Recent Papers

Asymptotic Expansion of Solutions of Second-Order Ordinary Differential Equations in Banach Spaces

The paper studies singularly perturbed second order ordinary differential equations in Banach spaces, with a small parameter multiplying the highest derivative. It defines asymptotic expansions in the Banach space setting and constructs fundamental solutions for a linear equation with a bounded oper…

Corrections to the article Numerical Solution of Algebraic and Transcendental Equations (DAN, Vol. 115, No. 3, 1957)

On the rigidity of an open surface of nonnegative curvature under a nonorthogonal sleeve connection

This paper studies infinitesimal rigidity of open convex surfaces of nonnegative curvature when holes in the surface are filled by rigid sleeves imposing a nonorthogonal contact constraint on boundary displacements. Using Blaschke’s integral formula, boundary decompositions of the bending and rotati…

On the Catalytic Properties of Calcium Oxide

This study examines the catalytic properties of calcium oxide as a solid base in reactions involving hydrogen elimination, focusing on isopropyl alcohol decomposition, cyclohexane dehydrogenation, and hydrazine decomposition. Calcium oxide prepared by vacuum dehydration of calcium hydroxide was test…

Corrections to the article “Introduction of deoxycarbonic, glyceric,

On the Arithmetic of Matrices

This paper develops arithmetic invariants for integral nonsingular matrices and integral skew-symmetric matrices, using canonical elementary-divisor forms under unimodular equivalence. It defines left and right matrix divisors, proves their equality in number, and gives an explicit product formula f…

SIGNAL-TO-NOISE RATIO IN A REGENERATIVE DETECTOR OF NUCLEAR PARAMAGNETIC RESONANCE

This paper analyzes the signal-to-noise ratio in a regenerative detector used for observing nuclear paramagnetic resonance, where weak resonance signals are often limited by detector noise. Using a simple self-oscillator model with nonlinear tube characteristics, the author derives expressions for a…

S. L. Sobolev spaces of fractional order and their application to boundary value problems for partial differential equations

The paper introduces anisotropic Sobolev spaces of fractional order defined by square integrability of derivatives and fractional difference quotients, including versions on product domains and smooth product surfaces. It proves embedding and trace-extension theorems for these spaces, giving norm es…

THE NEMYTSKII OPERATOR AND ITS POTENTIAL IN ORLICZ SPACES

This paper studies the Nemytskii operator defined by hu equals g(u(x), x) and its potential functional in generalized Orlicz spaces, extending earlier results for Lp spaces relevant to nonlinear Hammerstein integral equations. It establishes necessary and sufficient conditions, expressed through You…

Dipole Moments of Hexaalkyl Derivatives of Disiloxane

This study reports dipole moment measurements for four hexaalkyl derivatives of disiloxane: hexamethyl, hexaethyl, hexapropyl, and hexabutyl disiloxane. Dielectric constants, densities, and refractive indices of dilute solutions in n-hexane were measured at 25 degrees Celsius and used to calculate o…

Harmonic quadrics and some ruled surfaces of a congruence

This note studies line congruences whose harmonic ruled surfaces are quadrics, using Cartan’s method of exterior forms and differential invariants of a moving tetrahedron. It derives conditions for harmonic ruled surfaces of focal surfaces to be quadrics and shows that such congruences generate a sp…

Characteristic Parameters of the Wind Wave Field in the Ocean

This paper develops a parameterization of storm wind wave fields in the ocean by combining recent ocean measurements with storm basin experiments and a previously derived energy balance equation. It reformulates the dimensionless distance and time scales for wave growth, estimates the turbulent coef…

Thermodynamics of $\mathrm{CsCl}$ – $\mathrm{RbCl}$ solid solutions at $25^\circ$

This study investigates the CsCl, RbCl, H2O system at 25 degrees to determine the solubility limits and thermodynamic properties of CsCl, RbCl solid solutions. Equilibria between liquid and solid phases were established by isothermal removal of supersaturation with prolonged stirring, solid phases w…

