Recent Papers

Unicellularity Conditions for Dissipative Volterra Operators with Finite-Dimensional Imaginary Component

This paper studies simple Volterra dissipative operators in a separable Hilbert space whose imaginary component has finite dimension, using the characteristic matrix function as the main tool. It derives growth estimates for such matrix functions and gives necessary conditions for nondecomposability…

On estimating the spectrum of certain classes of linear operators

The paper develops spectral estimates for linear operators in Banach spaces semi-ordered by normal cones, extending earlier results for positive operators by relating spectral bounds to the action of operator powers on a single cone element. It proves resolvent existence and uniqueness results in or…

In the article by V. A. Kalyavin, T. A. Smolina, and O. A. Reutov, “On the monomolecular mechanism of the isotopic exchange of benzylmercury halides with radioactive mercuric halide,” published in *DAN*, vol. 156, no. 1, 1964:

Completely $FN$-factorizable groups

The paper studies groups in which subgroups, especially abelian subgroups, admit complements up to finite intersections satisfying a normality condition, termed completely F-factorizable and completely FN-factorizable groups. It proves that having all abelian subgroups FN-complemented is equivalent …

A Hypothesis on the Nature of Luminous Particles Observed by Cosmonauts

This paper proposes an explanation for luminous particles observed by cosmonauts near spacecraft entering Earth’s shadow, identifying them as micrometeorites heated by impact with the spacecraft or as heated fragments torn from the spacecraft surface. It estimates collision rates at orbital altitude…

On the Representation of Ultraspherical Polynomials as a Differential Operator Containing the Generating Function of These Polynomials

The note studies representations of ultraspherical polynomials through differential operators involving their generating function, extending a known construction for Hermite polynomials. Starting from the generating function for \(P_n^{(\lambda)}(x)\), it derives an identity expressing \(y^{n/2\lamb…

Phenyliodination of Some Triphenylphosphoranes

This paper examines the phenyliodonation of carbethoxy- and benzoylmethylenetriphenylphosphoranes as a route to substituted triphenylphosphoranes and as evidence for the nucleophilic character of the ylidic carbon atom. Phenyliodosoacetate was reacted with these phosphoranes in methanol, giving phen…

Optical Analog of the Mössbauer Effect

This paper examines ultranarrow phononless optical lines in low-temperature crystal spectra as an optical analogue of the Mössbauer effect. Using luminescence measurements on CdS single crystals in the bound-exciton narrow-line region, the authors compare the temperature dependence of phononless lin…

Crystal structure of synthetic sodium titanosilicate $\mathrm{Na}_2(\mathrm{TiO})[\mathrm{SiO}_4]$

The study determines the crystal structure of a synthetic sodium titanosilicate phase formed during hydrothermal crystallization in strongly alkaline NaOH solutions, with composition Na2TiSiO5, represented as Na2(TiO)[SiO4]. Single crystal X-ray analysis established a tetragonal unit cell with a = 6…

On the Theory of Integral Representations of Finite Groups

This note studies integral and local integral representations of finite groups, focusing first on cyclic groups of order mp squared with m prime to p. It determines the possible types of indecomposable representations over the ring of p-integral rational numbers by describing their rational irreduci…

Stimulating Effect of Certain Compounds on the Quenching of Chlorophyll Fluorescence by Nitro Compounds

This study examines whether electron donor compounds other than alcohols can enhance the quenching of chlorophyll a and pheophytin a fluorescence by aromatic nitro compounds in organic solvents. Fluorescence intensities were measured for pigment solutions in hexane, toluene, acetone, and pyridine wi…

Paramagnetic Resonance of Manganese Sulfide over a Wide Temperature Range

This paper reports measurements of paramagnetic resonance absorption in powdered manganese sulfide over the temperature range from +100 to -195 degrees Celsius at a frequency of 9285 Mc/s. Using a direct amplification radiospectrometer with a low temperature resonator system, the study records reson…

On compounds with the complex anion $[\mathrm{Hg}(\mathrm{SCN})_4]^{-2}$ and their precipitates

This paper examines compounds and precipitates containing the complex anion [Hg(SCN)4]2-, emphasizing the possible bridging role of thiocyanate through sulfur and nitrogen coordination. The authors relate the solubility and uptake behavior of zinc, cobalt, and cadmium tetrathiocyanatomercurate preci…

