Showing 50 of 25456 papers

Some Properties of Automorphisms of Nilpotent Groups

Unknown
1961 SovietRxiv: ru-196101.38969

This note studies automorphisms of nilpotent groups, focusing on when a finite set or group of automorphisms is nilpotent relative to the underlying group. It proves that for a nilpotent group, a finite set of automorphisms is nilpotent relative to the group exactly when it is nilpotent relative to …

Perturbation of a Linear Equation by a Small Nonlinear Term

Unknown
1961 SovietRxiv: ru-196101.38916

The paper studies a nonlinear perturbation of a normally solvable linear operator equation in complex Banach spaces, with a small parameter and polynomial nonlinear terms. By rescaling the unknown and applying branching theory, including Newton diagram arguments and a generalized Jordan chain relati…

Representation of the Solution of the Cauchy Problem for a System of Parabolic Type as a Wiener Integral

I. M. KOVALCHIK
1961 SovietRxiv: ru-196101.38740

The paper studies the Cauchy problem for a linear parabolic system with a bounded continuous matrix coefficient multiplying the unknown vector and bounded continuous initial data. It derives an integral equation formulation, expands its solution by successive substitutions, proves absolute and unifo…

Reactions of Diborane and Alkyldiboranes with Esters of Boric and Alkylboronic Acids and Their Thio Analogues

B. M. MIKHAILOV and L. S. VASIL’EV
1961 SovietRxiv: ru-196101.38515

This paper examines reactions of diborane, alkylboranes, and tetraalkyldiboranes with boric, alkylboronic, and dialkylborinic esters, including thio analogues. The authors propose reaction schemes involving reversible exchange of hydrogen, alkoxy, alkyl, and alkylthio groups at boron, showing that d…

On the Theory of Multiplication of Causal Functions

V. GARCHINSKII
1961 SovietRxiv: ru-196101.38095

This paper develops more explicit formulas for products of causal functions associated with strongly connected Feynman diagrams in quantum field theory. Using the incidence matrix of a diagram and Pauli-Villars regularization, it derives parametric momentum-space expressions whose characteristic det…

On the Best Uniform Approximation of Differentiable Functions

N. P. KORNEICHUK
1961 SovietRxiv: ru-196101.38091

This paper determines the exact upper bound for the best uniform approximation by trigonometric polynomials of degree at most n on the class of periodic differentiable functions whose first derivative has a prescribed convex modulus of continuity. The proof uses a lemma approximating functions with …

On the Mechanism of Initiation and Development of Pitting Corrosion on Stainless Steels

I. L. Rozenfel’d and I. S. Danilov
1961 SovietRxiv: ru-196101.38037

This paper examines the origin and growth of pitting corrosion on stainless steel in electrolytes containing chloride activators and oxidizing passivators. Using measurements of pit number, pit depth distributions, exposure time effects, and electrode potential, the authors show that both activator …

On the Divergence of Fourier Series

Unknown
1961 SovietRxiv: ru-196101.37889

This note studies prescribed convergence and unbounded divergence sets for trigonometric Fourier series, with attention to pairs of conjugate series. Building on constructions of Kolmogorov and the Herzog, Piranian, and Zeller method, it proves two auxiliary lemmas for producing trigonometric polyno…

On the Process and Products of Hydrolytic Decomposition of Titanium Tetrachloride

L. N. Shchegrov and Ya. E. Vilnyanskii
1961 SovietRxiv: ru-196101.37880

This study examines the vapor phase hydrolysis of titanium tetrachloride by water vapor in a dynamic system over 25 to 750°C, with several TiCl4:H2O molar ratios. The authors measured product composition, hygroscopic behavior, chloride retention, and phase structure using chemical analysis and X-ray…

Toward the Construction of the Theory of Elasticity

Unknown
1961 SovietRxiv: ru-196101.37631

The paper examines the construction of stress-strain relations for small deformations of isotropic elastic bodies that obey Hooke’s law in selected simple experiments, including hydrostatic compression, uniaxial tension and compression, and pure shear. Using a deformation potential expressed through…

Thermodynamic Properties of $\mathrm{Ag}$ – $\mathrm{Sb}$ Melts

A. A. VECHER and Ya. I. GERASIMOV
1961 SovietRxiv: ru-196101.37529

The study determines thermodynamic properties of liquid silver-antimony alloys by measuring the temperature and composition dependence of the electromotive force of a galvanic cell with an iodide melt electrolyte. Measurements for eight alloys between 10.3 and 79.5 atomic percent silver at 630 to 83…

