Recent Papers

HOMOGENEOUS DIFFERENCE SCHEMES

THE CRYSTAL STRUCTURE OF NITROBIS(ETHYLENEDIAMINE)NICKEL CHLORIDE \([\mathrm{Nien}_2\mathrm{NO}_2]\mathrm{Cl}\)

The paper reports an X-ray crystallographic determination of nitrobis(ethylenediamine)nickel chloride, synthesized as violet orthorhombic crystals with space group Fdd2 and eight formula units per unit cell. Using measured Mo K-alpha diffraction intensities and the material-point method, the authors…

Manifestation of Kirchhoff's Law in Gamma Spectroscopy

This paper examines how Kirchhoff’s law is manifested in gamma spectroscopy, where nuclear absorption and fluorescence lines are displaced from one another by photon recoil rather than coinciding as in the optical region. It compares the frequency contours required by Kirchhoff’s relation with line …

ON FIELDS ASSOCIATED WITH ENVELOPING ALGEBRAS OF LIE ALGEBRAS

This note studies skew fields of fractions associated with universal enveloping algebras of Lie algebras over a field of characteristic zero, motivated by noncommutative rings arising in analysis. It introduces a dimension invariant for arbitrary fields over a base field, proves that filtered algebr…

ESTIMATES OF GENERALIZED CHARACTERISTIC NUMBERS OF DIFFERENTIAL SYSTEMS

ON SOME CLASSES OF FUNCTIONS ANALYTIC IN MULTIPLE HARTOGS DOMAINS

This paper studies spaces of analytic functions in complete multiple Hartogs domains, with emphasis on domains whose projections may be unbounded. Using Hartogs series expansions, it establishes coefficient estimates, convergence criteria, and uniform convergence consequences for bounded analytic fu…

ON THE CUMULATIVE COLLAPSE OF CAVITATION (VAPOR) CAVERNS

This paper examines the collapse of cavitation vapor cavities and proposes that concave portions of their surfaces can act like cumulative recesses in shaped charges, producing high-velocity liquid jets. Using high-speed motion-picture observations and a hydrodynamic model of converging jets, the au…

On the Diameter of a Strongly Connected Graph

This paper studies lower bounds for the diameter of finite strongly connected directed graphs in terms of the number of vertices and the cyclomatic number. Building on a known radius inequality, it proves that for any such graph with cyclomatic number at least two, the product of the diameter and th…

Toward an Investigation of the Carbon Coma of Comet 1959 k

This paper revises a model for the surface brightness distribution of the carbon coma of comet 1959 k, focusing on the motion and photodissociation of C2 molecules under solar radiation pressure. It argues that the previously assumed initial molecular velocity is too low to reproduce the observed ne…

SOME CRITERIA FOR THE COMPLETENESS OF A SYSTEM OF ROOT VECTORS OF A LINEAR OPERATOR IN A SPACE WITH TWO NORMS

This note establishes criteria for completeness of systems of root vectors of completely continuous linear operators in a Banach space equipped with an additional weaker Hilbert norm. It extends Hilbert space completeness results to spaces with two norms, proving completeness theorems for perturbed …

SET-THEORETIC OPERATIONS

The paper develops a general framework for recursive hierarchies of length up to the least nonconstructive ordinal in an arbitrary space, using set-theoretic operations, bases, and effectively controlled numberings. It introduces standard operators on enumerated families of sets, defines recursive h…

GENERALIZATION OF THE LEIBNIZ–HÖRMANDER FORMULA

ON CERTAIN IMPROPERLY POSED PROBLEMS IN POTENTIAL THEORY

PRODUCTION OF A NEUTRINO PAIR DURING THE MOTION OF AN ELECTRON IN A MAGNETIC FIELD

This paper analyzes the production of neutrino, antineutrino pairs by an electron moving in an external magnetic field, treating the process within the universal V-A theory of weak interactions. Using electron wave functions in a magnetic field and quasiclassical asymptotics for high Landau levels, …

Correction to the article: General boundary value problem for second-order elliptic systems with constant coefficients (Vol. 2, No. 1)

ON THE POLES AND THE RADIUS OF CIRCULAR UNIVALENCE OF THE MEROMORPHIC CLASS \(\Phi\)

This paper determines the exact radius of circular univalence for a meromorphic subclass of the class Phi consisting of finite sums of principal parts with prescribed argument relations among coefficients and poles. Using a sharp lemma on positivity of real parts for products of powers, together wit…

On the stabilization of drift instability in traps with a magnetic field increasing toward the boundary

This paper examines whether an outwardly increasing magnetic field, known to suppress flute instability in low beta plasma traps, also stabilizes drift instability. Using a simplified cylindrical geometry with rarefied plasma, hot electrons, cold ions, quasineutrality, ion fluid equations, and a dri…

ON THE DENSITY OF FINITE FUNCTIONS IN WEIGHTED SPACES

The paper studies weighted Sobolev spaces on a bounded Lipschitz domain, where the weight depends on the distance to a smooth manifold that may lie on or inside the boundary. It formulates trace and zero boundary conditions according to whether a certain integral determined by the weight converges, …

