Recent Papers

Corrections to the Article “Experimental Substantiation of the Chain Mechanism of the Heterogeneous-Catalytic Hydropolymerization Reaction of Olefins Proceeding under the Influence of Carbon Monoxide and Hydrogen” (Doklady, Vol. 115, No. 6, 1957)

X-ray diffraction study of 1,4-dianilidoanthraquinone and 1,4-dimesidinoanthraquinone

This paper investigates the relation between molecular coplanarity, steric hindrance, and color in 1,4-diarylaminoanthraquinone dyes. X-ray measurements were carried out on crystals of 1,4-dianilidoanthraquinone and 1,4-dimesididoanthraquinone to determine unit-cell parameters, space groups, densiti…

Corrections to the article “Covering of Areas for Functions Regular in an Annulus” (DAN, Vol. 114, No. 1, 1957)

Rings of Linear Unbounded Operators with Decomposition of the Identity and Their Representations

This paper develops a theory of rings formed by closed, densely defined linear operators in a Hilbert space that commute with a possibly nonorthogonal resolution of the identity. It defines admissible classes and operator bases to make addition, multiplication, limits, inverses, and analytic functio…

On the Radiolysis of Heptane

This study examines gamma radiolysis of liquid normal heptane and of a dilute dibenzyl sulfide solution in heptane, with emphasis on early-stage kinetics, the effect of interrupting irradiation, and gas composition over a wide dose range. Using X-ray and cobalt-60 irradiation, pressure recording, do…

Invariant Constructions on an $m$-Dimensional Surface in an $n$-Dimensional Affine Space

This paper studies invariant constructions associated with an m-dimensional surface in an n-dimensional affine space using the invariant-group method. Starting from the sequence of fundamental objects obtained by prolonging the surface equations, it constructs relative tensors and invariants that ch…

Study of Changes in Ion Transference Numbers and the Suspension Effect in Liquid Suspensoid Diaphragms

This study examines how ion transference numbers change in liquid suspensoid diaphragms and how these changes relate to the suspension effect, measured as differences in hydrogen ion activity between suspensions and their separated liquids. Bentonite and size-classified quartz suspensions in potassi…

Investigation of Longitudinal and Transverse Galvanomagnetic Effects in an $n$-Type Germanium Single Crystal Along the Principal Crystallographic Axes

This paper investigates anisotropy in the longitudinal and transverse galvanomagnetic effects of an ultrapure n-type germanium single crystal along the principal crystallographic directions [100], [110], and [111] within the (110) plane. To avoid differences between separate specimens, the authors u…

Some Questions on the Computation of Polynomials

The paper studies arithmetic schemes for evaluating a polynomial when its coefficients may be preprocessed once into auxiliary parameters, a setting motivated by repeated evaluation at many arguments. It constructs, over the complex numbers, a family of schemes for every degree n that uses floor((n+…

On the Conditions for the Existence of a Stigmatic Image in Electron-Optical Systems with a Curvilinear Axis

The paper derives sufficient conditions for the formation of a stigmatic image in the paraxial region of electron optical systems whose principal trajectory, and hence optical axis, is curvilinear. Using curvilinear coordinates tied to the principal trajectory, the author expands nearby electron pat…

On the Activation Energy of the Diffusional Creep Process in Metallic Disordered Substitutional Solid Solutions

This paper examines the activation energy of diffusional creep in disordered substitutional metallic solid solutions, treating creep as the result of vacancy-mediated self-diffusion under an applied stress. It derives expressions linking the creep activation energy to component self-diffusion coeffi…

On the Absence of Superconductivity in Ferromagnets

This paper examines why superconductivity is not observed in ferromagnetic metals using the microscopic theories of superconductivity and the s-d exchange model of ferromagnetism. The authors argue that exchange interaction splits the Fermi surfaces for conduction electrons with opposite spin projec…

On Dehydration and Rehydration of the Quartz Surface

This paper examines the dehydration and rehydration of quartz surfaces, addressing discrepancies between crystal-chemical estimates of surface hydroxyl concentrations and values inferred from thermal dehydration. Vacuum calcination experiments on opaque quartz and rock crystal, combined with quantit…

