Showing 50 of 25456 papers

On a Copper Catalyst for the Oxidation of Propylene to Acrolein

O. V. ISAEV, M. Ya. KUSHNEREV, and L. Ya. MARGOLIS
1958 SovietRxiv: ru-195801.42350

This paper examines the phase composition and behavior of copper catalysts in the oxidation of propylene to acrolein, addressing uncertainty over whether cupric oxide, cuprous oxide, or metallic copper is the active form. Copper oxide, cuprous oxide, and reduced copper on pumice were tested in propy…

Synthesis of Methyl Esters of Isomeric Chondropholines, Chondodendrines, and Tubocurarines

V. G. Voronin, O. N. Tolkachev, and N. A. Preobrazhenskii
1958 SovietRxiv: ru-195801.42294

The paper examines the stereochemical complexity of curare alkaloids, especially chondropholine, chondodendrine, and tubocurarine derivatives, in light of asymmetric centers, nitrogen substituent geometry, tetrahydroisoquinoline conformations, and macrocyclic diether arrangements. The authors descri…

On a Principle of Existence of Bounded, Periodic, and Almost Periodic Solutions of a System of Ordinary Differential Equations

M. A. KRASNOSEL′SKII and A. I. PEROV
1958 SovietRxiv: ru-195801.42126

The paper establishes topological criteria for the existence of bounded, periodic, and almost-periodic solutions of systems of ordinary differential equations with continuous right-hand sides, without assuming uniqueness or global continuability of all solutions. The authors introduce a condition in…

SOME QUESTIONS OF INTERPOLATION BY MEANS OF ENTIRE FUNCTIONS

In the present paper we shall consider three interpolation problems in the class of entire functions.
1958 SovietRxiv: ru-195801.41964

This paper studies interpolation by entire functions at prescribed complex nodes, focusing on growth restrictions expressed through refined order and indicators. It introduces associated functions for node sequences of refined order growth and gives necessary and sufficient conditions, involving the…

On the extinction of transverse circulation

M. S. POKHRARYAN
1958 SovietRxiv: ru-195801.41374

This paper analyzes the decay of transverse circulation generated by channel curvature after the flow enters a straight reach, assuming the initial circulation distribution is prescribed. Starting from the viscous incompressible flow equations with constant turbulent mixing, hydrostatic pressure, an…

New Number-Theoretic Estimates

Unknown
1958 SovietRxiv: ru-195801.41146

This note announces new estimates for finite trigonometric sums with polynomial phase of degree n plus 1, under a condition relating the summation length to the leading coefficient. The main theorem improves the dependence on n in the exponent compared with earlier bounds, replacing a growth conditi…

Eigenvalues and eigenfunctions of some fourth-order differential operators with a small parameter at the highest derivative

Unknown
1958 SovietRxiv: ru-195801.41056

The paper studies a self-adjoint fourth-order boundary-value problem on an interval in which a small parameter multiplies the highest derivative, with the highest-derivative signs matching those of the limiting second-order operator. It identifies exceptional parameter values for which zero becomes …

On the connection between the theory of the distribution of zeros of $L$-series and the arithmetic of ternary quadratic forms

Unknown
1958 SovietRxiv: ru-195801.41042

This note relates the representation of large integers by primitive positive ternary quadratic forms to zero-free regions for Dirichlet L-series. Assuming a hypothesis excluding zeros near s = 1 for a family of characters depending on the represented integer, the paper removes an auxiliary prime-res…

Synthesis of Organosilicon Compounds Containing a Methacrylic Group

K. A. ANDRIANOV and A. K. DABAGOVA
1958 SovietRxiv: ru-195801.40987

This communication reports the synthesis of new unsaturated organosilicon compounds containing methacrylic groups attached through a methylene ester substituent at silicon. Methacrylatemethylalkoxysilanes were prepared from chloromethylalkoxysilanes and potassium methacrylate, and their boiling poin…

Dehydrocyclization of n-heptane over alumina-chromia catalysts

M. I. ROZENGART and B. A. KAZANSKII
1958 SovietRxiv: ru-195801.40959

The study examines the dehydrocyclization of n-heptane over potassium-promoted alumina-chromia catalysts, focusing on catalyst lifetime, regeneration, and the factors limiting aromatics formation. Long-duration tests at about 510 to 515°C showed that selected catalysts could operate without regenera…

On Bicompact Extensions of Topological Spaces

Academician P. Aleksandrov and Vl. Ponomarev
1958 SovietRxiv: ru-195801.40899

This note studies bicompact extensions of completely regular topological spaces through an axiomatic theory of subordination between closed and open sets. It formulates axioms for such subordinations and shows, in a form equivalent to Smirnov’s theorem, that every subordination yields a bicompact ex…

General Expression for the Phase Density of Finite Stationary Axisymmetric Self-Gravitating Stellar Systems and Their Differential Axial Rotation

G. M. IDLIS
1958 SovietRxiv: ru-195801.40706

This paper examines the phase density of finite stationary self-gravitating stellar systems with an axisymmetric potential, using Jeans’ theorem and the integrals of motion for individual stars. It argues that the general phase density should depend on three independent single-valued axisymmetric in…

