with even periodic functions and a Faber,…
The paper studies decompositions of infinitely divisible probability laws in Linnik’s class with an unbounded Poisson spectrum, focusing on whether a weakened decay condition on the spectral coefficients ensures that all components are infinitely divisible. It proves that if such a law satisfies sup…
This note develops a general framework connecting representations of automorphism groups of universal algebras with Ω-semigroups, Ω-rings, and their representations. It defines Ω-semigroups via left distributivity over a system of operations, studies distributive and strictly distributive elements, …
This paper studies the interpretation of formulas of Heyting propositional calculus as finite Kolmogorov-type problems and compares the resulting notion of general validity with Kleene and Rosser realizability. It proves that, for formulas omitting disjunction or implication, general validity implie…
This paper studies the restriction to the real Lorentz group of unitary irreducible representations in the principal series of the proper Lorentz group, formulated via the locally isomorphic group of complex unimodular two by two matrices. Using the Plancherel formula for the real subgroup, it const…
The paper introduces two classes of regular functions of two complex variables, defined by requiring their one variable restrictions on analytic plane sections to generate starlike univalent or convex univalent mappings. For functions regular in a bounded complete bicircular domain and normalized by…
This paper studies the index of systems of multidimensional singular integral equations on a smooth manifold bounding a ball, under the standard ellipticity condition that the determinant of the associated symbol is nonzero on the tangent unit bundle. It defines a topological integer associated with…
This paper develops an invariant differential geometry for an m-dimensional manifold whose elements are nondegenerate even-order algebraic hypersurfaces contained in hyperplanes of projective space. Using the moving-frame method, it derives the differential equations of the manifold, identifies an i…
This paper generalizes the Vietoris-Begle theorem for closed mappings of paracompact Hausdorff spaces by allowing non-acyclic point preimages, provided the exceptional sets have sufficiently small relative dimension. Using sheaf cohomology and Leray spectral sequences, it gives conditions under whic…
This paper studies decompositions of Lie algebras \(G = G' + G''\) in which the algebras involved are semisimple, relating them to locally transitive actions of Lie groups on homogeneous spaces. It proves that for reductive complex groups, and analogously for connected real semisimple groups, local …
This note studies dimension-theoretic characterizations of spaces by essential and zero-dimensional type mappings into cubes. Building on the theorems of Aleksandrov and Hurewicz, it proves that every compactum of dimension k admits a single mapping into the k-dimensional cube that is both essential…
This paper studies the absolute of a topological space, extending earlier constructions from paracompact spaces to arbitrary Hausdorff spaces through inverse spectra formed from finite decompositions. It defines the absolute as the set of marked points in the limit of a spectrum of finite discrete s…
This paper studies the first boundary value problem for a general second order nonlinear parabolic equation in a bounded cylindrical domain. Under Hölder smoothness, parabolicity, boundary regularity, and compatibility assumptions, but without imposing growth conditions on the nonlinear function in …
This paper develops a universal coefficient theorem for spectral cohomology groups of differential abelian groups. It defines spectral cohomology as an inverse limit over finitely generated differential subgroups, proves that this functor commutes with direct limits of differential groups, and relat…
The paper introduces the spaces M0(alpha), defined as a closed subspace of Lorentz type spaces M(alpha) by a vanishing small measure condition, and studies their relation to the spaces Lambda(alpha). It proves that M0(alpha) is the closure of bounded functions in M(alpha), that its dual is isometric…
The paper studies uniqueness and existence for the Cauchy problem for second order parabolic equations in several spatial variables, including equations that degenerate or have coefficients growing at infinity. It introduces function classes defined by integral growth conditions involving the ellipt…
This paper studies best approximation of periodic functions of several variables in the spaces Lp by trigonometric polynomials, comparing complete approximation in all variables with partial approximation in selected variables. It introduces a restricted form of partial best approximation whose coef…