AN EXACT INTERPOLATION THEOREM

This note studies whether the range conclusion in the Riesz-Thorin interpolation theorem can be sharpened from an ordinary Lebesgue space to a smaller rearrangement-invariant space. Using Lorentz-type spaces defined by decreasing rearrangements, the authors prove an interpolation theorem for operato…

Corrections to the Article On the Characteristic Temperature of Suspensions (DAN, Vol. 163, No. 6, 1965)

ON A GENERALIZATION OF CHANDRASEKHAR’S EQUATION

On the Energy of Postcritical Deformation of a Thin Elastic Shell

This note examines the postcritical deformation energy of a thin elastic shell when the ridge of an isometric transformation lies close to a clamped boundary, a situation in which the previously derived energy formula for an interior ridge is no longer directly applicable. The argument reformulates …

ON THE COLLISION OF AN ATOM WITH THE SURFACE OF A SOLID

This paper analyzes the classical dynamics of an atom colliding with and adsorbing on the surface of a solid, modeled as interaction with the end atom of a semi-infinite harmonic chain. Using generating functions and Laplace transforms, it derives closed-form solutions for the relative displacement …

ON QUASICONFORMAL MAPPINGS IN SPACE

The note studies quasiconformal mappings in three-dimensional Euclidean space, with emphasis on distortion estimates for self-mappings of the unit ball and on extremal mappings of domains with edges. Using modulus estimates for ring domains and comparisons with planar extremal mappings, it derives H…

ON THE SYSTEM OF BOUNDARY-LAYER EQUATIONS FOR AN UNSTEADY FLOW OF AN INCOMPRESSIBLE FLUID

The paper studies the initial and boundary value problem for the unsteady two-dimensional boundary-layer equations of a viscous incompressible fluid under monotonicity and smoothness assumptions on the prescribed data. By introducing von Mises type variables with the tangential velocity as an indepe…

On Primary Ideals in the Space $\mathscr{L}(0,\infty)$

The paper studies closed primary ideals in the convolution algebra of integrable functions on the positive half-line, using Fourier transforms on the closed lower half-plane and invariance under right shifts. It describes three cases: interior points yield a discrete chain of ideals defined by vanis…

ON THE THEORY OF OPEN RESONATORS FORMED BY PARALLEL DISKS

This paper develops an approximate theory of open electromagnetic resonators formed by two parallel disks for the case of large axial wave number product. Using reflection coefficients for waves near the critical frequencies of an open-ended plane waveguide, it derives impedance boundary conditions …

DESCRIPTION OF COMPLETELY IRREDUCIBLE REPRESENTATIONS OF A SEMISIMPLE COMPLEX LIE GROUP

This note studies the classification of completely irreducible representations of a connected semisimple complex Lie group in arbitrary complete locally convex spaces. It introduces notions of complete irreducibility and weak equivalence suitable for nonunitary representations, relates them to the c…

ON STABLE NORMALLY SOLVABLE EXTENSIONS OF DIFFERENTIAL OPERATORS IN PARTIAL DERIVATIVES

This paper studies stability of normal solvability and of the index for closed extensions of general partial differential operators with variable coefficients in a bounded domain. Using Hilbert space decompositions of domains between the minimal and maximal operators, it gives criteria under which s…

GENERAL CRITICAL STRESSED STATE OF A STRICTLY CONVEX SHELL

This paper examines the loss of stability of a sufficiently shallow, strictly convex elastic shell in a general stressed state with normal and shear stresses referred to the principal curvature directions. Assuming that buckling occurs through a uniformly distributed system of small elliptic regions…

THE GRID METHOD FOR THE NAVIER–STOKES EQUATIONS

This paper presents two finite-difference schemes for the initial-boundary value problem for the incompressible Navier-Stokes equations in a bounded three-dimensional domain. The authors formulate an implicit grid method with discrete solenoidality, boundary and initial conditions, prove layerwise u…

ON SOME STABILITY CONDITIONS CONNECTED WITH THE STUDY OF RESONANCES

The paper studies stability conditions for singularly perturbed systems with slow and fast variables, motivated by resonance problems in nonlinear oscillations. After shifting a nearby equilibrium, the authors reduce the problem to a linear system with a small parameter and nonlinear perturbations w…

DETERMINATION OF THE TEMPERATURE AND CONCENTRATION OF ELECTRONS IN AN ARC PLASMA FROM THOMSON SCATTERING OF LASER RADIATION

This paper reports an experimental determination of electron temperature and concentration in a direct-current helium arc plasma in an axial magnetic field using Thomson scattering of ruby laser radiation. Scattered light from a small plasma volume was observed at 90 degrees, separated from plasma g…

INTEGRAL CURVES OF THE DARBOUX EQUATION

On the Definition of a Class of Nonlinear Impulse Automatic Systems

This paper addresses the lack of a constructive definition for nonlinear pulse automatic systems with time quantization, a class including varied pulse modulation types, nonlinearities, and linear components. Using a system with one nonlinear element as a model, it proposes a general structural repr…

