Recent Papers

ON PROJECTION SPECTRA AND BICOMPACT EXTENSIONS

ON SOME SYSTEMS OF DIFFERENTIAL EQUATIONS OF MIXED AND MIXED-COMPOUND TYPES

SUMMATION OF UNBOUNDED SEQUENCES BY LINEAR REGULAR METHODS

This paper studies the summation of unbounded sequences by linear regular summability methods represented by regular matrices, with emphasis on fields of bounded summability and domains of effectiveness. It proves that when a regular matrix sums a bounded divergent sequence, its domain contains cont…

ON HYPOELLIPTIC PSEUDODIFFERENTIAL OPERATORS

This note extends Hörmander’s hypoellipticity results for differential operators with variable coefficients to pseudodifferential operators, using techniques developed by Kohn and Nirenberg. It formulates a Hörmander type condition on the symbol, allowing the operator’s strength to vary from point t…

On the group classification by Cartan's method of equations of one-dimensional gas flow

This paper applies Cartan’s method of exterior forms to the group classification of differential equations, focusing on one-dimensional gas flow in a tube of variable cross section with unspecified functions in the equation of state and geometry. It develops the canonization of the associated Pfaffi…

EXACT UNIQUENESS CLASSES FOR THE SOLUTION OF THE CAUCHY PROBLEM FOR SECOND-ORDER EQUATIONS

The paper studies uniqueness classes for normal solutions of the Cauchy problem for the second order equation u_t = a u_xx + q(x)u on the whole line, allowing complex nonzero a and unbounded real potentials q(x). It gives necessary and sufficient growth conditions for uniqueness in several weighted …

UNIFORM APPROXIMATIONS BY RATIONAL FUNCTIONS (ALGEBRAIC AND TRIGONOMETRIC) AND GLOBAL FUNCTIONAL PROPERTIES

This paper studies how the rate of uniform approximation of a function by algebraic or trigonometric rational functions controls global regularity properties expressed through generalized variation, generalized absolute continuity, and Orlicz space moduli. Using estimates for the Phi-variation and O…

THE FIRST BOUNDARY-VALUE PROBLEM

The paper studies the first boundary-value problem for a class of differential equations and systems in function spaces more general than weighted or unweighted Sobolev spaces, whose polynorms include both derivatives and differential expressions. It formulates geometric and weight conditions on pos…

ON THE SPECTRUM OF THE SCHRÖDINGER OPERATOR USED IN THE OPTICAL MODEL OF THE NUCLEUS

The paper studies the spectral and scattering theory of a three-dimensional Schrödinger operator for spinor wave functions that includes a spin-orbit interaction term, as used in the optical model of the nucleus. Under decay and regularity assumptions on the scalar potential and spin-orbit coefficie…

ON CONJUGATE FUNCTIONS

This paper studies conjugate functions associated with periodic summable functions and the regularity of integral transforms built from them. For even one variable functions, it establishes continuity and uniform convergence results for transforms defined through the conjugate function, including a …

POSITIVE MIXED PROBLEMS

This note studies mixed initial-boundary value problems in a cylindrical domain for general first-order hyperbolic systems whose coefficients need be Hermitian only on the lateral boundary. Under generalized Petrovskii hyperbolicity, a noncharacteristic boundary condition, and Friedrichs-type positi…

INFINITESIMAL BENDINGS OF SURFACES OF REVOLUTION OF POSITIVE CURVATURE WITH A CONICAL OR PARABOLIC POINT AT THE POLE

The paper studies infinitesimal bendings of surfaces of revolution with positive curvature when the pole is a conical or parabolic singular point. It develops a reduction of a first order generalized Cauchy, Riemann type system with singular coefficients to a second order elliptic equation, then app…

AUTONOMY IN MULTIVARIABLE AUTOMATIC CONTROL SYSTEMS WITH VARIABLE STRUCTURE

This paper addresses the synthesis of autonomous control for multivariable automatic control systems whose controlled coordinates are coupled and whose plant parameters vary over wide ranges. It proposes using variable-structure control, with discontinuous regulator coefficients and sliding modes on…