A Generalization of the Group Principle of Duality

Unknown
1961 SovietRxiv: ru-196101.37104

This note proposes a generalization of locally compact unimodular groups, called ring groups, intended to accommodate both groups and the noncommutative objects arising as their duals. The construction replaces the commutative algebra of bounded functions on a group by a standard operator ring equip…

On the Theory of Crystals

Unknown
1961 SovietRxiv: ru-196101.36883

This paper proposes an exactly tractable model for a crystal based on a second-quantized Hamiltonian that retains density interactions associated with the periodic reciprocal lattice. It argues that, in the thermodynamic limit, the relevant density operators commute asymptotically with particle oper…

On a Mapping of a Hilbert Space into Itself

Unknown
1961 SovietRxiv: ru-196101.36788

The note constructs a homeomorphic embedding of separable Hilbert space into itself whose image consists only of points with coordinates between zero and one in a fixed orthonormal basis. The construction first replaces signs by separate coordinate directions to obtain nonnegative coordinates, then …

Properties of Phenylferrocene

A. N. Nesmeyanov, È. G. Perevalova, S. P. Gubin, T. V. Nikitina, A. A. Ponomarenko, L. S. Shilovtseva
1961 SovietRxiv: ru-196101.36786

This study examines how a phenyl substituent affects electrophilic substitution in phenylferrocene, focusing on aminomethylation, sulfonation, competitive acetylation, and nitration. Product isolation, elemental analysis, infrared spectra, and derivative transformations showed that aminomethylation …

HEAT OF DISSOCIATION\* OF KURNAKOV COMPOUNDS

I. I. Kornilov and N. M. Matveeva
1961 SovietRxiv: ru-196101.36737

This paper examines whether ordering transformations in nickel-based solid solutions correspond to the formation and dissociation of distinct Kurnakov compounds rather than merely homogeneous atomic rearrangements. Using a thermographic method with separate iron and nickel standards, the authors mea…

“Thermal” rearrangement of hydrazo compounds

L. G. KROLIK and V. O. LUKASHEVICH
1961 SovietRxiv: ru-196101.36409

This study examines the products formed when benzene and naphthalene hydrazo compounds are heated under inert conditions, challenging the view that thermal decomposition gives only disproportionation products. By heating representative hydrazo compounds under varied temperatures and solvents and qua…

Partitioning of the Composition Diagram and Exchange Reactions of the Quinary Reciprocal System of Nine Salts: Chlorides, Bromides, and Sulfates of Lithium, Sodium, and Thallium

Unknown
1961 SovietRxiv: ru-196101.36395

This paper examines the decomposition of the composition diagram and exchange reactions in the quinary reciprocal system of nine salts formed by lithium, sodium, and thallium chlorides, bromides, and sulfates. Using vertex indices for a four dimensional nine vertex polytope, the authors identify cut…

On the Catalytic Hydrogenation of Esters

N. I. SHUIKIN, I. F. BEL’SKII, and V. M. SHOSTAKOVSKII
1961 SovietRxiv: ru-196101.36009

This paper examines the behavior of ester carbalkoxy groups under catalytic vapor-phase hydrogenation, focusing on whether esters are reduced to alcohols or undergo hydrogenolysis to acids and hydrocarbons. Using flow hydrogenation at atmospheric and elevated hydrogen pressures, the authors compare …

On the Jost–Lehmann–Dyson Integral Representation

V. S. VLADIMIROV and V. F. NIKITIN
1961 SovietRxiv: ru-196101.35984

The paper examines the scope of Dyson’s conjecture concerning the support of the weight function in the Jost, Lehmann, Dyson integral representation for causal commutators. After recalling earlier validity results for domains satisfying convexity conditions with respect to timelike curves, the autho…

On the Duration of Ultraviolet Fluorescence of Some Aromatic Compounds

T. V. IVANOVA, P. I. KUDRYASHOV, and B. Ya. SVESHNIKOV
1961 SovietRxiv: ru-196101.35979

This paper reports an adaptation of a phase fluorometer for measuring ultraviolet fluorescence lifetimes and applies it to benzene, methyl-substituted benzenes, naphthalene, and several related aromatic compounds in hexane and alcohol solutions. The authors describe ultraviolet excitation and spectr…

ON THE PRINCIPLE OF LOCAL CODING AND THE REALIZATION OF FUNCTIONS FROM CERTAIN CLASSES BY CIRCUITS OF FUNCTIONAL ELEMENTS

Unknown
1961 SovietRxiv: ru-196101.35903

The paper develops a general synthesis method, the principle of local coding, for realizing selected classes of Boolean functions and operators by circuits of functional elements in a finite weighted basis. It formalizes codings in which the value of an operator on an input is determined from a shor…

