This paper studies values of L(1, χD) for real Dirichlet characters when the modulus D is restricted to sparse arithmetic progressions and related sets. Using estimates for double sums with quadratic Dirichlet characters, it derives a main lemma reducing asymptotics for moments of modified L-values …
MATHEMATICS
This paper studies observability for a class of nonlinear differential equations in a Hilbert space with a Lipschitz nonlinear term and a possibly noninvertible observation operator. It introduces exact, finite time approximate, and asymptotic approximate observability, then constructs an auxiliary …
Unknown
This paper studies the large-time behavior of the energy of solutions to a mixed initial-boundary value problem for the wave equation in an unbounded exterior-type domain in Euclidean space. Using scattering eigenfunctions for the corresponding exterior domain, the solution and its energy are repres…
PHYSICS
This paper proposes and tests a spectroscopic method for measuring nonequilibrium electric fields in turbulent plasma using Stark broadening and splitting of hydrogen spectral lines. The authors apply high-speed electro-optical spectrochronography to collisionless magnetosonic shock waves in a theta…
MATHEMATICS
This note extends earlier results on R and Rc operations from countable to uncountable systems of sets, using branching tables of strongly inaccessible cardinal rank and two branching hypotheses related to rank attainment and large disjunctive subsets. It formulates equivalent forms of these hypothe…
MATHEMATICS
This note studies when a sequence of approximate extremal minimization problems converges to a given original problem, both in the value of the functional and in the construction of minimizing elements. It formulates necessary and sufficient conditions using comparison mappings between the approxima…
Unknown
This paper analyzes the radial stability of an infinite cylindrical incompressible conductor placed eccentrically inside a cylindrical surface carrying an azimuthal traveling-wave current. Using the quasi-stationary approximation, the Leontovich boundary condition, and Bessel-function expansions, it…
HYDROMECHANICS
This paper studies the unsteady magnetohydrodynamic flow of a supersonic electrically conducting ideal gas in a plane dielectric channel as it enters or exits a nonuniform transverse magnetic field. The authors formulate the coupled gas-dynamic and electrodynamic problem for finite magnetohydrodynam…
Academician of the Academy of Sciences of the Moldavian SSR A. V. ABLOV
The study determines the crystal structure of the anhydrous plate form of copper DL-alpha-alaninate, a compound unsuitable for conventional X-ray analysis because it forms very thin, brittle plates. Electron diffraction patterns from textured polycrystalline specimens and spot patterns were indexed …
MATHEMATICS
This paper studies harmonic vector functions in the upper half-space satisfying generalized Cauchy-Riemann conditions, with emphasis on multidimensional analogues of classical results on conjugate harmonic functions. It defines Hardy-type classes H^p and S^p, gives a Fourier-transform characterizati…
MATHEMATICS
This paper studies a Cauchy problem for second order hyperbolic equations containing a small positive parameter, with initial data that produce an initial jump in the singular limit. It constructs a matched asymptotic expansion in powers of the parameter, combining regular terms satisfying reduced f…
GEOPHYSICS
Unknown
This paper studies how the geometry of weak discontinuities affects absolute and quasi-absolute convergence of multidimensional Fourier series and eigenfunction expansions of elliptic operators. For functions on the two-dimensional torus weakly discontinuous along a smooth curve, it introduces quasi…
MATHEMATICS
This paper studies stability of the residual method for ill-posed linear operator equations of the first kind in Banach spaces, where only a convex closed neighborhood filter of the exact right-hand side is given. The method selects the minimum-norm element among points whose image lies in the presc…
MATHEMATICS
The paper studies normalized equilibrium points in concave n-person games and develops iterative methods generalizing the conditional-gradient approach for computing them under convexity and regularity assumptions. It proves convergence results for three step-size rules, including subsequential conv…
Unknown
The paper studies absolute continuity of measures generated by solutions of differential equations with random Gaussian forcing in finite-dimensional Euclidean space. It compares a linear equation with a corresponding nonlinear equation containing an additional drift term, formulates conditions invo…
Unknown
This paper gives criteria for estimating the rotation, or topological degree, of finite-dimensional vector fields that do not vanish on the boundary of a bounded domain. It proves nonnegativity results for fields in even-dimensional real spaces whose derivatives commute with matrices having no real …
MATHEMATICS
