Recent Papers

ON PERIODIC SOLUTIONS OF A CERTAIN NONAUTONOMOUS SYSTEM OF DIFFERENTIAL EQUATIONS

BEHAVIOR OF A SPATIAL QUASICONFORMAL MAPPING ON PLANE SECTIONS OF THE DOMAIN OF DEFINITION

This note studies how spatial quasiconformal mappings in three-dimensional domains are reflected on plane sections. It introduces a notion of two-dimensional quasiconformality for mappings of plane domains into Euclidean three-space and uses it to characterize spatial quasiconformal mappings by thei…

EMBEDDING THEOREMS FOR SPACES WITH MIXED NORM

This paper studies embedding theorems for function spaces with mixed norms, focusing on removing earlier monotonicity restrictions on the norm parameters. It defines the relevant mixed norm and Sobolev-type spaces, proves ordering and interpolation lemmas, and establishes a general boundedness theor…

ON THE TRANSCENDENCE AND ALGEBRAIC INDEPENDENCE OF VALUES OF \(E\)-FUNCTIONS THAT ARE SOLUTIONS OF A LINEAR DIFFERENTIAL EQUATION OF THIRD ORDER

The paper develops a method for proving algebraic independence of values of E-functions satisfying linear differential equations, with particular attention to homogeneous equations of third order. It introduces a criterion of differential reducibility for algebraic differential equations, expressed …

ON A GENERAL THEOREM ON THE ALGEBRAIC INDEPENDENCE OF VALUES OF \(E\)-FUNCTIONS

This paper strengthens a key rank lemma used in Shidlovskii’s general theorem on transcendence and algebraic independence of values of E-functions satisfying linear differential equations with rational-function coefficients. By modifying Siegel-type auxiliary polynomial constructions and the estimat…

SOME CONDITIONS FOR UNIQUENESS OF THE SOLUTION OF INVERSE PROBLEMS OF POTENTIAL THEORY

The paper studies uniqueness in inverse problems for metaharmonic and Newtonian potentials in Euclidean space: determining a density from a known exterior potential, and determining the shape of a body with prescribed density from exterior or interior potentials. It establishes a series of uniquenes…

APPLICATION OF THE THEORY OF ADDITIVE FUNCTIONALS TO STOCHASTIC DIFFERENTIAL EQUATIONS

AN ANALOGUE OF ONE THEOREM OF BASS FOR MODULES OF REPRESENTATIONS OF NONCOMMUTATIVE ORDERS

This paper extends a theorem of Bass on decompositions of torsion-free modules into ideals from commutative domains to representation modules over noncommutative orders. For an order over a Dedekind ring in a finite-dimensional semisimple separable algebra, it proves that if every right ideal of the…

THE WATER VAPOR DIMER AND ITS SPECTRUM

The paper develops a model for the rotational spectrum and absorption of the water vapor dimer treated as a linear complex with hindered internal rotation about the hydrogen bond axis. Using the internal-axis formalism, the Hamiltonian is approximated by external symmetric-top rotation plus internal…

ON ABSOLUTE AND UNCONDITIONAL CONVERGENCE

This note studies absolute and unconditional convergence of Fourier series with respect to the Haar system, emphasizing distinctions between pointwise absolute convergence, absolute convergence of coefficients, and almost-everywhere absolute convergence. It gives sufficient conditions in terms of in…

ON MULTIDIMENSIONAL HYPERBOLIC EQUATIONS OF ARBITRARY ORDER WITH DISCONTINUOUS COEFFICIENTS

The paper studies a mixed problem for a class of multidimensional hyperbolic equations of arbitrary order whose coefficients, free term, and initial data may have jump discontinuities across prescribed analytic surfaces. It formulates general initial, boundary, and conjugation conditions, together w…

ON THE REGULARIZATION OF THE EARTH

This note examines the regularization of the Earth in potential theory, focusing on whether masses outside the geoid can be transferred inside while preserving total mass and leaving the geoid potential unchanged. Using sweeping-out arguments, it shows that no regularization method can simultaneousl…

