RussiaRxiv · Open Access in English
Translated research papers from Russian journals and repositories
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Generated abstract This paper studies criteria for faithful matrix representations of solvable torsion-free groups over fields of characteristic zero, in relation to Mal’tsev’s theorem on solvable matrix groups. It introduces conditions using powered locally nilpotent groups, finite rank, and compatible inner automorp…
Generated abstract 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 …
Generated abstract The paper studies a binary additive problem for representations of an integer N as N = n1 + n2, where all prime divisors of n1 are small and all prime divisors of n2 are large, relative to powers of N. It defines the counting function L(N, N1/alpha, N1/beta) and proves an asymptotic estimate for all…
Generated abstract The paper addresses computation of optimal controls for discrete systems in cases where the direct discrete analogue of Pontryagin’s maximum principle may fail. It proposes replacing the original problem by auxiliary convexified problems whose solutions satisfy maximum conditions, then constructing …
Generated abstract 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…
Generated abstract 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-…
Generated abstract This paper studies regularity conditions for properties of bases of Delta Sigma operations obtained by uniting chains of an original base, over an index space of strongly inaccessible cardinality. It defines regular and semiregular bases, proves lemmas giving sufficient closure conditions, and estab…
Generated abstract This paper reports an experimental study of the enthalpy of the chemically reacting nitrogen tetroxide system involving dissociation to nitrogen dioxide, nitric oxide, and oxygen, with emphasis on conditions where available caloric data were insufficient for reliable thermodynamic descriptions. Enth…
Generated abstract This note studies optimization of cubature formulas for approximate integration of functions of many variables in weighted Hilbert spaces defined by Fourier transform weights. The full minimax problem is reduced to optimizing coefficients for fixed nodes, with special attention to lattice node syste…
Generated abstract The paper introduces multilevel dynamic games as a formal framework for complex hierarchical systems composed of relatively autonomous subsystems. It defines a finite tree of positions, local games at each position, probabilistic transitions between states across levels, and several important subcla…
Generated abstract This paper studies finite p-groups through enumeration of subgroups, normal subgroups, and epimorphic images, with emphasis on deriving existence results from congruences for subgroup counts. It proves divisibility and congruence theorems for subgroups of prescribed order, exponent, and structure, i…
Generated abstract The paper examines statistical-physics problems in strongly elongated Bose systems, questioning claims that elongation by itself lowers the onset temperature of Bose condensation, superfluidity, or superconductivity. For an ideal Bose gas, the authors analyze particle occupation, thermodynamic funct…
Generated abstract This paper studies decoding automata for memoryless encodings that can self-adjust after input substitution errors, certain state failures, and, in a generalized finite case, shifts of the input sequence. It introduces semibounded and \((l,m)\)-semibounded automata, characterizes them through comple…
Generated abstract Experiments are reported on heat propagation along a magnetic field in a cylindrical hydrogen or argon plasma column after localized rapid heating by a nonlinear oblique magnetosonic wave. Diamagnetic, magnetic, interferometric, and electric probe measurements show that the plasma pressure perturbat…
Generated abstract 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…
Generated abstract This paper investigates the early dynamics of optical breakdown in air produced by a train of ultrashort mode-locked neodymium laser pulses. The authors use an FER-2 image-converter photochronograph with a modified laser-triggered spark-gap sweep circuit, reducing the trigger delay to about 10 to 15…
Generated abstract Bochvar analyzes comprehension axioms in the formal system K0 through the introduced notion of a measure of a kernel. For a kernel of a comprehension axiom, the paper defines maximal included and minimal covering predicates, called internal and external measures, and formulates extensions of K0 in w…
Generated abstract This paper studies tensor invariants of subgroups of the Lorentz group that can be defined by invariance of a finite set of tensors. It states that any invariant tensor of arbitrary rank for such a subgroup can be expressed as a linear combination of tensors obtained from basic invariant tensors by …
Generated abstract This paper addresses a problem of Aleksandrov and Urysohn on the possible cardinalities of bicompact topological spaces satisfying the first axiom of countability. Using transfinite constructions, branching systems, and the notion of a free sequence, it proves a general cardinal estimate for Hausdor…
Generated abstract The paper studies infinite nonabelian groups satisfying the minimality condition for noninvariant abelian subgroups, with emphasis on locally soluble and periodic cases. It proves that any such group containing elements of infinite order is a JH-group, having an infinite abelian normal divisor of fi…
Generated abstract This study examines how cobalt affects the electron paramagnetic resonance signals of Cu2+, VO2+, Mn2+, and W5+ ions in borate, silicate, and phosphate oxide glasses at liquid nitrogen temperature. Measurements show that even small Co additions can strongly reduce the EPR intensity of these ions whe…
Generated abstract This note studies decomposability and maximal decomposability of Hausdorff spaces using dispersion character, pi-bases, characteristic spaces, and relaxations of topologies by ideals. It proves that spaces with sufficiently small pi-weight, and more generally dense-in-itself pi-spaces, are maximally…
Generated abstract This paper develops a perturbation theory for two-time retarded spin Green’s functions arising in the calculation of kernels for integro-differential equations describing the macroscopic magnetic moment of a paramagnet in an external magnetic field. Under high magnetic-temperature assumptions, fixed…
Generated abstract This note studies bifurcation of almost periodic solutions from an equilibrium in nonlinear differential systems with a small parameter, a setting where standard compactness and normal solvability assumptions for classical bifurcation theory fail. Using averaging, simple-solution methods, cone techn…
Generated abstract The paper studies bounded solvability, termed stability, for boundary value problems involving systems of linear partial difference equations with operator coefficients in a complex Banach space, without assuming commutativity of the coefficients. It derives necessary and sufficient spectral conditi…