This paper studies uniform best rational approximation of convex functions and functions of bounded variation on finite intervals, comparing the decay of rational approximation errors with polynomial approximation. It proves upper bounds for continuous convex functions, including an order n inverse …
MATHEMATICS
The paper studies solvability of quasielliptic nonstationary differential equations and Sobolev type problems in cylinders infinite in the time direction, including settings motivated by equations such as Laplace and heat conduction without initial conditions. It introduces weighted Sobolev spaces w…
MATHEMATICS
This paper studies first boundary-value problems with weighted boundary conditions for higher-order degenerate elliptic equations in bounded domains whose boundary includes a flat degeneracy portion. It introduces weighted Sobolev-type spaces defined by iterated differential operators with measurabl…
MATHEMATICAL PHYSICS
The paper presents a double reduction method for solving infinite systems of linear equations that arise when expanding unknown functions with edge or corner singularities in boundary value problems of mathematical physics. Instead of truncating all higher expansion coefficients to zero, the method …
PHYSICS
This study examines the high pressure polymorphic transformation of silver chloride and the crystal structure of the AgCl II phase, addressing discrepancies between earlier volumetric and X-ray interpretations. X-ray diffraction patterns were obtained for AgCl over 40 to 115 kbar, and for AgCl mixed…
PHYSICS
This paper examines how phase transitions in cyclopentane are manifested in low-temperature infrared absorption spectra, focusing on the temperature dependence of the 546 cm⁻¹ band width from 300 to 80 K. Measurements show changes in slope or discontinuous jumps at crystallization and at the crystal…
Unknown
This note analyzes features of the interband Faraday effect in heavily doped semiconductors near the absorption edge, focusing on how electron degeneracy and randomly distributed impurity potentials modify ellipticity and rotation. Using a simple band model with Landau-level summation and a classica…
MATHEMATICS
The paper studies the first boundary value problem for a second order elliptic equation in a planar domain where the equation degenerates parabolically on part of the boundary. Using Sobolev space formulations, adjoint integral identities, and a priori estimates under sign and boundary coefficient c…
PHYSICS
This paper examines theoretical properties of solid-state lasers with very long resonators, motivated by the increased coupling of longitudinal modes, changes in spectral behavior, and possible approach to nonresonant feedback when resonator mode bands overlap. It proposes using an optical delay lin…
MATHEMATICS
This note studies the rate of uniform approximation of continuous periodic functions by partial sums of their Fourier series, using best trigonometric approximation and quantities measuring the tails of Fourier coefficients or remainders in related \(L_q\) metrics. It proves an estimate for \(\|f-S_…
Unknown
This paper experimentally examines the spatial intensity distribution of stimulated radiation from a ruby traveling-medium laser with a small circular diaphragm placed inside a plane-parallel resonator. Near-field patterns at the resonator mirror and far-field patterns in the focal plane were record…
HYDROMECHANICS
This paper applies the principle of maximum stability to determine the mean velocity profile in the viscous sublayer and buffer region of turbulent channel flow. Using a generalized Van Driest mixing-length formula with adjustable parameters, the authors analyze local hydrodynamic stability of short…
CRYSTALLOGRAPHY
This paper examines apatite-like phases formed in the MeO, Nd2O3, SiO2 systems, where Me is Mg, Ca, or Ba, through heterovalent substitution of Nd3+ by divalent cations. Samples with nominal compositions of the type Me x Nd5-x(SiO4)3Oy were synthesized by prolonged firing at 1450 degrees C and analy…
MATHEMATICS
The paper constructs compact Hausdorff spaces, bicompacta, whose covering dimension and small and large inductive dimensions do not coincide. Using lexicographically ordered zero-dimensional compacta, decompositions and gluings over marked subsets of the square and the Sierpiński carpet, it gives ex…
Unknown
The paper studies singular integral operators in weighted Hölder spaces on smooth contours, with weights having prescribed power singularities at finitely many boundary points. It establishes compactness of commutators with Hölder coefficients and gives necessary and sufficient Fredholm type conditi…
GEOPHYSICS
This paper investigates long-period zero drift in seismometers as a possible manifestation of a nonlocal geophysical phenomenon. Using continuous records from a thermocompensated SVKD seismometer, spectral comparison, smoothing, and correlation analysis, the study finds stable drift spectra, weak as…
MATHEMATICS
This paper studies the asymptotic behavior of cubature error functionals in Sobolev type spaces \(L_2^{(m)}(\Omega)\), extending earlier results for the whole Euclidean space \(L_2^{(m)}(E_n)\). Using Hilbert space decompositions, extension operators, and bounded inverse arguments, it proves that a …