On substitution reactions in the methylene group of $\beta$-ketoacetals

This paper reports preliminary studies on substitution at the methylene group of β-ketoacetals, a reaction mode proposed to broaden their synthetic use beyond carbonyl condensations and transformations typical of β-dicarbonyl compounds. Bromination, dehydrobromination, oxidation with lead tetraaceta…

Exact Integral of the Field Equation for Wind Waves in the Ocean and Its Physical Significance

This paper derives and interprets an exact integral of a dimensionless quasilinear field equation describing the growth and spatial distribution of wind wave heights in the ocean. Using previously obtained exact solutions for steady wave-height distribution with fetch and for temporal growth at effe…

THE EMBEDDING PROBLEM FOR SPLIT EXTENSIONS

This note addresses the Galois embedding problem for a normal extension of algebraic number fields when the prescribed group is a split extension of the given Galois group. It announces that the problem is solvable for any algebraic number field when the kernel is nilpotent, thereby including earlie…

Plasma Radiation in a Magnetic Field

This paper analyzes radiation emitted by electrons rotating in a uniform magnetic field, with emphasis on high harmonics relevant to solar and cosmic radio sources. Starting from the single-electron spectrum, the author derives angle-averaged emissivities for ordinary and extraordinary polarizations…

Chlorination of Diacetylene. Synthesis of Hexachlorobutadiene-1,3

This paper reports a route for preparing hexachlorobutadiene-1,3 from diacetylene, addressing the lack of published data on diacetylene chlorination. Diacetylene was chlorinated in carbon tetrachloride at low temperature to give liquid and crystalline isomers of 1,1,2,3,4,4-hexachlorobutene-2, which…

Optical Sensitization of the Photoelectric Effect in Silver and Thallium Bromides by Organic Dyes

This study investigates the conditions under which organic dyes can optically sensitize the internal photoeffect in powdered silver bromide and thallium bromide, a question left unclear by earlier contradictory results. Using the capacitor method to measure spectral photo-emf in dyed and undyed brom…

Effect of Tetravalent Titanium Ions on the Electrochemical Properties and Corrosion Behavior of Titanium

This paper examines how tetravalent titanium ions affect the passivation, electrode potential, and corrosion rate of titanium in sulfuric and hydrochloric acid solutions. The authors relate titanium’s corrosion resistance to a protective titanium dioxide surface film and test whether adding Ti4+ shi…

On the Results of Determining the Electron Concentration of the Outer Region of the Ionosphere from Observations of Radio Signals from the First Earth Satellite

This paper analyzes observations of the 40 MHz radio signals from the first Earth satellite to infer the electron concentration in the outer ionosphere above the F2 maximum. The authors derive a geometrical optics method relating radio rise and set ranges to ionospheric refraction, using modeled ver…

On Some Types of Homogeneous Riemannian Spaces

This paper studies homogeneous Riemannian spaces with positive definite metric whose isotropy group fixes a subspace of the tangent space and acts irreducibly on its orthogonal complement, in the case where commuting rotations may exist. Using invariant moving frames, Maurer-Cartan equations, and al…

Synthesis of silicon olefin oxides from chlorohydrins

This study examines the synthesis of organosilicon olefin oxides from chlorohydrins obtained by reacting silicon-containing Grignard reagents with monochloroacetone. The authors show that this reaction proceeds selectively to give several tertiary-primary chlorohydrins, which can be converted to bet…

Preparation and Properties of Some Trichlorotitanium Alkoxy Compounds with Secondary and Tertiary Alkyl Groups

This paper reports the synthesis and characterization of several trichlorotitanium alkoxy compounds of the type TiCl3OR containing secondary or tertiary alkyl groups, motivated by interest in organotitanium species related to olefin polymerization catalysts. Isopropyl, sec-butyl, and cyclohexyl deri…

SOME ESTIMATES OF THE INTENSITIES OF HELIUM LINES IN THE SPECTRA OF NONSTATIONARY STARS

This paper examines rapid temporal changes in helium line intensities in nonstationary stellar spectra, especially lines connected with the metastable helium level 2 triplet S and the solar 10830 angstrom absorption line. It develops a simple kinetic model for a thin stellar shell in which electron …

On the Interaction of $\beta$-Cyanovinyl Ketones with Secondary Amines

This study examines reactions of β-cyanovinyl ketones with secondary amines, focusing on how aryl and aliphatic substrates differ in their behavior toward nucleophilic addition and substitution. Aryl-β-cyanovinyl ketones are shown to add diethylamine, piperidine, and morpholine at the double bond to…