Generated abstract The paper studies how to assign mathematical meaning to the infinite Feynman diagram series for the coefficient functions in the normal-product expansion of the scattering matrix for a real scalar field with quartic interaction. It derives two systems of relations for these functions in the Euclidea…
Generated abstract This note studies the choice of step parameter in descent methods for minimizing twice continuously differentiable strongly convex functions in finite-dimensional space, where exact line search would require solving a nonlinear equation. It proposes a simple backtracking rule, including bisection as…
Generated abstract This paper applies the principle of maximum stability of averaged turbulent flows to determine the turbulent friction law in the core region of channel flow. Using a generalized Prandtl-Taylor representation with a constant near-axis mixing length, the authors reduce the mean velocity profile to a p…
Generated abstract This paper extends Lyapunov’s principle of comparison of indices for stabilizing set-theoretic transformations to broader classes of operations on topological spaces of weight τ, including Z, T, Q, R, and ΔΣ operations with transfinite chain depth under suitable cardinal and base conditions. It prov…
Generated abstract This note derives asymptotic formulas for the plane and spherical albedo of a planet with an atmosphere of infinite optical thickness, allowing an arbitrary scattering indicatrix and assuming the single-scattering parameter is close to unity. Using relations between the atmospheric reflection coeffi…
Generated abstract This paper studies linear automatic-control systems with monotonically varying parameters whose time dependence can be represented by convergent infinite exponential series. Applying the Laplace transform and the shift theorem, the authors reduce the governing differential equation to a one-sided in…
Generated abstract This paper studies a one-dimensional nonlinear model of firehose instability in an anisotropic plasma with finite ion Larmor radius effects included in magnetohydrodynamic equations. For a circularly polarized monochromatic perturbation, the authors derive an analytic nonlinear solution in which the…
Generated abstract The paper addresses the ill-posed synthesis problem for a linear radiator with a prescribed radiation pattern, formulated as a regularized integral equation for the amplitude-phase current distribution. It proposes solving this equation by expanding the current in eigenfunctions of the kernel, ident…
Generated abstract This paper reports the development and testing of the EMV-100L electron microscope, designed to approach the theoretical resolving power set by objective spherical aberration and diffraction. The authors discuss the optical formulas for the theoretical limit, identify practical factors that degrade …
Generated abstract This paper studies proximally open, or equi-open, mappings of proximity spaces, with emphasis on metrizability and completeness of their images. Using quasiuniform covers and Leader’s metrization criterion, it proves that the equi-open image of a metrizable proximity space is metrizable, and derives…
Generated abstract This paper examines how hydrostatic compression affects the luminescence decay time of europium benzoylacetonate, focusing on the rare-earth ion transition from the excited state to the split ground multiplet. The authors argue that pressure can increase the probability of normally parity-forbidden …
Generated abstract This paper evaluates whether large lunar craters and round maria can be explained by meteoritic explosions using experimental scaling relations for large ejection explosions rather than simple extrapolations from terrestrial craters and smaller explosions. It calculates meteorite penetration depths …
Generated abstract The paper analyzes induced one-quantum transitions of a relativistic electron in a homogeneous constant magnetic field under interaction with a plane monochromatic electromagnetic wave. Using exact electron wave functions with spin projection fixed along the magnetic-field direction, it derives matr…
Generated abstract This paper studies upper semicontinuity and Hausdorff upper semicontinuity of the metric projection onto convex subsets of Banach spaces, relating these continuity properties to geometric conditions on the unit sphere and supporting hyperplanes. It introduces several conditions, including EPS, compa…
Generated abstract The paper studies the index of singular integro-functional operators on Hölder vector functions defined on a finite system of Lyapunov contours, where the functional shifts are generated by an orientation-preserving homeomorphism of finite cyclic order. It relates these operators to a broader class …
Generated abstract The paper studies resonant transfer of optical excitation in collisions of identical heavy one-electron atoms, with particular attention to the case where fine splitting of the excited P state is large. Using a semiclassical straight-line collision model and dipole-dipole interaction, it derives cou…
Generated abstract This paper studies when embeddings of simple arcs and closed contours in three-dimensional Euclidean space can be obtained from polyhedral models by pseudoisotopies of the ambient space. It proves that every locally unknotted simple arc admits a pseudoisotopy carrying a line segment onto it, with no…
Generated abstract This paper develops an infinitesimal and operational formulation of partial invariance for manifolds under local Lie groups of point transformations. For a regularly defined manifold, it proves that the defect of invariance equals the generic rank, on the manifold, of the matrix obtained by applying…
Generated abstract The paper extends magnetic-translation symmetry from the nonrelativistic charged particle to the Dirac equation for a relativistic charged particle in a uniform magnetic field. It shows that the corresponding unitary magnetic-translation operators commute with the Dirac Hamiltonian and, using the sq…
Generated abstract The paper develops a form of optimality conditions intended for large multidimensional optimal process problems, especially those with phase coordinate constraints and suitability for machine implementation. Using a generalized Lagrange method in Banach-type spaces, it derives necessary conditions f…
Generated abstract This note extends several notions from linear spectral theory to nonlinear operators in Hilbert and Banach spaces, focusing on regular values, spectra, and eigenfunctions. It proves localization results for the spectrum of continuous operators in Hilbert space, establishes openness of the set of reg…
Generated abstract This paper examines nonlinear instability of homogeneous magnetization precession in ferromagnetic resonance when both shape anisotropy and cubic crystallographic anisotropy are included, without restricting the precession angle to be small. Starting from the Landau-Lifshitz equation with damping an…
