Recent Papers

Excitation Spectrum of Excitons in a Crystal Lattice*)

Toward a Quantitative Consideration of the Process of Latent Photographic Image Formation by Ionizing Particles

The paper develops a quantitative treatment of latent photographic image formation in nuclear emulsions by relating the observed track density of ionizing particles to the probability that a struck silver halide crystal becomes developable. It extends Zhdanov’s track density formula by introducing a…

UNIQUE DETERMINATION OF CERTAIN CONVEX SURFACES IN LOBACHEVSKY SPACE

This paper studies intrinsic rigidity for several classes of convex surfaces in Lobachevsky space. It defines caps, generalized horospherical caps, and acute infinite convex surfaces, then proves that under bounded specific curvature and stated boundary or asymptotic conditions, an isometric convex …

Effective cross section for the “transfer” of a $\mu$-meson from a proton to a deuteron

This paper calculates the effective cross section for transfer, or stripping, of a mu meson from a proton to a deuteron, a process central to the deuterium concentration dependence of muon catalysis in the reaction between hydrogen and deuterium. The author formulates the three-body proton, deuteron…

Synthesis of the Alkaloid Emetamine

This paper reports a synthesis of racemic emetamine, a minor alkaloid of ipecacuanha roots whose structure had been inferred from its relationship to emetine and from oxidative degradation studies. Using a previously developed route to emetine, the authors prepared an ester precursor, coupled it wit…

On Double Salts of Lanthanum, Cerium, Praseodymium, and Neodymium with Triphenylbenzyl Arsonium Nitrate

This paper investigates double nitrates formed by lanthanum, trivalent cerium, praseodymium, and neodymium with triphenylbenzylarsonium nitrate, extending earlier work on related organic-base salts of rare-earth elements. The compounds were prepared by combining rare-earth nitrates with triphenylben…

On the Tautomerism of Diphenyl Phosphite

This paper examines whether replacing alkoxy groups in dialkyl phosphites with more electrophilic phenoxy groups can shift phosphite tautomerism toward a form displaying trivalent phosphorus reactivity. Diphenyl phosphite was synthesized by hydrolysis of diphenyl chlorophosphite and characterized by…

X-ray Study of the Crystal Structure of $\mathrm{TiSi}$ and $\mathrm{TiGe}$

This study addresses the previously undetermined crystal structures of the binary titanium compounds TiSi and TiGe. Using chemically synthesized samples, single crystal and powder X-ray diffraction, phase and chemical analyses, density measurements, and intensity calculations, the authors establish …

On the Uniform Convergence of Eigenfunction Expansions under Summation in Order of Increasing Eigenvalues

This paper studies uniform convergence of eigenfunction expansions for the equation Δu + λu = 0 in arbitrary domains of even dimension, under homogeneous boundary conditions of the first, second, or third kind, when terms are summed by increasing eigenvalues. It proves that the usual smoothness assu…

Activity of Zinc Oxide in Lead- and Copper-Smelting Slags Subjected to Fuming

This paper examines the activity of zinc oxide in lead-smelting slags during fuming, with comparison to previously studied copper-smelting slags. Using fuming-rate data, gas-phase equilibrium relations for reduction by carbon monoxide and hydrogen, and an oxygen material balance, the authors calcula…

ON THE PROBLEM OF GENERAL ANAMORPHOSIS

This paper addresses the nomographic problem of determining when an equation of the form z = F(x,y) can be represented by a Soreau determinant and thus solved by an aligned-points nomogram. Assuming sufficient differentiability and nonvanishing first partial derivatives, it derives differential cond…

On elliptic equations containing small parameters in the highest derivatives

The paper studies linear elliptic partial differential equations in which a small parameter multiplies the highest derivatives, under homogeneous first boundary-value conditions. For even-order operators satisfying positivity, ellipticity, and characteristic root assumptions, it analyzes how solutio…

Stability of Periodic Solutions of Quasilinear Autonomous Systems with Many Degrees of Freedom

This paper studies the stability of periodic solutions in quasilinear autonomous systems with many degrees of freedom when the associated linear system has a multiple zero root and may have multiple purely imaginary roots, while the remaining roots have negative stability exponents after the chosen …