ON ALLOWING FOR THE COULOMB INTERACTION IN A TWO-BAND MODEL OF A SUPERCONDUCTOR

This paper examines how electron Coulomb interaction modifies the critical temperature and isotope effect in a two-band model of a superconductor, including the case of a nonmagnetic impurity. Using the Bardeen-Pines Hamiltonian, the authors derive the screened boson Green’s function, obtain coupled…

CRYSTALLINE STRUCTURE OF IRON MOLYBDATE

The paper determines the crystal structure of iron molybdate, Fe2(MoO4)3, the active component of iron molybdenum oxide catalysts, for a class of small-cation molybdates whose structures had not previously been described. Single-crystal X-ray diffraction data were analyzed using Patterson methods, F…

ON F. SEVERI’S CONJECTURE CONCERNING SIMPLY CONNECTED ALGEBRAIC SURFACES

This paper addresses Severi’s question whether a complex algebraic surface with vanishing first homology and geometric genus zero, or more strongly a simply connected surface with geometric genus zero, must be rational. Using the theory of principal homogeneous spaces over elliptic fibrations and re…

ON A METHOD FOR INVESTIGATING NONLINEAR SINGULAR EQUATIONS

This note proposes a method for studying a nonlinear singular integral equation with Cauchy-type kernel in a weighted Hölder class introduced by Guseinov. It establishes a series of functional inequalities relating weighted Hölder norms and weighted \(L_p\) norms, then uses them to show that the ass…

HYPERFINE STRUCTURE OF THE RAYLEIGH LINE OF LIGHT SCATTERING IN A PARAMAGNET

This paper analyzes how spin, phonon interaction in a paramagnetic crystal modifies the Rayleigh light scattering line when phonon energies are close to splittings between spin levels of paramagnetic ions. Using Green’s functions for phonon correlation functions and a weak interaction truncation, it…

ON THE HILBERT PROBLEM FOR A HOLOMORPHIC VECTOR

The paper studies the Hilbert linear conjugation problem for holomorphic vectors on a Lyapunov surface, with Hölder continuous boundary data and a matrix coefficient satisfying a positivity condition expressed through its minors. By reducing the boundary value problem to a system of singular integra…

ON AN APPROXIMATE METHOD FOR SOLVING BOUNDARY-VALUE PROBLEMS FOR THE BIHARMONIC EQUATION

This paper develops an approximate solution method for rectangular boundary value problems for the biharmonic equation with homogeneous conditions on the function and its normal derivative. A 13 point finite difference analogue is formulated, and the associated eigenfunctions and eigenvalues of the …

ASYMPTOTIC FORMULAS

This paper derives asymptotic formulas and bounds for trigonometric sums of the form \(\sum_{x \leq P}\exp(2\pi i ax^n/p^t)\), where \(P=(p^t)^{1/r}\) and the parameters lie in specified ranges. Using a reduction to shorter sums, a previously established estimate for polynomial exponential sums, and…

ON THE STRUCTURE OF A DISLOCATION IN A CRYSTAL LATTICE AND THE MECHANISM OF DISLOCATION MULTIPLICATION

This paper proposes a model of dislocation structure that emphasizes the finite disordering energy and threshold stability of a crystal lattice near a dislocation axis. It defines a “physical core” as the region where dislocation-induced shear strain reaches the critical value for lattice instabilit…

APPROXIMATE SOLUTION OF THE PROBLEM OF ANALYTIC CONSTRUCTION OF A REGULATOR FOR AN EQUATION WITH RETARDATION

ON THE INFLUENCE OF EXCITATION DIFFUSION ON THE REGIME OF MULTIMODE GENERATION

The paper analyzes how excitation diffusion affects multimode generation in a Fabry Perot quantum generator, focusing on axial modes at pump powers not restricted to the immediate threshold region. It solves stationary coupled equations for the inverted population and photon densities by successive …

Corrections to the paper Structure of Periodic Linear Groups and Algebraic Groups (DAN, Vol. 160, No. 3, 196

ON THE THEORY OF FREDHOLM EQUATIONS OF THE FIRST KIND

This paper studies Fredholm integral equations of the first kind, formulated as Ax equals f in a Hilbert space with A a completely continuous linear operator. It derives necessary and sufficient solvability conditions in terms of orthogonality to solutions of the adjoint homogeneous equation and a c…

EXTREMAL QUASICONFORMAL MAPPINGS

This paper solves an extremal problem for q-quasiconformal mappings of the unit disk onto plane domains containing two prescribed points, normalized by fixing 0 and a, where a differentiable real function of finitely many image points is to be maximized. Using variational methods for conformal and q…

ON THE SOLUTION OF A ONE-PHASE PROBLEM OF STEFAN TYPE

The paper proves local existence for a one-phase Stefan-type free-boundary problem for a heat equation with piecewise constant coefficients and transmission conditions at an internal interface. Using auxiliary moving boundaries, maximum-principle comparisons, and an approximation by delayed free-bou…