On the Radiolytic Properties of Amino Acids and Peptides

This study examines how functional groups and molecular structure affect the radiolytic behavior of amino acids, peptides, and cottonseed globulin. Dry polycrystalline samples were irradiated under vacuum at low and room temperatures, and radical yields and electron paramagnetic resonance spectra we…

Polymerization of o-hydroxyphenyl vinyl ketone

This study examines the radical polymerization of o-hydroxyphenyl vinyl ketone as a route to polymers containing chelating hydroxyketone groups without subsequent polymer-analogous modification. The monomer was synthesized from o-hydroxyacetophenone and polymerized in bulk, benzene solution, and sus…

Structure of X-ray $K_{\beta_5}$ Emission Bands of Titanium in Oxides $(\mathrm{TiO}_{0,85} - \mathrm{TiO}_{1,20})$

This study examines the fine structure of the titanium X-ray K beta 5 emission band in single-phase titanium monoxide samples spanning the homogeneity range TiO0.85 to TiO1.20, with comparison to earlier data on lower oxides and to a near-stoichiometric nitride. The authors prepared and characterize…

Corrections to the Article “On an Upper Estimate of Some Number-Theoretic Functions in Fields of Algebraic Numbers” (Doklady Akademii Nauk, Vol. 150, No. 2, 1963)

On Sufficient Conditions for a Strong Extremum in the Class of Curves with Bounded Derivative

The paper studies sufficient conditions for a strong extremum in variational and optimal-control problems when admissible curves have bounded derivatives or controls range over a compact set. It shows that, under the maximum principle, competitors uniformly close to an extremal and improving the fun…

Rearrangement of $\alpha,\alpha$-bis-(n-butylthio)ethylbenzene to $\alpha,\beta$-bis-(n-butylthio)ethylbenzene under the action of tert-butyl peroxide

This paper examines the thermal behavior of acetophenone di-n-butyl mercaptal, specifically the rearrangement of alpha,alpha-bis-n-butylthioethylbenzene to alpha,beta-bis-n-butylthioethylbenzene in chlorobenzene under tert-butyl peroxide. Experiments varying peroxide amount and substrate concentrati…

Perturbation of Solutions and Perturbation of Eigenvalues and Eigenfunctions of Second-Order Elliptic Equations under Boundary Perturbation

This note studies how solutions, eigenvalues, and eigenfunctions of second order elliptic boundary value problems change when the boundary of the domain is analytically perturbed. For a disk whose boundary is displaced by a small analytic radial perturbation, the paper constructs formal power series…

Mutual Transformations of Stereoisomeric 1,3-Dimethylcyclopentanes during Analytical Dehydrogenation

This paper examines a side reaction affecting analytical dehydrogenation of gasoline-range hydrocarbons: mutual isomerization of cis- and trans-1,3-dimethylcyclopentanes over a platinum, iron on carbon catalyst. Narrow boiling fractions enriched in one or the other stereoisomer were dehydrogenated a…

EPR spectra of radicals formed during gamma irradiation of polyamides

This study addresses conflicting assignments of radicals formed in polyamides under gamma irradiation by comparing electron paramagnetic resonance spectra of poly-epsilon-caproamide and related compounds with selective deuterium substitution. Spectra were recorded for irradiated samples containing d…

On Some Features of Linear Codes Correcting Asymmetric Errors

This paper studies binary linear codes for discrete asymmetric channels, where only one direction of symbol error is treated as significant, and formulates the correction problem in terms of a distance adapted to asymmetric distortions. It proves that correction of r asymmetric errors is possible ex…

On Boundary Value Problems for Partial Differential Equations with the Bessel Differential Operator

This note studies boundary value problems for partial differential equations involving a differential Bessel operator in weighted Sobolev type spaces on half spaces and quadrant domains. It establishes trace theorems for derivatives defined through the operator x partial x and, equivalently in suita…

Genetics of the spectra of benzylideneaniline and benzylidene-1-naphthylamine derivatives containing $\mathrm{NO}_2$ and $\mathrm{NMe}_2$ groups