Investigation of Systems of Normal Paraffin Hydrocarbons $\mathrm{C}_{30}$ – $\mathrm{C}_{34}$ and $\mathrm{C}_{30}$ – $\mathrm{C}_{36}$

Binary systems of high molecular weight normal paraffins, triacontane with tetratriacontane and triacontane with hexatriacontane, were investigated to establish their phase behavior, which had not previously been described. Synthesized and purified hydrocarbons were examined mainly by differential t…

LUMINESCENCE OF TRIVALENT URANIUM

This paper reports the observation of infrared luminescence from uranium-doped alkaline-earth fluoride single crystals grown under strongly reducing conditions, challenging the view that uranium luminescence is confined to hexavalent uranyl compounds. Absorption and emission spectra of CaF2, SrF2, a…

Some Data on Heterodiffusion Coefficients in $\mathrm{Cu}$ – $\mathrm{Ni}$, $\mathrm{Fe}$ – $\mathrm{Ni}$, and $\mathrm{Fe}$ – $\mathrm{Cr}$ Alloys with Distorted and Undistorted Crystal Lattices

This study determines heterodiffusion coefficients in Cu, Ni, Fe, and Cr alloy systems using an X-ray method applied to electrolytically coated metal disks and films. Specimens were prepared with distorted nonequilibrium lattices, with preliminarily annealed equilibrium components, or with mixed ini…

On an Equation of Elliptic Type Degenerating on the Boundary of the Domain

This paper studies boundary value problems for a second-order elliptic equation that degenerates on part of the boundary, with analytic lower-order coefficients and nonpositive zeroth-order term. It introduces an auxiliary singular weight describing the behavior of solutions near the degeneracy set …

On Nitroperfluoroalkyl Nitrites

This paper examines the chemistry of beta-nitroperfluoroalkyl nitrites, newly accessible from fluoroolefins and nitrogen oxides, with emphasis on their hydrolysis and alcoholysis. The authors show that hydrolysis gives unusually stable alpha-nitroperfluorocarboxylic acids rather than the behavior ty…

On the Nature of Catalytic Hydrogen Currents in Polarography

This paper examines the mechanism of catalytic hydrogen waves in polarography, focusing on cases produced by organic bases such as pyridine. It argues that these currents are not caused by a lowering of the activation energy for hydrogen ion discharge, but by a reversible discharge of the protonated…

Two Methods for the Technical Synthesis of Methylpentadiene

This paper presents two technical routes for synthesizing methylpentadiene, a diene of interest for polymer and copolymer production but previously of limited industrial accessibility. The first method involves catalytic cleavage of 2,4,4,6-tetramethyldioxane-1,3 with steam at 300 to 325°C, giving a…

On the Process of Halogenation of Coals under the Action of Ultrasonic Waves

This paper examines the use of ultrasonic waves to accelerate the halogenation of coal, a heterogeneous process relevant to rare element extraction but ordinarily slow and inefficient under mild conditions. Experiments with long flame coal show that insonation at 380 kc and 8 W per square centimeter…

Theoretical Model of a Cumulus Cloud

This paper develops a theoretical, plane, stationary model of ordered thermal convection in an atmosphere without general air motion, intended to describe conditions under which cumulus cloud formation may occur. Starting from simplified thermohydrodynamic equations with small temperature and pressu…

Embedding Theorems for Abstract Set Functions

This note extends Sobolev embedding theorems to abstract functions of sets in the space Ψp, defined as the closure of step measurable functions and characterized by absolute continuity and continuity under shifts. It defines integrals of such set functions against Lp′ kernels, proves continuity resu…

Synthesis and Properties of Mono-, Di-, and Tri-$n$-tolylalkylsilanes

This study addresses the limited knowledge of organosilicon hydrocarbons containing p-tolyl groups, particularly alkyl-substituted mono-, di-, and tri-p-tolylsilanes and related ethoxy derivatives. The authors synthesize these compounds through reactions of p-tolyl organolithium or Grignard reagents…