On Determining the Order of Reactions by Acidity

This paper examines how to determine the reaction order with respect to acidity in acid-catalyzed reactions, focusing on cases where simple plots of rate constants against the Hammett acidity function may give misleading values. Using kinetic data for the decomposition of formic acid in sulfuric aci…

The Effect of Replacing Hydrogen with Deuterium on the Polarizability of Molecules

This study examines how substituting hydrogen with deuterium affects molecular polarizability in liquids. Dispersion of light, refractive indices, densities, and static polarizabilities were measured for twelve deuterated compounds and their hydrogen analogues, with static values obtained by extrapo…

On the Influence of Surface Imperfections on the Propagation of Rayleigh Waves

This paper experimentally investigates how isolated surface imperfections affect the propagation of Rayleigh waves, a question relevant to seismology, nondestructive testing, and acoustic delay lines. Using pulsed measurements at 3 MHz on duralumin and steel rods, the study examines reflection, tran…

A Criterion for Semiconduct

The paper studies when a homogeneous proper Riemannian space whose stationary subgroup splits as a direct product acting on two orthogonal tangent subspaces admits a corresponding orthogonal decomposition into submanifolds. Using invariant moving frames, structure equations, and a lemma on matrices …

EXTENSION OF A GENERALIZED RANDOM PROCESS TO A COMPLETELY ADDITIVE MEASURE

The paper studies whether generalized random processes, specified as consistent cylindrical probability measures on the dual of a topological vector space, can be extended to completely additive measures on a full Borel sigma algebra. Using Gel'fand's formulation and an extension criterion of Erokhi…

STUDY OF THE ADSORPTION OF CATIONS ON PLATINIZED PLATINUM BY THE METHOD OF MEASURING ADSORPTION POTENTIALS

This study examines the specific adsorption of lead, cadmium, and zinc cations on platinized platinum by measuring adsorption-induced potential shifts and changes in anodic charging curves. Experiments in acid supporting electrolytes show positive potential shifts for these cations, strongest for le…

Polymerization of isobutylene under the action of boron fluoride adsorbed on silica gel

This study examines the polymerization of isobutylene at atmospheric pressure using boron fluoride adsorbed on silica gel, with emphasis on conversion and the fractional composition of low molecular weight products. Experiments varied temperature, space velocity, catalyst boron fluoride loading, cat…

On Universal Classes of Algebras

This paper studies universal classes of algebras of a fixed finite type, understood as abstract classes definable by universal first order axioms without quantifiers in the matrix. It introduces a closure operation and associated notions of relative universality, closed classes defined through conve…

On rhenium borides

This study investigates the poorly characterized rhenium, boron system, focusing on the phase composition of sintered alloys prepared across compositions corresponding to possible rhenium borides. Pressed mixtures of high-purity rhenium and boron powders were sintered in vacuum at 1900 degrees Celsi…

Corrections to the Article (DAN, 109, No. 4, 1956)

In the article by L. G. Mikhailov, “Investigation of One Type of Two-Dimensional Integral Equations,” published in *DAN*, vol. 119, no. 1, 1958:

A Remark on Dispersion Relations for the Scattering of $\pi$-Mesons on Nucleons

This note examines the assumptions needed to derive dispersion relations for pion, nucleon scattering amplitudes. Contrary to claims that the pion must be treated as an elementary local field, the argument assumes locality only for the nucleon and treats the pion as a possible bound complex, using s…

ON SOME EXACT SOLUTIONS OF THE EQUATIONS OF GAS DYNAMICS

The paper examines whether an ideal, nonconducting gas can contain a shock wave followed by a region where sound speed is nonzero but disturbances, including another shock wave, never overtake the leading shock. It constructs exact limiting self-similar solutions of the one-dimensional unsteady gas-…

On the Aizerman Problem for the Case of a System of Three Differential Equations

This paper studies the Aizerman problem for a three-dimensional system of differential equations reducible to a canonical form with one scalar nonlinearity satisfying generalized Hurwitz conditions. It classifies parameter regimes for which the zero solution is globally stable for every admissible n…