Infrared Absorption Spectra of Oxybenzylamines

This paper investigates the use of infrared absorption spectroscopy to identify structural features of oxybenzylamines, proposed intermediates in the curing of phenol formaldehyde resins with hexamethylenetetramine. Spectra were obtained for model dibenzylamine and tribenzylamine compounds, low mole…

Temperature Changes in Intermolecular Distances in Paraffin n - $\mathrm{C}_{30}\mathrm{H}_{62}$. Refinement of the Shape of Paraffin Molecules

This paper examines anomalous intermolecular hydrogen distances in normal paraffin crystals, using temperature-dependent subcell parameters of n-C30H62 to distinguish thermal effects from features of molecular packing. The authors extrapolate measured rhombic subcell dimensions to low temperature an…

Phase transformations during compression of water by strong shock waves

This paper investigates phase transformations in water under dynamic compression by strong shock waves over pressures from 20,000 to 800,000 atm. The authors determine shock-wave and mass velocities using electrical-contact gauges and known aluminum screen Hugoniots, then derive pressure and density…

Chromatographic Analysis of Hydrocarbon Mixtures of Composition $\mathrm{C}_5$

This paper addresses the quantitative analysis of complex C5 hydrocarbon mixtures formed in isopentane dehydrogenation and present in light gasoline fractions, where conventional physical and chemical analyses are laborious. The authors develop a rapid chromatographic procedure combining chromatothe…

Sulfuric acid alkylation of toluene with $\mathrm{C}_{10}$ olefins

This study examines sulfuric acid catalyzed alkylation of toluene with C10 olefins obtained from polymerized pentane amylene fractions, motivated by the need to consider alternatives to benzene for alkylarylsulfonate detergent intermediates. Laboratory experiments varied acid concentration, temperat…

Polymerization of Isobutylene under the Influence of Boron Fluoride on Aluminum Oxide

This study examines the atmospheric pressure polymerization of isobutylene using boron fluoride adsorbed on aluminum oxide, with attention to temperature, space velocity, boron fluoride introduction, catalyst lifetime, and support effects. Experiments show high conversion over BF3 on alumina without…

On the Mercuration of Polystyrene

This paper examines the mercuration of polystyrene as a route to new high molecular weight derivatives, treating the polymer itself as a substrate for further synthesis. Polystyrene was reacted with mercury acetate under several solvent and temperature conditions, with acetic acid giving mercuriacet…

Mechanics of Stretched Polymer Systems

This article develops a mechanical approach to the stretching of polymer systems, using idealized rubber as the main example, and contrasts it with prevailing statistical thermodynamic treatments. It argues that deformation is governed by elastic stretching of polymer segments organized into primary…

On the Theory of Radiation Diffusion in a Semi-Infinite Medium

This note addresses radiation diffusion in a semi-infinite plane medium with spherical scattering indicatrix, following Sobolev’s reduction of luminosity problems to an integral equation for the function Phi of optical depth. Using one-sided Laplace transforms, inversion, and contour integration, th…

Catalytic Synthesis of $4$-Methyl-$2$-Phenyl-$5{,}6$-benzoquinoline and $2{,}4$-Diphenyl-$5{,}6$-benzoquinoline and Their Derivatives

This paper addresses the limited availability of convenient syntheses for 4-methyl-2-phenyl-5,6-benzoquinoline, 2,4-diphenyl-5,6-benzoquinoline, and related derivatives. The authors propose and test a catalytic condensation of Schiff bases derived from 2-naphthylamine and substituted aromatic aldehy…

GROWTH OF FERRITE SINGLE CRYSTALS BY THE VERNEUIL METHOD

This paper reports the preparation of ferrite single crystals by the Verneuil method in an oxygen-hydrogen flame, addressing the need for larger single crystals than those previously available from melt-solution growth. Charges were prepared by calcining ferric ammonium alum with sulfate salts of di…

On the Solubility of Finely Ground Quartz in Water

This paper investigates the solubility of finely ground quartz sand in distilled water at room temperature, motivated by the role of quartz in lime-sand binders, concretes, and grinding processes. Quartz powders produced by dry vibratory milling were characterized by nitrogen adsorption surface-area…

