Showing 50 of 25456 papers

On the Convergence of Galerkin-Type Methods

Unknown
1958 SovietRxiv: ru-195801.55808

This paper presents a general Hilbert space framework for studying convergence of Galerkin type approximation methods for equations of the form Au plus lambda Ku equals v, where A is invertible and K is a linear perturbation. Using Kantorovich’s abstract scheme, it formulates determinant and compact…

ON SCATTERING AND POLARIZATION OF LIGHT IN THE ATMOSPHERE UNDER THE CONDITIONS OF THE LIBYAN DESERT

![Fig. 1](image)
1958 SovietRxiv: ru-195801.55796

This paper reports visual photometric observations of clear daytime sky brightness and polarization made in the Libyan Desert near Aswan in October and November 1957, using measurements along the solar almucantar with a yellow filter and Polaroid. From brightness measurements at three Polaroid orien…

Study of Hydrogen Peroxide Formation Reactions during the Oxidation of $2$-Ethylanthrahydroquinone and Isopropanol by the Isotopic Method

Corresponding Member of the Academy of Sciences of the USSR A. I. Brodskii, V. I. Franchuk,
1958 SovietRxiv: ru-195801.55734

This study examines the mechanism of hydrogen peroxide formation during oxidation of 2-ethylanthrahydroquinone, tetrahydro-2-ethylanthrahydroquinone, and isopropanol by elemental oxygen. Using oxygen enriched in oxygen-18 and deuterium exchange in hydroxyl groups, the authors trace the origins of th…

On the Expansion in Eigenfunctions of Self-Adjoint Operators

Unknown
1958 SovietRxiv: ru-195801.55682

This note extends constructions of generalized eigenfunction expansions for self-adjoint operators from function spaces with differential basic operators to an abstract separable Hilbert space setting. The author defines basic elements as the domain of a closed densely defined operator with bounded …

SOLID SOLUTIONS IN THE SYSTEM AlSb—GaSb

N. A. GORYUNOVA and I. I. BURLIYAN
1958 SovietRxiv: ru-195801.55535

This paper investigates the pseudobinary AlSb, GaSb section of the Al, Sb, Ga ternary system, addressing earlier reports that the components form a eutectic system with negligible mutual solid solubility. Alloys of selected compositions were prepared and examined by thermal analysis, microstructure,…

Calculation of the Lower Bound of the Explosion Frequency Curve

L. G. BOLKHOVITINOV and P. F. POKHIL
1958 SovietRxiv: ru-195801.55469

This paper derives an estimate for the lower limit of the explosion frequency curve in drop weight impact tests of explosives, focusing on a stamp apparatus in which the material can flow freely. Assuming that initial heating arises from plastic deformation and that explosion begins early in the col…

Formation of Free Radicals in Bimolecular Reactions. Reaction Between Triphenylchloromethane and Ethyllithium

F. S. DYACHKOVSKII, N. N. BUBNOV, and A. E. SHILOV
1958 SovietRxiv: ru-195801.55334

This paper examines Semenov’s hypothesis that bimolecular reactions forming free radicals can have low activation barriers when the radical-forming step is nearly thermoneutral or exothermic. The authors study the reaction of triphenylchloromethane with ethyllithium in solution using electron parama…

Experimental Study of the Statistical Characteristics of the Scintillation of a Terrestrial Light Source

Unknown
1958 SovietRxiv: ru-195801.55272

This paper reports an experimental test of theoretical predictions for scintillation of a terrestrial light source propagating through atmospheric turbulence. Measurements were made over flat steppe paths of 250 to 2000 m using a modulated optical source, photomultiplier receivers with variable aper…

Estimating the domain of convergence of periodic series solutions of differential equations with a small parameter

Unknown
1958 SovietRxiv: ru-195801.55200

The paper develops a Lyapunov-based method for estimating the convergence domain of small-parameter series representing periodic solutions of nonlinear differential systems near a generating periodic solution, including resonant cases where characteristic roots are integral imaginary values. It deri…