A DIFFERENCE METHOD FOR SOLVING CERTAIN COEFFICIENT BOUNDARY-VALUE PROBLEMS

This paper studies inverse coefficient boundary-value problems in which both the solution of a differential equation and an unknown coefficient are to be determined. It treats a parabolic problem with a time-dependent coefficient and a one-dimensional elliptic problem with an unknown constant coeffi…

ON THE STATISTICAL CHARACTERIZATION OF SYMMETRIC STABLE DISTRIBUTION LAWS

The paper studies statistical characterization of linear types of distributions under transformations of location and scale, focusing on symmetric stable laws. It proves that the linear type generated by a symmetric stable distribution belongs to the union of the classes characterized by invariant s…

ON THE CONFINEMENT OF HIGH-TEMPERATURE PLASMA IN A TRAP WITH MAGNETIC MIRRORS

This paper reports experiments on confinement of high-temperature deuterium plasma with hot electrons in a magnetic mirror trap, using turbulent heating produced by a pulsed direct discharge. Plasma energy and electron temperature were inferred mainly from diamagnetic measurements of magnetic-flux e…

ASYMPTOTICS OF EIGENVALUES AND EIGENFUNCTIONS OF ONE-DIMENSIONAL SINGULAR DIFFERENTIAL OPERATORS

This paper studies asymptotic properties of solutions, spectra, and eigenfunctions for one-dimensional singular differential systems of the form y' equals mu A(x)y under structural and regularity assumptions on the matrix coefficient at infinity. It proves a fundamental matrix asymptotic expansion f…

ON AN INTEGRAL REPRESENTATION OF SMOOTH FUNCTIONS AND SOME FAMILIES OF FUNCTION SPACES

The paper develops an integral representation for sufficiently smooth functions of several variables using mixed finite differences and derivatives indexed by subsets of coordinate directions, extending a representation associated with V. P. Il’in in a special case. It introduces and compares severa…

EMBEDDING THEOREMS FOR FUNCTIONS DEFINED ON UNBOUNDED DOMAINS, AND THEIR APPLICATION TO BOUNDARY-VALUE PROBLEMS FOR THE POLYHARMONIC EQUATION

The paper studies embedding theorems for weighted Sobolev type spaces of functions defined on unbounded Euclidean domains, including half-spaces and traces on lower-dimensional hyperplanes. It defines appropriate weighted norms, including fractional-order variants, establishes several trace and embe…

On Gaussian Linear Functionals on a Countably Hilbert Space

This paper studies Gaussian probability measures on the space of continuous linear functionals over a real separable countably Hilbert space. It characterizes the possible mean and covariance functionals, showing that they arise from a continuous linear form and a positive nuclear operator with resp…

ON FINITE GROUPS WITH A GIVEN SYLOW 2-SUBGROUP

This paper studies finite groups whose Sylow 2-subgroups have a specified presentation and relates them to earlier classification results of Gorenstein and Walter. It proves that if the centralizer of a distinguished involution in such a group is soluble, then the group has one of three described st…

ON THE QUESTION OF THE UNITARITY OF THE $S$-MATRIX IN BROKEN $SL(6)$ SYMMETRY

The paper addresses claims that invariance under broken SL(6) symmetry is incompatible with S-matrix unitarity. It argues that the contradiction arises only if strict SL(6) invariance is imposed on physical amplitudes, whereas the appropriate formulation introduces 36-dimensional momenta, for which …

ON THE POSSIBILITY OF TAKING THREE-PARTICLE FORCES INTO ACCOUNT IN THE RELATIVISTIC THREE-BODY SCATTERING PROBLEM

The paper examines how three-particle forces can be incorporated into the relativistic three-body scattering problem formulated through Faddeev-type integral equations and Bethe-Salpeter kernels. Starting from the pair-interaction case, it derives coupled equations for transition amplitudes involvin…

STUDY OF FILAMENTOUS CRYSTALS OF MAGNESIUM OXIDE

This paper reports the preparation and characterization of filamentary single crystals of magnesium oxide, an oxide of interest because of its high melting temperature. The crystals were grown by heating polycrystalline magnesium oxide at 1600 to 1700 degrees in a cryptol furnace, where transport re…

ON THE SMOOTHNESS OF THERMAL POTENTIALS. III\*)