On the Possible Existence of a Second Neutral $\pi$ Meson

The paper examines a discrepancy between calculated and measured values of the Panofsky ratio in pion absorption and considers whether it may be resolved by hypothesizing a second neutral pion with isotopic spin zero. The authors analyze consequences of this hypothesis for charge-exchange scattering…

ASYMPTOTIC SOLUTION OF THE THOMAS–FERMI EQUATION

This paper derives an asymptotic representation for the solution of the Thomas-Fermi equation governing the statistical electron distribution in an atom, subject to the standard boundary conditions at the origin and infinity. By transforming the dependent variable around the known particular solutio…

On an Equation of Infinite Order with Polynomial Coefficients

This note studies differential equations of infinite order with polynomial coefficients, relaxing earlier restrictions that the polynomial degrees be uniformly bounded and that associated characteristic functions be analytic near the origin. Using the theory of infinite systems of linear algebraic e…

Determination of a Convex Surface by a Given Function of Its Principal Curvatures

This paper studies existence questions for convex surfaces whose principal curvatures satisfy prescribed elliptic relations involving the product and sum of the principal curvatures. It extends the associated curvature operators from twice differentiable convex graphs to arbitrary convex functions b…

Synthesis of Silicon-Containing Vinyl Ethers

This paper describes the synthesis of silicon-containing vinyl ethers, a class not readily accessible by conventional base-catalyzed vinylation because of the hydrolytic instability of silanol-derived alkoxy and alkenyloxy silanes. The authors develop a method based on chloroplatinic acid catalyzed …

Crystal structure of natrochalcite $\mathrm{NaCu}_2(\mathrm{OH})[\mathrm{SO}_4]_2\cdot\mathrm{H}_2\mathrm{O}= \mathrm{Na}[\mathrm{SO}_4]_2[\mathrm{Cu}_2,\mathrm{OH}_2\mathrm{H}_2\mathrm{O}]$

The study determines the crystal structure of natrochalcite from Chuquicamata and revises earlier crystallographic data, particularly the monoclinic cell parameter c. X-ray rotation and layer-line photographs, extinction analysis, heavy-atom methods, electron-density projections, and weighted Patter…

On the multidimensional limiting distribution of the numbers of busy lines in second-stage switches of a loss telephone system

This paper studies the stationary distribution of busy connecting lines in the second-stage switches of a two-stage loss telephone system operating under free search. Assuming independent Poisson input streams to first-stage switches, exponential holding times, and sufficient second-stage outlets to…

On the Influence of Oxygen on Paramagnetic Resonance Absorption in $\alpha\alpha$-Diphenyl-$\beta$-Picrylhydrazyl

This study examines how oxygen affects paramagnetic resonance absorption in finely powdered alpha,alpha-diphenyl-beta-picrylhydrazyl at 127 MHz. Measurements of line intensity and half-width under vacuum, atmospheric air, liquid oxygen, and liquid nitrogen show that lowering oxygen pressure increase…

Interaction of Alkyl Radicals with Nitrogen Dioxide

This study examines the elementary interaction of alkyl radicals with nitrogen dioxide, a key step proposed in vapor-phase alkane nitration, and tests whether nitro compounds and alkyl nitrites are formed by parallel pathways. Alkyl radicals were generated from hydrogen atoms and ethylene under low-…

Dipole Magnetic Field in Planetary Nebulae

This paper develops a quantitative model in which planetary nebulae possess their own dipole magnetic fields, generally of nonpoint character, rather than fields inherited directly from the central star. Using expressions for the magnetic field, pressure balance, and ion concentration, it derives ho…

Spectroscopic Study of the Adsorption and Catalytic Conversion of Cyclohexadiene on Transparent Palladium Films

This study develops a spectroscopic method for examining adsorption and catalytic transformations on transparent palladium films deposited in vacuum on optical cell windows, avoiding complications from extraneous gases. Ultraviolet and infrared spectra of cyclohexadiene-1,3 vapors in cells with pall…

On the Synthesis of Esters and Other Carboxylic Acid Derivatives under Acid Catalysis from Carbon Monoxide, Olefins, and Acylatable Compounds

This paper examines the acid-catalyzed synthesis of carboxylic acid esters and related derivatives from carbon monoxide, olefins, and acylatable compounds under comparatively mild conditions. The authors propose a two-stage method in which olefins and carbon monoxide first form an acylating complex …