ON A CLASS OF DISCRETE GROUPS OF LOBACHEVSKY SPACE HAVING AN INFINITE FUNDAMENTAL DOMAIN OF FINITE MEASURE

The note constructs infinite families of discrete groups acting on three-dimensional Lobachevsky space whose fundamental domains are noncompact but have finite volume. The construction begins with polyhedra associated to fine square decompositions of a horosphere, chooses dihedral angles of the form…

On Singular Points of Topological Embeddings of Manifolds and the Union of Locally Flat Cells

This note studies singular points of topological embeddings of manifolds in Euclidean space and the local flatness of unions of locally flat cells. It proves that, in dimensions \(n \ge 5\), singular interior points are removable except in codimension two, where local flatness is characterized by th…

MODELING LARGE CRATERING EXPLOSIONS

This paper develops a similarity approach for modeling large cratering explosions by treating crater formation as the expulsion of fragmented rock by an expanding gas cavity, after an initial fragmentation stage. Dimensional analysis is used to express the crater radius in terms of gas energy or pre…

Bibliography of Journal Articles

This bibliographic survey records recent journal literature on differential equations, primarily from Soviet and Eastern European mathematical publications of 1965 and early 1966. The entries are organized under ordinary differential equations and cover qualitative theory, stability, asymptotic meth…

On the Mechanism of Fragmentation of Small Meteoroid Bodies in the Atmosphere

This paper examines why faint photographic meteors show shortened trails, rapid initial brightening, increased terminal deceleration, and blurred interruptions, phenomena often attributed to unusually loose meteoroid structure. The authors develop a thermal and aerodynamic model for a rotating spher…

A GENERAL THEORY OF INTEGRAL EQUATIONS WITH A POWER KERNEL

On the Theory of Steep Waves

This paper develops a kinematic theory of steep surface waves, including limiting swell and wind waves with sharpened crests, by representing particle motion with elliptical rather than circular orbits and by accounting for pulsations of Stokes and drift currents. Using Lagrangian incompressibility …

ON THE INVARIANT COMPLEMENTABILITY OF SOME SUBSPACES GENERATED BY A LINEAR OPERATOR

This paper studies when the subspace of null elements of a linear operator on a vector space admits an invariant complement. It proves several sufficient conditions, including bounded height of null elements, finite-dimensionality of the null subspace, stabilization conditions on kernels intersected…

ON THE NORMAL STRUCTURE OF FINITE GROUPS

This note studies the normal structure of finite groups through systems of cyclic chief factors, with particular attention to groups whose chief factors have cyclic Sylow p-subgroups. Using auxiliary results from modular representation theory, it gives criteria involving the Frattini subgroup, gener…

ON THE GROWTH OF ENTIRE FUNCTIONS OF SEVERAL COMPLEX VARIABLES

This note studies the growth of entire functions of several complex variables with respect to one variable when the remaining variables are fixed. Using notions of order, type, capacity, and exceptional sets defined by conditions of massiveness and rarity, it extends earlier results for two variable…

THE INTEGRAL FUNCTIONAL AND ITS NORM

The paper studies integral functionals on algebraic polynomials generated by moment segments of nondecreasing functions on the unit interval, extending a problem concerning the functional with moments 1, xi/2, xi squared/3, and so on. Using determinant criteria for absolutely monotone segments and r…

Group-Theoretical Classification of States of a Pair of Exchange-Coupled Ions in a Crystal

The paper develops a group-theoretical classification of the states of pairs of exchange-coupled impurity ions in crystals, motivated by optical quantum generators using such ion pairs. It defines the symmetry group of an ion pair through the intersection of the crystal point symmetry at the pair mi…

On Solving the Kinetic Transport Equation by the Splitting Method

This paper studies the stationary one-velocity kinetic transport equation with isotropic scattering in a bounded convex domain and proposes a splitting method for its solution. The authors formulate the boundary-value problem in an operator setting, define a class of generalized solutions in an \(L_…