Some Types of Local Nomograms

This note studies local nomographic representation of sufficiently smooth functions of two variables near a point where the first partial derivatives are nonzero. Building on earlier results using the Massau determinant and Saint-Robert invariant, it derives conditions under which such functions can…

On the Convergence of the Method of Lines under Various Schemes of Its Application to the Solution of Certain Boundary Value Problems

This note examines convergence difficulties in the method of lines when applied to boundary value problems for nonrectangular planar domains, focusing on the Dirichlet problem for the Laplace equation. It shows that the customary scheme can require artificial continuation of boundary data and may le…

Study of the Oxidation-Reduction Potentials of Plutonium in Nitric Acid

This study determines formal oxidation-reduction potentials of several plutonium couples in nitric acid, where previous data were limited, and examines the disproportionation of Pu(IV). Potentials were measured at 25 degrees Celsius under nitrogen, with plutonium oxidation states determined spectrop…

Toward the Theory of Multiple Generation of Elementary Excitations

This paper develops a statistical theory for multiple production of elementary excitations in superfluid helium when a localized compound system with finite energy decays into quasiparticles. Using Fermi’s equal a priori probability approach, the author derives phase space expressions for relative d…

Thermal and X-ray phase analyses of the $\mathrm{CsF}$ – $\mathrm{BeF}_2$ system and its relationship with systems of the $\mathrm{Me^IF}$ – $\mathrm{BeF}_2$ type

The study investigates the CsF, BeF2 binary system as a fluoride model relevant to structural relationships in oxide systems. Using differential thermal analysis and X-ray phase analysis, the authors construct a phase diagram, identify four cesium fluoroberyllates, Cs3BeF5, Cs2BeF4, CsBeF3, and CsBe…

Reaction of Free Radicals in Solutions. Interaction of Free Radicals with Internal and External Double Bonds

This study examines the relative reactivity of internal and external double bonds toward free radicals in solution and polymer media. Methyl radicals generated from methylphenyltriazene and dimethylcyanomethyl radicals generated from azoisobutyric acid dinitrile were reacted with hydrocarbons and po…

Effect of Sodium Nitrate Concentration in Aqueous Solution on the Degree of Its Radiolytic Transformation

This study examines how sodium nitrate concentration affects nitrite formation during gamma radiolysis of strongly alkaline aqueous solutions. Using cobalt-60 irradiation, the authors measured initial sodium nitrite yields over sodium nitrate concentrations from 10^-7 to 6 M, and compared solutions …

Equilibrium Potentials of Titanium in Chloride Melts

This study measures the equilibrium potentials of titanium electrodes in molten lithium and potassium chloride eutectics containing dissolved titanium chloride, motivated by their relevance to electrolytic titanium deposition and refining. Using sealed argon cells, titanium introduced by anodic diss…

On the Application of Some Integro-Differential Operators

This note develops special integro-differential operators related to Riemann-Liouville and Weyl fractional integration and applies them to Dirichlet series and generalized quasianalytic classes. It defines operator classes for functions on half-lines, proves a Taylor-type expansion whose coefficient…

On the General Theory of Optimal Processes

This note gives a brief proof of Pontryagin’s maximum principle for a general optimal control problem in which a trajectory of a controlled differential system joins two prescribed points while minimizing an integral functional. The argument treats admissible controls as bounded measurable mappings …

Kinetics of Polycondensation of Dicarboxylic Acid Chlorides with Dihydric Phenols

This study examines the kinetics of polyester formation by exchange decomposition between dicarboxylic acid chlorides and dihydric phenols, a comparatively little studied route to polyesters. Reactions of isophthaloyl, terephthaloyl, and sebacoyl chlorides with several phenols were carried out in di…

Formation of the Structure of a Plasma during the Development of a Discharge

This study investigates how spatially stable luminous layers form in the positive column during the temporal development of pulsed hydrogen discharges. Using a cylindrical discharge tube at pressures of 2.8, 3.8, and 4.5 mm Hg and rectangular microsecond voltage pulses, the authors interrupted disch…