Tautomerism of arylazotropolones

This communication investigates the tautomerism of 5-arylazotropolones, whose observed reactivity was found to be inconsistent with a simple arylazotropolone structure. A series of compounds prepared by azo coupling of substituted tropolones with diazonium salts was examined through reactions with o…

On Annual and Semiannual Oscillations of the General Circulation of the Oceans

This paper examines why major northern ocean currents, including the Kuroshio and Gulf Stream, often show semiannual variations in transport that exceed their annual component, even though the atmospheric wind stress over the oceans is largely annual. Fedorov argues that the effect arises from the i…

New Data on the Relationship Between the Structure of Polysaccharides (Cellulose) and the Direction of Chemical Reactions Occurring During Their Thermal Decomposition

This study examines how the physical structure of cellulose, especially macromolecular packing density, influences the direction of chemical reactions during thermal decomposition in vacuum. Cellulose preparations of similar chemical composition but different structural states were produced by disso…

On Non-Molecular Scattering of Light in the Upper Layers of the Atmosphere

This paper examines nonmolecular scattering of light in the upper atmosphere using searchlight sounding and refines the sounding equation to account for atmospheric attenuation, broad background radiation from the searchlight beam, and nonuniform photocathode sensitivity. It derives approximate and …

Some Theorems on the Stability of Solutions of Parabolic Systems

This note studies Lyapunov stability of the trivial solution for systems parabolic in the sense of I. G. Petrovskii, including systems with time-dependent coefficients in a half-space. Using estimates for the Green matrix, it gives sufficient conditions for stability and asymptotic stability in weig…

Corrections to V. N. Ivanov’s Article “The Multiplicative Integral and an Almost-Periodic Matrix” (DAN, Vol. 109, No. 5, 1956)

Ternary fission of uranium by fast particles

On the numerical solution of a boundary value problem for a system of ordinary differential equations

This paper studies a finite difference approximation for a boundary value eigenvalue problem involving a system of ordinary differential equations with piecewise discontinuous coefficients and matching conditions at interior points. Under symmetry, positivity, smoothness, and equal mesh size assumpt…

ON FILTRATION IN A RECTANGULAR COFFERDAM WITH A VERY LARGE HEIGHT OF CAPILLARY RISE

This paper analyzes steady filtration through a very high rectangular cofferdam when the capillary rise is also taken to be very large and the capillary zone is fully saturated. Using a complex potential formulation, conformal mapping, and Christoffel-Schwarz transformations, it derives integral rel…

Embedding Theorems for a Space with a Metric Degenerating at a Finite Number of Interior Points of a Bounded Domain

This paper proves embedding results for function spaces on a bounded plane domain whose metric degenerates at an interior point. It defines completions of smooth functions vanishing near the boundary and the singular point under weighted quadratic forms involving first, and then second, generalized …

A. F. Ioffe. Semiconductor Thermoelements. Publishing House of the Academy of Sciences of the USSR, Moscow–Leningrad, 1956, 103 pp., price 3 rubles 80 kopecks, 20,000 copies.

On the Question of Periodic Solutions of Nonlinear Systems with a Small Parameter

This note addresses whether an asymptotically stable periodic solution of a nonlinear system persists, in a suitable sense, under small periodic perturbations. For a system with continuous periodic right hand side and a small parameter, the argument reduces the unperturbed solution to the origin, us…

On the Existence of Eigenfunctions for the Schrödinger Equation

This note proves the existence of an infinite sequence of eigenvalues for a many-particle Schrödinger operator in Euclidean space with attractive Coulomb terms to a fixed center and repulsive pair interactions. Under the condition that each attractive coefficient exceeds the sum of the corresponding…

ON THE MECHANISM OF ACTION OF REAGENTS IN FLOTATION

This paper examines the role of the three-phase contact line in the action of collector reagents during froth flotation, addressing earlier hypotheses that reagent molecules concentrate preferentially at the mineral, water, and air boundary. Using potassium ethyl xanthate labeled with radioactive su…