On the Mechanism of the Emulsifying Action of Solid Emulsifiers

A. B. TAUBMAN and A. F. KORETSKII
1958 SovietRxiv: ru-195801.55064

This study examines the mechanism by which highly dispersed solid emulsifiers, specifically bentonite clay, stabilize oil in water emulsions, questioning whether selective wetting and monolayer particle coverage alone are sufficient. Emulsion stability and interfacial layer properties were measured …

The synthesis of organomercuric compounds via diaryliodonium salts

Corresponding Member of the USSR Academy of Sciences O. A. REUTOV, O. A. PTITSYNA, and XU XUN-WEN
1958 SovietRxiv: ru-195801.55007

This study examines the synthesis of organomercury compounds by decomposing diaryliodonium salts and their mercuric chloride double salts with metallic reducing agents. Experiments with the diphenyliodonium chloride mercuric chloride double salt showed that mercury in water gave the best yield of ph…

On the Mass Spectra of Large Molecules

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1958 SovietRxiv: ru-195801.54651

This paper examines the mechanism of electron impact dissociation in large organic molecules, challenging the view that mass spectra arise mainly through simple bond rupture. The authors synthesize n-nonane labeled with carbon 13 at the central carbon and compare its mass spectrum with that of norma…

On Thermophoresis in an Aerosol Flow

N. A. FUKS and S. S. YANKOVSKII
1958 SovietRxiv: ru-195801.54619

This paper examines thermophoresis of aerosol particles in a gas flow, focusing on discrepancies between established limiting theories and deposition patterns observed in thermoprecipitators. After reviewing expressions for thermophoretic force and velocity for particles much smaller or larger than …

Kinetic Isotope Effect in the Reaction of Hydrogen and Tritium with Oxides of Some Metals

V. A. SHUSHUNOV and B. Ya. ANDREEV
1958 SovietRxiv: ru-195801.54400

This study investigates kinetic isotope effects in topochemical reduction reactions of selected metal oxides with hydrogen and tritium, using gas mixtures containing hydrogen and trace HT. Reaction progress was measured from pressure decrease, while isotope composition was followed radiometrically, …

On the Non-Uniqueness of the Solution to the Hydrofoil Problem

N. N. MOISEEV and A. M. TER-KRIKOROV
1958 SovietRxiv: ru-195801.54173

This paper examines nonuniqueness in the nonlinear plane hydrofoil problem for flows with a free surface, especially for Froude numbers near the critical value. Using a conformal mapping formulation and Lavrent’ev-type estimates for the free boundary, the authors derive an approximate nonlinear diff…

Characteristics of Electromagnetic Cascades in Photoemulsion Taking into Account the Influence of the Medium on Radiation Processes

A. A. VARFOLOMEEV, D. I. GOLENKO, and I. A. SVETLOLOBOV
1958 SovietRxiv: ru-195801.54113

Monte Carlo calculations are presented for electromagnetic cascades in Ilford G-5 photographic emulsion initiated by electrons of 10^11 and 10^12 eV over depths up to 1.5 radiation lengths. The simulations use nonasymptotic cross sections for bremsstrahlung, pair production, Compton scattering, phot…

Study of the Radiolysis of Hydrocarbons by Spectral Methods

Unknown
1958 SovietRxiv: ru-195801.53955

This study examines the liquid-phase products formed during gamma radiolysis of hydrocarbons, with emphasis on normal alkanes and especially heptane. Ultraviolet and infrared absorption spectroscopy were used to identify unsaturated products after irradiation in sealed, evacuated, deoxygenated ampou…

On the theory of fractional differentiation and integration of periodic functions belonging to the class $L_p$, $p>1$

I. I. OGIEVETSKII
1958 SovietRxiv: ru-195801.53866

This paper studies Weyl fractional integration and differentiation of periodic functions in \(L_p\), \(p>1\), through the behavior of best trigonometric approximation in the \(L_p\) metric. It proves that fractional integration increases, and fractional differentiation decreases, the order of best a…

ELECTROCHEMICAL BEHAVIOR OF ZIRCONIUM IN SULFURIC ACID

Unknown
1958 SovietRxiv: ru-195801.53765

The study examines the cathodic and anodic behavior of high-purity zirconium in 1 N sulfuric acid at 25°C, with particular attention to the role of surface oxide films. Using polished, air-oxidized, and anodically oxidized electrodes under nitrogen, the authors measured open-circuit potential change…