ON A BOUNDARY-VALUE PROBLEM FOR THE BLASIUS EQUATION

In the present paper the existence of a solution of the following boundary-value problem will be proved:
1961 SovietRxiv: ru-196101.35899

This paper proves existence for a boundary value problem for the Blasius equation \(y''' + 2yy' = 0\) with matching conditions at the origin and prescribed limiting values of \(y'\) at positive and negative infinity. The argument develops qualitative properties of solutions, including nonvanishing a…

Stereodirected Syntheses Based on Diacetylene and Isomeric Transformations of 1,4-Bis(arylthio)buta-1,3-dienes and Their Disulfones

A. V. BOGDANOVA, M. F. SHOSTAKOVSKII, and G. I. PLOTNIKOVA
1961 SovietRxiv: ru-196101.35858

This study examines the stereodirection of reactions of diacetylene and ethynylvinyl phenyl sulfide with thiophenol in the synthesis of 1,4-bis(phenylthio)-1,3-butadienes and their corresponding disulfones. By varying ionic, radical, and mixed reaction conditions, the authors isolated and characteri…

On the Hilbert Boundary Value Problem

I. M. MELNIK
1961 SovietRxiv: ru-196101.35805

The paper studies a Hilbert boundary-value problem for analytic functions in a finite or infinite domain bounded by a smooth contour, with a boundary condition involving a homeomorphic involution of the contour. The problem is reduced to equivalent conjugation conditions and then to Fredholm integra…

Organosilicon monomers with fluorine-containing cyclobutyl rings

G. V. Odabashyan, V. A. Ponomarenko, Yu. N. Kovalev
1961 SovietRxiv: ru-196101.35729

This paper describes an alternative synthesis of organosilicon monomers containing fluorinated cyclobutyl rings, compounds of interest as precursors to fluorinated organosilicon polymers. Instead of direct condensation of fluoroolefins with alkenylsilanes under prolonged pressure conditions, the aut…

On the Mechanism of Ozone Formation during Electrolysis of Concentrated Perchloric Acid Solutions

M. A. GEROVICH, R. I. KAGANOVICH, Yu. A. MAZITOV, and L. N. GOROKHOV
1961 SovietRxiv: ru-196101.35615

This study investigates the mechanism of anodic ozone formation during electrolysis of concentrated perchloric acid solutions at low temperature. Using oxygen isotope tracers in labeled perchloric acid or labeled water, combined with polarization measurements and mass spectrometric analysis of evolv…

THE RIEMANN BOUNDARY-VALUE PROBLEM FOR \(n\) PAIRS OF FUNCTIONS WITH MEASURABLE COEFFICIENTS AND ITS APPLICATION TO THE STUDY OF SINGULAR INTEGRALS IN THE SPACES \(L_p\) WITH WEIGHTS

We formulate the problem.
1961 SovietRxiv: ru-196101.35386

This paper studies the Riemann boundary value problem on Lyapunov contours for one or several pairs of analytic functions when the boundary coefficient is only measurable. Using functional analytic methods, it establishes Fredholm type results for scalar coefficients in a specified class, including …

SPECIAL TYPES OF PAIRS OF \(T\)-CONGRUENCES

Unknown
1961 SovietRxiv: ru-196101.35366

This paper studies special pairs of T-congruences whose corresponding rays have equal focal distances and equal angles between their focal planes. Using a moving rectangular trihedron along the congruence of common perpendiculars, the author derives differential systems characterizing two types of s…

Divinyl sulfoxide and divinyl sulfone in the diene synthesis reaction with symmetric dienes

E. G. KATAEV and F. R. TANTASHEVA
1961 SovietRxiv: ru-196101.35294

This study examines the participation of divinyl sulfoxide and divinyl sulfone in Diels-Alder diene-synthesis reactions with butadiene, 2,3-dimethyl-1,3-butadiene, and cyclopentadiene under varied temperature and reactant-ratio conditions. Divinyl sulfoxide was found to form mono-adducts with butadi…

Organosilicon Compounds with Hydrocarbon Bridges between Silicon Atoms. Thermal Transformations

V. M. VDOVIN, K. S. PUSHCHAYA, and A. D. PETROV
1961 SovietRxiv: ru-196101.35004

This study examines the thermal behavior of organosilicon compounds containing hydrocarbon bridges between silicon atoms, with emphasis on silacycloalkanes and alpha, omega hexamethyldisilylalkanes heated in sealed ampoules up to 400°C. The authors compare stability and polymerization behavior using…