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ON THE PRODUCTION OF SINGLE CRYSTALS OF OXIDES OF RARE-EARTH ELEMENTS BY THE VERNEUIL METHOD

This study examines the growth of single crystals of rare-earth oxides by the Verneuil method, with particular attention to whether lanthanides of variable valence form nontrivalent oxides under different flame conditions. Oxides of lanthanides with atomic numbers 62 to 71 were crystallized under va…

FURTHER ON THE BREAKING OF WAVES IN SHALLOW WATER

This paper revisits the breaking of long waves in shallow water and seeks analytical support for an earlier hypothesis that instantaneous phase velocity can be approximated by substituting the instantaneous depth, rather than the still-water depth, into classical wave formulas. For gently sloping ti…

THE BEHAVIOR OF METRIZABILITY UNDER QUOTIENT MONOTONE MAPPINGS

This paper studies when metrizability is preserved under quotient monotone mappings in set-theoretic topology. After showing that pseudo-open bicompact images of metric spaces can be represented as pseudo-open, bicompact, monotone images of another metric space, it proves the main theorem: a quotien…

TOPOLOGY OF FUNCTION SPACES

This paper studies topological properties of function spaces arising in the variational theory of closed geodesics, focusing on spaces of unoriented loops and unoriented closed paths on Riemannian manifolds diffeomorphic to spheres. Using a grading of homology groups by critical values of the length…

ELECTRON PARAMAGNETIC RESONANCE OF $\mathrm{Gd}^{3+}$ IONS IN THE CHALCOGENIDE GLASS $\mathrm{Tl_2SeAs_2Se_3}$

Electron paramagnetic resonance was studied in glassy Tl2SeAs2Se3 samples doped with 0.2 to 0.5 wt.% gadolinium, using spectra recorded from room temperature down to liquid helium temperature and compared with gadolinium-doped As2Se3 glass. The Tl2SeAs2Se3 spectra were complex but reproducible, with…

Maximal and Normal Series of Finite Groups

This note studies how structural relations among maximal subgroups of a finite group constrain its normal structure, especially nilpotency, solvability, and supersolvability. It proves that quasireachability or permutability conditions on first through fourth terms of maximal series force strong res…

AN EXISTENCE THEOREM FOR THE SOLUTION OF THE PROBLEM OF SHORT-RANGE WEATHER FORECASTING

The paper proves a local existence theorem for a smooth solution of a mixed initial boundary value problem for a quasilinear system modeling aspects of short-range weather forecasting in a domain unbounded in the horizontal variables. The solution is constructed by the method of fractional steps, re…

OBSERVATIONS OF ULTRA-LOW-FREQUENCY RADIATION AT TWO CONJUGATE POINTS

This paper reports joint Soviet and French observations of natural ultra-low-frequency emissions at the magnetically conjugate stations Sogra and Kerguelen from 1964 to 1965, using identical continuous recording equipment and spectral analysis of magnetic tapes. The authors compare the occurrence an…

Structural method for determining dimensionality

This paper develops a structural approach to dimension by first defining dimension for partially ordered sets in terms of chains of filters, then applying this notion to basic lattices of closed sets in topological spaces. It proves that zero-dimensional distributive lattices with zero and unit are …

ON GAS FLOWS IN THE NEIGHBORHOOD OF A WEAK DISCONTINUITY

The paper studies the matching of two-dimensional unsteady isentropic polytropic gas flows to a region of gas at rest across a weak discontinuity, where the flow variables are continuous but their first derivatives jump. It formulates the problem using potential double waves, derives governing equat…

DEGENERATE CASES OF SINGULAR INTEGRAL EQUATIONS WITH CAUCHY KERNEL

ON THE LIQUATION NATURE OF THE CHEMICALLY INHOMOGENEOUS STRUCTURE OF LOW-ALKALI SODIUM SILICATE GLASSES

This paper examines whether the chemically inhomogeneous structure of low-alkali sodium silicate glasses has a liquation origin. The authors compare small-angle X-ray scattering measurements of mean-square electron-density fluctuations with calculations based on an extrapolated clearing-temperature …