Complex Compounds of Trivalent Cobalt Containing Thiourea

A. V. ABLOV and N. M. SAMUS’
1958 SovietRxiv: ru-195801.53548

This paper reports the preparation and characterization of trivalent cobalt dimethylglyoxime complexes containing thiourea in the inner coordination sphere, a class not previously described in the cited literature. The authors synthesize mono- and dithiourea complexes by substitution from chloro-bis…

UNSTEADY FLOW WITH HEAT TRANSFER IN A VISCOUS INCOMPRESSIBLE FLUID BETWEEN TWO ROTATING DISKS IN THE PRESENCE OF INJECTION

Unknown
1958 SovietRxiv: ru-195801.53368

This paper formulates an exact similarity reduction for unsteady axisymmetric motion of a viscous incompressible fluid between two parallel rotating disks with time-dependent angular velocities and injection velocities. The Navier-Stokes equations are reduced to a coupled system of one-dimensional n…

Adsorption of Hydrocarbons at Elevated Temperatures

I. V. SMIRNOVA and K. V. TOPCHIEVA
1958 SovietRxiv: ru-195801.53364

This study examines adsorption from n-heptane solutions of selected aromatic and cyclic hydrocarbons on industrial alumina at elevated temperatures relevant to heterogeneous catalysis. Interferometric adsorption measurements for benzene, propylbenzene isomers and unsaturated analogues, allylbenzene,…

Synthesis of Aromatic Hydrocarbons

Unknown
1958 SovietRxiv: ru-195801.53224

This paper describes a preparative method for synthesizing fluorene and substituted fluorene hydrocarbons by treating aryl-substituted tetrahydrobenzoic acid derivatives with phosphorus pentoxide. The authors show that phenyltetrahydrophthalic anhydride gives fluorene rather than diphenyl, and propo…

On the Deoxidizing Ability of Carbon in Vacuum

A. M. Samarin and R. A. Karasev
1958 SovietRxiv: ru-195801.53035

This study examines the deoxidizing ability of carbon dissolved in liquid iron under vacuum, addressing the discrepancy between thermodynamic predictions and observed behavior in vacuum melting. Experimental heats at 1590 degrees C were carried out at pressures of about 10^-2 and 10^-6 mm Hg, with p…

Proportional Navigation as a Problem of Cybernetics

A. S. KELZON and O. V. GRIGOR'EVA
1958 SovietRxiv: ru-195801.52809

This paper treats proportional navigation as a cybernetic guidance problem rather than only a kinematic problem of two moving points. For a target moving at constant speed and direction and an object with constant speed, the authors derive closed form expressions for the ideal trajectory, line of si…

Retention of the configuration of the propenyl radical in reactions of cis- and trans-propenyllithium with oxo compounds

A. N. NESMEYANOV, A. E. BORISOV, and N. V. NOVIKOVA
1958 SovietRxiv: ru-195801.52808

This study examines whether electrophilic replacement of lithium by carbon in cis- and trans-propenyllithium preserves the geometrical configuration of the olefinic radical. The authors prepared stereoisomeric propenyllithium from the corresponding propenyl bromides and reacted each with acetone, ac…

Radio Image of the Sun at a Wavelength of 3.2 cm

Unknown
1958 SovietRxiv: ru-195801.52734

This paper reports early observations of the two-dimensional radio brightness distribution of the Sun using a newly commissioned 31 m radio telescope at the Crimean station of the P. N. Lebedev Physical Institute. The authors describe a scanning method in which the antenna pattern was swept in decli…

ON THE STABILITY OF QUASILINEAR SYSTEMS WITH AFTEREFFECT

Unknown
1958 SovietRxiv: ru-195801.52711

This paper extends Lyapunov stability criteria for ordinary quasilinear systems to functional differential systems with aftereffect in a Banach space. The linear delayed equation is represented as an abstract ordinary equation on a space of continuous history segments, generated by an unbounded oper…

On the Theory of Newton's and Chaplygin's Methods

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1958 SovietRxiv: ru-195801.52595