Nitrogen Adsorption Isotherm at Low Pressures

This study examines nitrogen adsorption at very low pressures, a range important for adsorption thermodynamics, heterogeneous surface analysis, and vacuum technology. Using volumetric measurements at 77.6 and 90.1 K on several porous and nonporous adsorbents, the work compares the applicability of c…

Construction of Tie-Lines in Two-Phase Regions of Phase Diagrams of Metallic Systems by the Microhardness Method

This paper addresses the difficult problem of locating tie-lines in two-phase regions of ternary metallic phase diagrams, where direct determination of phase compositions is often laborious. It proposes a microhardness-based geometrical method that uses the dependence of solid-solution microhardness…

Effect of Silicon on the Solubility of Oxygen in Iron and Chromium Melts

This study examines how silicon additions up to 1.5 percent affect the solubility of oxygen in liquid iron and chromium melts at 1600°C. Equilibrium experiments measured oxygen concentrations after formation of an oxide phase, with additional observations for iron, chromium, and nickel-containing al…

APPLICATION OF THE THEORY OF ENTIRE FUNCTIONS TO THE CONSTRUCTION AND STUDY OF \(N'\)-FUNCTIONS COMPLEMENTARY TO GIVEN \(N'\)-FUNCTIONS

The paper studies the construction and asymptotic analysis of Orlicz complementary \(N'\)-functions without imposing prior growth restrictions on a given \(N'\)-function. It associates to \(M(u)\) the entire function \(F(z)=\sum_{n\ge 0} e^{-M(n)}z^n\) and proves that \(\ln F(e^v)\) is equivalent to…

GENERAL RELATIONS BETWEEN ABSORPTION AND EMISSION FOR MODULATION SPECTRA OF POLYATOMIC MOLECULES

The paper derives general relations between absorption and emission spectra for polyatomic molecules whose spectra can be treated as modulation spectra, with electronic and vibrational states considered separable. Using equilibrium between luminescent molecules and blackbody radiation, together with…

Spectral Study of the Interaction of Two Dyes in Solution

This study examines the interaction of thiazine and acridine dyes in aqueous solution using absorption spectroscopy. Spectra of dye mixtures were compared with additive calculated curves, and mass action calculations were used to estimate bound fractions, dissociation constants, and spectra of the h…

Production of 2,3-Dimethylbutadiene by a Catalytic Method

This study examines catalytic routes to 2,3-dimethylbutadiene-1,3, a potential precursor for rubber-like polymers and preparative organic synthesis, from branched hexenes obtainable from petroleum fractions. tert-Butylethylene and tetramethylethylene were dehydrogenated over industrial butylene-to-d…

Inversion of “Nonplanar” Circuits

This paper addresses the inversion of spatial or “nonplanar” relay-contact circuits, arguing that apparent nonplanarity does not affect circuit operation because such circuits can be transformed into equivalent planar H-shaped circuits with only a fictitious increase in single-valued elements. It pr…

Steepness of developing waves at different wind speeds

This paper examines how wind speed affects the steepness of developing wind waves, especially the intermediate stage between the attainment of maximum steepness and the later decrease toward limiting oceanic conditions. Storm-basin experiments at approximately 7, 11, and 15 m/sec used direct photogr…

On first-order differential equations in a Hilbert space with a variable positive-definite self-adjoint operator whose fractional power has a constant domain of definition

This note studies the Cauchy problem for first order differential equations in a Hilbert space with a time dependent positive definite self-adjoint operator whose full domain may vary, but whose fractional power has a fixed domain. Under a Lipschitz condition on the fractional-power conjugates \(A^\…

The phenomenon of zone formation on electrodes during the electrocrystallization of metals

This study examines the formation of concentric zones on electrodes during electrocrystallization, extending earlier observations from lead peroxide and copper deposition to multiple metal alloys, pure metals, and copper anodic dissolution. Using a cell with a small opening or electrode facing a lar…