GEOMETRIC ISOMERS OF ALKENYL COMPOUNDS OF GERMANIUM

This paper reports the synthesis and characterization of previously undescribed stereoisomeric propenyl derivatives of germanium and related isopropenyl compounds. Tetra-cis-propenylgermane, tetra-trans-propenylgermane, tetraisopropenylgermane, cis- and trans-triethylpropenylgermane, and triethyliso…

ON A GENERALIZATION OF THE CONCEPT OF A LIE ALGEBRA

The paper introduces left, right, and two-sided D-algebras as distributive algebras satisfying differential identities that generalize the Lie algebra identity while also encompassing structures equivalent to modules over Lie algebras. It proves that the quotient of a left D-algebra by its left cent…

On the Nature of the Ultraweak Luminescence of Irradiated Solutions of Deoxyribonucleic Acid (DNA)

This study examines the origin of ultraweak luminescence observed in aqueous DNA solutions after irradiation. Using chemiluminescence measurements, hydroperoxide analysis, temperature variation, pH control, irradiation under argon, and inhibition by propyl gallate, the authors compare luminescence d…

On Conditions for Unitary Equivalence of Commutative Symmetric Algebras in the Space $\Pi_k$

This paper gives necessary and sufficient conditions for unitary equivalence of commutative symmetric algebras in a Pontryagin space with only real eigenfunctionals, using the structural realization developed in the author’s preceding work. The argument analyzes how an isometric equivalence transfor…

ON A PROBLEM FOR A SYSTEM OF DIFFERENTIAL EQUATIONS OF ENERGY AND MASS TRANSFER

ON THE QUESTION OF UNIQUENESS OF SOLUTIONS OF VOLTERRA INTEGRAL EQUATIONS WITH RETARDED ARGUMENT

This note studies uniqueness for systems of Volterra integral equations with retarded argument, extending earlier results on differential equations with delay. It formulates conditions linking the modulus of continuity of the kernel in the unknown function to the rate at which the delayed argument a…

Asymmetry and angular anisotropy of the mass distributions of $\mathrm{U}^{238}$ fission fragments induced by 14 MeV neutrons

This paper examines the angular anisotropy and mass asymmetry of fission fragments produced when uranium 238 is bombarded by 14 MeV neutrons. The authors interpret the observed dependence of fragment yield on emission angle and mass ratio as a superposition of fission from uranium 239, uranium 238, …

The structure of vincarine

This paper determines the structure and stereochemical relationship of the alkaloid vincarine, isolated from the roots of Vinca erecta. Using mass spectrometry, NMR, UV and IR spectroscopy, acetylation, reduction, and oxidation reactions, the authors refine its formula to C21H24O3N2 and identify key…

Nonlinear theory of motion of fast charged particles in helical toroidal magnetic fields

This paper develops a nonlinear theory for the motion of fast charged particles in helical magnetic fields wound on a torus, with possible application to strong focusing and particle channeling. Using averaging methods for the rapidly rotating transverse force, the analysis derives slow-motion equat…

On the Mechanocaloric Effect at Ordinary Temperatures

This paper examines the mechanocaloric effect at ordinary temperatures during liquid flow through a fine porous partition, in relation to the reciprocal thermomolecular effect predicted by irreversible thermodynamics. The authors argue that surface forces in small pores can alter the enthalpy of mob…

New data on electric puncture of aluminium suspension in dielectrics

This paper investigates the electric breakdown of suspensions of powdered aluminum in liquid dielectrics, using aluminum in gasoline and related powder systems as models for structuring and puncture in inhomogeneous insulating media. Cinematographic observations record the formation, rupture, restor…

Synthesis and Structure of 1,4-Dinitro-1,3-butadienes

A general synthesis of 1,4-dinitrobutadienes-1,3 is described, based on oxidation of disodium salts of substituted 1,4-dinitrobutene-2 with bromine, iodine, ferricyanide, or silver nitrate in ether or aqueous media. Raman spectral intensity analysis is used to assess conjugation and assign cis-cis a…

ON THE DIFFERENCE BETWEEN THE SUPRAMOLECULAR STRUCTURES OF AMORPHOUS POLYARYLATES OBTAINED BY INTERFACIAL POLYCONDENSATION AND BY HIGH-TEMPERATURE POLYCONDENSATION IN A HOMOGENEOUS MEDIUM