This paper develops operator-theoretic generalizations of Newton and Chaplygin methods for solving nonlinear equations in ordered Banach-type and K-spaces. It replaces derivative inverses in iterative schemes by more general auxiliary operators, not necessarily invertible, and gives convergence cond…

Compounds of beryllium oxyacetate with sulfur dioxide

A. I. GRIGOR'EV, Corresponding Member of the Academy of Sciences of the USSR A. V. NOVOSELOVA
1958 SovietRxiv: ru-195801.52496

This study examines the interaction of beryllium oxyacetate with sulfur dioxide, a system expected to form weak inclusion type compounds rather than ordinary coordination complexes. Composition and vapor pressure isotherms between about minus 10 and minus 30 degrees Celsius were measured with a tens…

Genus of a Fibered Space

Unknown
1958 SovietRxiv: ru-195801.52483

This note introduces the genus of a locally trivial fiber space as the least cardinality of an open cover of the base over which local cross-sections exist, generalizing both earlier equivariant genus notions and the Lusternik-Schnirelmann category. It establishes basic functorial properties, compar…

On the Synthesis of Infusible but Soluble Polymers

Corresponding Member of the Academy of Sciences of the USSR K. A. ANDRIANOV,
1958 SovietRxiv: ru-195801.52440

This paper investigates whether polymers can be prepared that remain soluble in organic solvents while being infusible, a combination presented as contrary to the usual relation between solubility, melting, and molecular structure. The authors synthesize polyalumophenylsiloxane and polyalumoethylsil…

THE MEMBERSHIP PROBLEM FOR DIRECT PRODUCTS OF GROUPS

Unknown
1958 SovietRxiv: ru-195801.52405

The paper studies strong and weak membership problems for finitely presented groups under direct products, distinguishing them from the identity problem. It proves that the weak membership problem is unsolvable for the direct product of two free groups on two generators, by reducing Novikov’s unsolv…

Condensation of Acetals with Ethoxyisoprene. A New Method for the Synthesis of Polyene Aldehydes of the Isoprenoid Type

Academician **I. N. Nazarov** and Zh. A. Krasnaya
1958 SovietRxiv: ru-195801.52403

This paper describes the use of ethoxyisoprene as a reagent for synthesizing polyene aldehydes of the isoprenoid type, extending earlier applications of vinyl ethers to carotenoid-related aldehyde synthesis. The authors show that acetals, exemplified by dimethylacrolein aldehyde acetal, add to ethox…

Study of the phase composition and adsorption properties of an iron–carbon catalyst

S. M. Samoilov, A. A. Slinkin, and A. M. Rubinshtein
1958 SovietRxiv: ru-195801.52398

This study examines the phase composition, magnetic properties, adsorption behavior, and catalytic activity of two unused iron-carbon catalysts prepared on activated carbon and generator dust supports. X-ray diffraction, magnetic susceptibility measurements, thermomagnetic analysis, adsorption of to…

On the Connection of the Method of Nearby Systems in Special Linear Topological Spaces with Certain Questions in the Perturbation Theory of Linear Operators in Banach Spaces

Unknown
1958 SovietRxiv: ru-195801.52325

The paper studies how results from the perturbation theory of linear operators in Banach spaces extend to linear topological spaces formed from nested families of Banach spaces. It proves that Fredholm type properties of Phi operators, including normal solvability, finite defect characteristics, and…

Some Results of a Study of the Boundaries of the Elastic State of Plastically Stretched Nickel Specimens

Yu. I. Yagn and O. A. Shishmarev
1958 SovietRxiv: ru-195801.52232

This paper reports an experimental study of the boundary of the elastic state in thin walled nickel tubes plastically prestrained in tension and then subjected to combined tension and torsion. Using carefully controlled loading, deformation measurements, varied holding times, and specified tolerance…

On the Brittle Fracture of Zinc Single Crystals

V. I. Likhtman, L. A. Kochanova, L. S. Bryukhanova
1958 SovietRxiv: ru-195801.52162

This paper examines brittle fracture in high-purity zinc single crystals under two embrittling conditions: low temperature in an inactive medium and room-temperature deformation in the presence of mercury as a surface-active medium. Using uniaxial tension tests on crystals with varied basal-plane or…