Mass Spectroscopic Study of Discharge Products in Water Vapor

This study investigates atoms and radicals formed in a glow discharge in water vapor, with emphasis on the possible presence of oxygen atoms alongside hydrogen atoms and free hydroxyl. The authors used a specially designed mass spectrometer with a modulated molecular beam to reduce background and wa…

On surfaces $V_n$ with multidimensional isotropic conjugate directions in spaces $R_N$ or $S_N$

This paper studies multidimensional surfaces in Euclidean and non-Euclidean spaces whose tangent spaces decompose into completely isotropic, pairwise weakly conjugate directions. Using the moving frame method and Cartan exterior forms, it derives restrictions on the first normal plane and proves tha…

ON ALKYL ESTERS OF ETHYLTHIOARSINOUS ACID

This paper describes the preparation and properties of alkyl esters of ethylthioarsinous acid of the general formula C2H5As(SR)2, a class of compounds previously little studied. The authors synthesize several ethyl, propyl, butyl, isoamyl, and hexyl derivatives by reactions of ethyldichloroarsine wi…

ASYMPTOTIC BEHAVIOR OF SOLUTIONS OF A NONLINEAR BOUNDARY-VALUE PROBLEM IN BOUNDARY-LAYER THEORY

This note studies the large argument behavior of solutions to a nonlinear third order boundary value problem arising in boundary layer theory, with parameters beta at least zero and positive limiting slope k. The authors transform the problem by using the dependent variable as the independent variab…

Oxides of Some Derivatives of $\alpha$-Pinene and Their Isomerization

This study examines whether substituted derivatives of alpha-pinene oxide undergo the skeletal isomerization previously observed for alpha-pinene oxide itself. The authors synthesized a series of myrtenyl-derived alpha-pinene oxides by oxidation with acetyl hydroperoxide and treated selected oxides …

Tungsten–boron phases

This study refines the phase relations in the tungsten, boron system using hot-pressed and annealed alloys examined by chemical, microhardness, metallographic, and X-ray methods. Alloys with nominal compositions from very low boron content to boron-rich preparations were analyzed to identify phase f…

Intercrystalline interlayers in gypsum

This paper investigates the nature and properties of intercrystallite boundaries in natural polycrystalline gypsum dihydrate, a nonmetallic material relevant to building practice. Using polarizing microscopy of thin sections, acid etching, dye adsorption, in situ heating, fracture observation, and c…

ON A FAMILY OF CLASSES OF FUNCTIONS OF THE ALGEBRA OF LOGIC AND THEIR REALIZATION IN THE CLASS OF $\Pi$-CIRCUITS

This paper studies the realization of Boolean functions by parallel series contact circuits, focusing on the classes of functions of n variables that take the value 1 on exactly k input sets. It presents a synthesis method based on grouping identical columns in the matrix of the satisfying assignmen…

Further Considerations on the Physical Interpretation of Lorentz Transformations

In the present article, I will not consider all the problems discussed in the previous work, but will examine in greater detail certain selected aspects of the problem. In particular, I will consider, in much more detail than before, questions of the dynamics of a rigid body (or a closed physical sy…

Saponification and transesterification of complete esters of phosphorous acid

This study examines the saponification of full phosphorous acid esters, P(OR)3, by water and the transesterification of trialkyl phosphites with alcohols. Using dilatometric and refractometric measurements, the authors compare hydrolysis rates for several trialkyl and triphenyl phosphites, finding s…

Sequence of Hydrogenation of the Double Bonds of Cyclopentadiene on Pd and Pt Blacks

This study examines the liquid-phase hydrogenation of cyclopentadiene on palladium and platinum black catalysts at 25 °C and atmospheric pressure, using cyclohexane or ethanol as solvent. By following hydrogen uptake kinetics and testing for residual cyclopentadiene, the authors compare the sequence…

Addition of Trialkyl Phosphites to $\alpha$ , $\beta$-Unsaturated Aldehydes

This paper investigates the addition of trialkyl phosphites to alpha,beta-unsaturated aldehydes, chiefly acrolein and crotonaldehyde, as an extension of earlier work on related unsaturated acids. The authors prepare and characterize several addition products, examine their behavior under distillatio…