THEORY OF ELASTICITY
This paper studies self-similar dynamic plane-strain elasticity problems for an infinite isotropic body containing a rectilinear crack that begins at a point source and expands at constant subsonic velocity. Using displacement potentials and the Smirnov-Sobolev transformation, the boundary condition…
S. A. LOSEV, O. P. SHATALOV, M. S. YALOVIK
This paper examines how molecular anharmonicity affects the apparent vibrational relaxation time during excitation behind shock waves and during deactivation. Using shock tube ultraviolet absorption measurements for a 10 percent oxygen and 90 percent argon mixture and for nitrogen, the authors show …
Unknown
This paper derives sufficient conditions for using Euler’s static method to study the stability of deformation of isotropic nonlinearly elastic bodies under finite subcritical deformations. Starting from the linearized equations and boundary conditions in Lagrangian coordinates for a body with an ar…
MATHEMATICS
The paper studies how extreme order statistics contribute to large deviations of sums of independent identically distributed random variables with mean zero and finite variance. It derives conditional limiting distributions for the maximum, second maximum, and in some cases the minimum, under condit…
MATHEMATICS
This paper extends classical potential theory from Lyapunov surfaces to domains whose boundaries belong to the Lyapunov-Dini class, characterized by controlled variation of the surface normal. Using previously established uniqueness for the homogeneous Neumann problem and local geometric estimates f…
Unknown
A method is developed for solving Dirichlet and Neumann boundary-value problems for open surfaces, motivated by applications in diffraction, electrostatics, and analytic function theory. For the inhomogeneous Helmholtz equation, the construction introduces auxiliary closed surfaces and uses Green’s …
R. A. VOLKOV, V. I. SKOBELKIN
The paper analyzes propagation of the boundary between superconducting and normal phases in type-II superconducting thin films, where the film thickness is small compared with the magnetic-field penetration depth. Starting from the Maxwell-London equations, the authors introduce current functions fo…
A. A. BOVDI, S. V. MIKHOVSKII
This paper studies idempotents in crossed products of groups and associative rings, focusing on the subgroup generated by the group elements occurring in the finite support of an idempotent. It proves that the support subgroup of any central idempotent in an arbitrary crossed product is a finite nor…
PHYSICS
This paper develops a theoretical description of gamma-magnetic resonance in a single-domain ferromagnetic absorber, extending earlier treatment of multidomain specimens where domain-wall nuclei dominated the effect. Using perturbation theory for a two-quantum process involving Mössbauer gamma absor…
MATHEMATICS
This paper studies criteria for the existence of nilpotent and supersolvable subgroups of prescribed order in finite groups, using invariant series, index series, and arithmetic conditions on sequences of indices. Extending earlier results on groups whose Sylow subgroups are invariant, it introduces…
GEOPHYSICS
This paper develops a similarity and dimensional analysis theory for estimating large-scale atmospheric circulation on terrestrial planets without requiring detailed numerical modeling or prescribed temperature contrasts. Treating the atmosphere as gray and using solar energy input, heat capacity, p…
GEOPHYSICS
This paper examines how shear stresses affect the acoustic parameters of longitudinal and transverse elastic waves in rock samples, a topic for which little experimental evidence was available compared with compression studies. Cylindrical samples of granite, sandstone, and marble were subjected to …
CRYSTALLOGRAPHY
This paper proposes a small-angle X-ray scattering method for estimating distances between heavy atoms introduced into macromolecules in solution. The authors derive the scattering contributions from the macromolecule, the heavy atoms, and their interference, arguing that the heavy-atom term can pro…
Unknown
The paper introduces the polyhedron defined by positive quadratic forms with fixed arithmetic minimum and develops its basic properties in the coefficient space of quadratic forms. It shows that this polyhedron is locally finite, invariant under integral unimodular transformations, has vertices corr…
MATHEMATICS
The paper introduces the notion of a variational structure, a partially ordered Hilbert space in which every finite set has a unique upper bound minimizing a natural quadratic functional over all its upper bounds. It develops basic properties of these variational upper and lower bounds, showing that…
HYDROMECHANICS
This paper studies the one-dimensional reflection of a rarefaction wave from a rigid wall in the products of an instantaneous explosion in a constant gravitational field, for a gas obeying a polytropic equation of state. Starting from the general solution of the gas-dynamic equations for discrete ad…