This paper examines the ultraviolet absorption spectra of benzylideneaniline and benzylidene-1-naphthylamine derivatives containing nitro and dimethylamino substituents. Spectra measured in 1,2-dichloroethane are interpreted by separating contributions from a stilbene-type conjugated system and from…

Quantities of Angular Momentum Theory with Negative Parameters Representing Angular Momentum Quantum Numbers

This note extends the standard mathematical apparatus of angular momentum theory to negative values of angular momentum quantum numbers using the transformation j to minus j minus 1, which leaves the eigenvalue of the squared angular momentum operator unchanged. The authors introduce a phase convent…

THE NATURE OF POLARIZATION DURING ANODIC DISSOLUTION OF COPPER IN CONCENTRATED SOLUTIONS OF $\mathrm{H_3PO_4}$

This paper examines the origin of polarization and limiting current during anodic dissolution of copper in concentrated orthophosphoric acid, where earlier explanations based on surface saturation or depletion of acceptor ions were considered inadequate. The authors propose a concentration polarizat…

Relaxation of the vibrational energy of air molecules behind the front of a direct shock wave

This paper examines vibrational energy relaxation of nitrogen and oxygen molecules behind a normal shock wave in air, focusing on when exchange of vibrational quanta between components becomes significant. Treating air as a binary diatomic mixture, the authors couple conservation equations for the n…

Corrections to the article Invariants of Linear Representations of the Rotation Group of the Plane and the Center Problem (DAN, vol. 151, no. 3, 1963)

Collapse of a Star Taking into Account Counterpressure

This paper presents a numerical study of relativistic spherical collapse for a cold Fermi gas star whose mass exceeds the maximum static Oppenheimer, Volkoff mass. Using comoving coordinates, Einstein’s equations are written in divergence form with a conserved mass function, and initial data are spe…

On Perfect Mappings of Paracompact Spaces

This paper studies paracompact spaces that admit perfect mappings onto metric spaces and their approximation by inverse spectra of metric spaces with perfect bonding maps. It proves a factorization theorem: given a perfect map from a paracompact space onto a metric space, every open cover admits a p…

The Problem of Adding Prime and "Almost" Prime Numbers in Algebraic Number Fields

This note studies an additive problem for algebraic number fields, extending sieve methods to representations of large algebraic integers as sums of prime and almost prime elements. For a number field K, it proves that every sufficiently large “even” integer, in the specified ideal-theoretic sense, …

Investigation of the Analytical Properties of the Scattering Amplitude in the Nonrelativistic Three-Body Problem

The paper examines analytic properties of scattering amplitudes in the nonrelativistic three-body problem, focusing on scattering of a particle by a bound state of two others in the complex orbital angular momentum plane. Using modified Faddeev equations and a perturbation expansion, it discusses am…

Corrections to the Article “Quotient Spaces of the Idele Group of an Algebraic Group and Sheaf Cohomology” (DAN, Vol. 150, No. 3, 1963)

This document is a contents and corrections page for a 1964 issue, listing contributions in chemical technology, microbiology, biophysics, biochemistry, plant physiology, evolutional morphology, and physiology, with page references. The listed papers address topics including hydrothermal reactions o…

On the $\varepsilon$-entropy of Some Compact Sets of Differentiable Functions in Spaces with a Monotone Norm

The paper studies the asymptotic epsilon entropy of compact sets of differentiable functions in functional Banach spaces equipped with an arbitrary monotone translation invariant norm. It defines classes controlled by anisotropic and mixed smoothness norms, then derives lower entropy estimates for s…

Radiolysis of Hydrocarbons on a Semiconductor Adsorbent

This study investigates changes in the electrical conductivity of zinc oxide semiconductor films during gamma radiolysis of adsorbed hydrogen, butane, and isobutylene, using the adsorbent itself as a probe for active surface particles. The experiments show that irradiation in hydrocarbon atmospheres…

On the Quasi-Peanity of Functions

This paper studies criteria for quasi-Peano functions in countably valued logic, where a function is called quasi-Peano if, together with all functions depending on at most one variable, it generates the full class of functions under superposition. It introduces two classes of binary functions based…

On Expansion in Eigenfunctions of Systems with Summable Potential

The paper studies eigenfunction expansions for self-adjoint systems of second-order differential equations on the half-line with Hermitian matrix potentials whose norm is summable. Using Jost-type solutions, finite-interval approximation, and the unitarity of the associated scattering matrix, it der…