This study examines how polycondensation conditions affect the supramolecular structure and mechanical behavior of amorphous polyarylate F-7, prepared either by interfacial polycondensation or by high-temperature polycondensation in a homogeneous dissolving medium. Electron microscopy of platinum-ca…

Construction of a Functional Equation with a Given System of Particular Solutions

This paper constructs a functional equation whose prescribed particular solutions are functions of the form A(z, lambda_n), where A(z,h) is expanded in a parameter h and the sequence lambda_n satisfies a finite growth condition. The method introduces an auxiliary entire function L vanishing on the s…

Nitrogen Fixation on Transition Metal Complexes Activating Hydrogen

This study examines whether transition-metal complexes known to activate hydrogen can also fix molecular nitrogen under mild homogeneous conditions, and how added hydrogen affects this process. Systems formed from transition-metal acetylacetonates or tetraethoxytitanium with organolithium, Grignard,…

Study of the Electrical Conductivity of Lithium Alkyl Solutions in Relation to the Polymerization Process

This study examines the electrical conductivity of lithium alkyl solutions in nonpolar solvents as a probe of their role in stereoregular diene polymerization and of the effects of electron donor additives. Conductivity measurements were carried out for ethyllithium and n-butyllithium in benzene or …

ON THE CONNECTION BETWEEN THE STABILITY OF STOCHASTIC DIFFERENCE AND DIFFERENTIAL SYSTEMS

A representation for the scattering matrix in quantum field theory

The paper develops an operator representation of the relativistic scattering matrix in quantum field theory using an invariant one-dimensional parameter and the Fourier transform of the interaction Lagrangian. Starting from an integral equation for the reaction matrix, it introduces auxiliary quasip…

On the mutual solubility in the water–nitric acid–$(\mathrm{C}_4\mathrm{H}_ 9\mathrm{O})\mathrm{PO}(\mathrm{C}_4\mathrm{H}_9)_2$ system at $25^\circ$

The paper examines mutual solubility in the ternary system water, nitric acid, and butyl ester of dibutylphosphinic acid at 25°C, motivated by the use of this compound as an extractant for metal salts and acids. Solubility boundaries and conjugate phase compositions were determined by Alekseev’s met…

ON THE INTERATOMIC DISTANCES OF LANTHANOIDS IN METALLIC CRYSTALS

This paper examines anomalous variations in interatomic distances among metallic lanthanoids against the general trend of lanthanoid contraction. Using a previously derived formula relating distance to coordination number, atomic number, core and bonding electrons, and the contribution of 4f electro…

Nonlinear Magnetohydrodynamic Waves

THE LONGITUDINAL HALL EFFECT IN CUBIC CRYSTALS

This paper analyzes the longitudinal Hall effect in cubic semiconducting crystals with complex band structure, focusing on intermediate magnetic fields whose direction does not coincide with a crystal symmetry axis. It develops a tensor formulation of Ohm’s law for the antisymmetric part of the gene…

ON A PERIODIC BOUNDARY VALUE PROBLEM FOR A LINEAR DIFFERENTIAL EQUATION OF THE FOURTH ORDER

Experimental Proof of the Absence of Absolute Electrotransport in Liquid $\mathrm{Pb}$ , $\mathrm{Sn}$ , $\mathrm{In}$ , $\mathrm{Ga}$

This study investigates whether absolute electromigration, previously observed in solid pure metals and alloys, also occurs in liquid Pb, Sn, In, and Ga. Using a capillary method, the authors introduced suspended colloidal Co-60 particles as inert markers in liquid metal samples and measured their p…

Nonenzymatic Stereospecific Cyclization of Isoprenoids

This paper examines whether acid-induced, nonenzymatic cyclization of acyclic isoprenoids can proceed stereospecifically in the formation of a decalin system. Using individual cis-6,7-trans-10,11 and trans-6,7-trans-10,11 stereoisomers of farnesylacetone, the authors carried out low-temperature sulf…