ON A CLASS OF OPERATORS

The paper studies bounded linear operators in Hilbert spaces equipped with an indefinite metric, focusing on plus-operators, \(J\)-noncontracting operators, and their adjoints. It develops an elementary theorem on Hermitian sesquilinear forms and applies it to show when plus-operators are collinear …

CONDITIONING IN GENERAL COMPUTATIONAL PROBLEMS

The paper formulates a general notion of conditioning for computational problems involving a continuous operator between normed linear spaces, where input data are known only within a prescribed error ball. It defines a condition measure as the maximal ratio of relative output error to relative inpu…

ON THE ALGORITHMIZATION OF SOLVING PROBLEMS IN HARMONY AND OF THE ANALYSIS OF HARMONIZATION

This paper describes an algorithmic approach to four-part harmonization of a given melody, and by extension a bass, within the norms of elementary harmony. It formalizes chord construction through encoded scale degrees, chord types, inversions, doublings, dispositions, and octave placement, then sel…

ON THREE LINEARIZED INVERSE PROBLEMS FOR HYPERBOLIC EQUATIONS

This paper formulates and analyzes three linearized inverse problems for hyperbolic equations arising from wave propagation. The first concerns recovery of a refractive coefficient from boundary travel times, and in a special background medium it is reduced to determining a perturbation from its int…

ON SOME PROPERTIES OF ALGEBRAS OF CONTINUOUS FUNCTIONS

This note studies closed subalgebras of the algebra of continuous complex functions on a compact Hausdorff space, focusing on antisymmetry, weak analyticity, and partitions associated with such algebras. It introduces antisymmetric measures and sets of weak analyticity, proves reconstruction criteri…

A SUBGROUP CHARACTERIZATION OF SOME FINITE GROUPS

This note studies how structural and embedding properties of selected subgroups determine the structure of finite groups. It formulates a series of classification results for groups whose maximal, higher maximal, or maximal solvable subgroups satisfy restrictions such as being minimal nonnilpotent, …

RELATION BETWEEN THE SHAPE OF THE HOMOGENEITY REGION OF THE β-PHASE ON THE PHASE DIAGRAM OF THE NIOBIUM–TIN SYSTEM AND THE SUPERCONDUCTING PROPERTIES OF $\mathrm{Nb}_3\mathrm{Sn}$

This study examines how the homogeneity region of the beta phase in the niobium-tin system relates to the superconducting properties of Nb3Sn, particularly the observed dependence on heat-treatment temperature. Alloys with varied tin content were prepared, annealed at temperatures from 700 to 1800°C…

EXTREMAL PROBLEMS IN THE THEORY OF POLYNOMIAL OPERATIONS

This paper studies extremal norm problems for linear polynomial operations on translation-invariant spaces of periodic functions, especially continuous and integrable periodic functions. For convolution-type operations determined on trigonometric polynomials of order at most n by a kernel, the paper…

ON MEASURES IN LINEAR SPACES

This paper studies when a premeasure defined on cylindrical sets in a real linear space can be extended to a countably additive measure without assuming a topology on the space. It proves that, when the chosen linear functionals separate points, such an extension exists exactly when the image of the…

ON SPACES DECOMPOSABLE INTO SPECTRA CONSISTING OF METRIC SPACES

This paper studies spaces representable as limits of inverse spectra whose terms are metric spaces, extending earlier work on spectral decomposability. It introduces notions of extremal spectra and uniform extremal spectra, then proves that the completion of a uniform space is the limit of a unique,…

HYPERSCALES OF BANACH STRUCTURES

This paper develops the notion of hyperscales of ideal Banach function structures within the setting of measurable functions ordered almost everywhere. It defines hyperscales by a logarithmic convexity type inequality, establishes existence and properties of maximal hyperscales, and proves interpola…

A METHOD FOR PARAMETER-FREE INTERPRETATION OF THREE-LAYER ELECTROMAGNETIC SOUNDING CURVES OF TYPES $K$ AND $Q$

This paper presents a parameter-free method for interpreting three-layer electromagnetic frequency-sounding curves of types K and Q. The argument begins from two-layer curves, showing that when the lower layer has effectively zero resistivity the thickness of the upper layer can be determined indepe…