On the Reaction of White Phosphorus with Alkyl Halides via Ionic and Radical Mechanisms

This paper examines the reaction of white phosphorus with alkyl halides and distinguishes conditions favoring radical and ionic pathways. The authors argue that white phosphorus can behave as a pseudometal and as a donor through lone electron pairs, enabling addition of active alkylating agents, whi…

GENERATION AND ACCELERATION OF NEUTRINOS IN A TURBULENT PLASMA

The paper examines how weak neutrino electron interactions in a turbulent plasma can generate neutrino-antineutrino pairs and accelerate existing neutrinos through induced Cherenkov emission and absorption of plasmons. Using weak turbulence theory and perturbative expressions for plasmon decay and n…

Binary collisions of metastable helium atoms in plasma

This paper investigates the destruction of metastable helium atoms in the \(2^3S\) state in a decaying helium plasma, focusing on inelastic pair collisions at liquid nitrogen temperature. Using absorption measurements of the 3889 Å line after termination of a high-frequency discharge, the authors me…

Nonlinear Theory of the Drift-Cyclotron Instability of Nonisothermal Plasma

This paper develops a nonlinear theory of drift-cyclotron instability in an inhomogeneous nonisothermal plasma with electron temperature much greater than ion temperature. Starting from the Vlasov equation expanded to third order in the electrostatic wave amplitude, it derives weak-turbulence equati…

A METHOD FOR CALCULATING A POINT EXPLOSION IN GASES

A numerical method is developed for calculating the propagation of blast waves from a point explosion in an inviscid perfect gas with counterpressure, for plane, cylindrical, and spherical symmetry and for various adiabatic exponents. The approach combines central asymptotic formulas with the method…

Density theorem for finite functions in the space $L_{p,a}^{(m)}(E_n)$

The paper studies density in weighted Sobolev-type spaces on Euclidean space, defined by integrability of generalized derivatives of order m with respect to a positive measurable weight. Under local boundedness conditions and radial assumptions on the weight at infinity, together with additional int…

Problems of Universality in the Theory of Growing Automata

This note studies universality questions for growing automata built from finite elements capable of reproduction, extending earlier results for pulsating elements and relating the model to Kolmogorov, Uspenskii, and von Neumann style automata. It defines reproducing elements, simulation by block rep…

Electron Capture by Acceptor Additives during the Radiolysis of Polyvinyl Chloride

This study examines whether electron-acceptor additives can capture electrons during low-temperature gamma radiolysis of polyvinyl chloride and thereby influence ionic processes and gaseous product formation. Polyvinyl chloride films containing small amounts of anthracene, n-terphenyl, benzoquinone,…

IR Spectroscopic Study of the Mechanism of Formation of $n$-Nitrophenyl Esters of Benzoyl Amino Acids and Acyl Peptides by the Carbodiimide Method

This study examines the mechanism by which p-nitrophenyl esters of benzoylamino acids and acylpeptides form under dicyclohexylcarbodiimide conditions, with particular attention to racemization. Infrared spectroscopy was used to follow reactions over time and to compare diagnostic carbonyl bands of a…

Influence of the Nature of the Initiator and the Phase State of Acetaldehyde on the Chemical Structure of Macromolecules Formed During Its Polymerization

This study examines how the initiator and phase state of acetaldehyde affect the chemical structure of polymers formed during polymerization. Acetaldehyde was purified, co-condensed in vacuum with sodium or magnesium, and polymerized in crystalline or glassy states and during melting, with products …

On Some Properties of Polybenzimidazoles

This study compares the structure, thermal behavior, and electrophysical properties of two polybenzimidazoles synthesized from 3,3′-diaminobenzidine and diphenyl esters of terephthalic or isophthalic acid. X-ray diffraction, infrared spectroscopy, volatile-yield measurements, and conductivity studie…

On the mechanism of coprecipitation of trace amounts of yttrium with hydroxides of polyvalent metals

This study examines the mechanism by which trace amounts of carrier-free yttrium-90 coprecipitate with polyvalent metal hydroxides, focusing on ferric and zirconium hydroxides. Building on Ratner’s theory of secondary adsorption, the authors test whether the pH dependence of yttrium distribution bet…