On the Structure of Water

I. Z. FISHER and V. K. PROKHORENKO
1958 SovietRxiv: ru-195801.40530

This paper examines the local structure of liquid water using radial distribution functions derived from X-ray scattering data. Applying previously developed relations, the authors estimate fluctuations in the first two oxygen coordination numbers at several temperatures, as well as the correlation …

On a variational principle in the many-body problem

N. N. BOGOLYUBOV
1958 SovietRxiv: ru-195801.40404

This paper formulates a variational approximation for a many-fermion system with two-body interactions by applying a canonical linear transformation of Fermi amplitudes and minimizing the vacuum expectation value of the Hamiltonian subject to orthonormality constraints. The resulting stationarity eq…

Relationship between the Ratios of the Quantum Yields of Phosphorescence and Fluorescence and the Position of the Fluorescence Spectrum

V. V. Zelinskii and V. P. Kolobkov
1958 SovietRxiv: ru-195801.40217

This study examines whether the probability of transition to a metastable state in phthalimide derivatives is related to the position of the fluorescence spectrum. Because direct phosphorescence yield measurements at low temperature are often prevented by crystallization or opacity of frozen solutio…

Synthesis of Methylferrocene

A. N. NESMEYANOV, E. G. PEREVALOVA, L. S. SHILOVTSEVA
1958 SovietRxiv: ru-195801.40166

This paper reports two preparative routes to methylferrocene and compares the products obtained. Methylferrocene was synthesized by reduction of methyl ferrocenecarboxylate with lithium aluminum hydride in 83% yield and by reduction of N,N-dimethylaminomethylferrocene iodide with sodium amalgam in u…

ON ENTIRE FUNCTIONS OF FINITE DEGREE AND ON FUNCTIONS OF COMPLETELY REGULAR GROWTH OF SEVERAL VARIABLES

Unknown
1958 SovietRxiv: ru-195801.39978

This paper studies entire functions of finite exponential degree in several complex variables and the behavior of their growth indicators when some variables are fixed. It proves measure and exceptional set results showing that points where the degree or directional indicator falls below its maximal…

On a Certain Nonlinear Operator

Unknown
1958 SovietRxiv: ru-195801.39848

This note studies a nonlinear operator arising from the minimization of integral functionals of higher derivatives in Orlicz spaces, with homogeneous boundary conditions and a linear term determined by a right-hand side in the complementary Orlicz space. Under growth, convexity, and semicontinuity a…

On the Thermodynamics of Superconductivity

V. A. MOSKALENKO
1958 SovietRxiv: ru-195801.39780

This paper develops a thermodynamic treatment of superconductivity starting directly from the Fröhlich electron phonon Hamiltonian. Using Feynman’s operator calculus to eliminate phonon variables and applying a variational principle for the grand statistical sum, the author introduces Bogolyubov qua…

THREE-DIMENSIONAL SPACE WITH A CUBIC SEMIMETRIC

Unknown
1958 SovietRxiv: ru-195801.39535

This paper studies three-dimensional Finsler spaces whose metric is defined by a cubic differential form with nonzero discriminant, using algebraic concomitants of the fundamental tensor to construct affine connections. It derives the transformation law of Tonooka’s connection under conformal change…

On the approximate construction of certain conformal mappings

B. A. VERTGEIM
1958 SovietRxiv: ru-195801.39520

The paper studies the approximate construction of conformal mappings from the unit disk onto domains bounded by sufficiently smooth closed contours that need not be star-shaped. It reduces the mapping problem to a nonlinear singular integral equation and argues that Theodorsen’s iteration is inadequ…

Results of Seismic Studies in the Black Sea near Anapa

Unknown
1958 SovietRxiv: ru-195801.39462

This paper reports the first stage of systematic marine seismic investigations of the Black Sea bottom structure near Anapa, undertaken to clarify the relation of submerged Caucasus structures to the broader Black Sea depression. Using refracted-wave profiling from an expedition vessel, with explosi…

On inductive limits of normed spaces

B. M. MAKAROV
1958 SovietRxiv: ru-195801.38300

This note studies inductive and projective limits of normed spaces, with particular attention to limits formed from reflexive normed spaces. It formulates conditions under which bounded sets in an inductive limit are already contained, and in the normed case bounded, in one of the constituent spaces…

Polarography at High Pressures

S. G. MAIRANOVSKY, M. G. GONIKBERG, and A. A. OPEKUNOV
1958 SovietRxiv: ru-195801.38122

This communication describes an apparatus and procedure for polarographic measurements with a dropping mercury electrode at pressures up to 3000 kg/cm², and reports initial tests on Tl⁺, Cd²⁺, Zn²⁺, and H⁺ in potassium chloride supporting electrolyte. The authors find that the half-wave potential an…

Limit complexes of cubic resolvents

M. M. POSTNIKOV
1958 SovietRxiv: ru-195801.38010

This note gives an internal characterization of cubic complexes that arise as limiting complexes of cubic resolvents, proving that this occurs exactly for complexes satisfying the stated EN conditions. The proof constructs the associated resolvent inductively from the groups of cubes belonging to a …

QUASI-STATIONARY THERMAL REGIME OF EXPLOSIVE REACTIONS

Unknown
1958 SovietRxiv: ru-195801.37824

The paper analyzes a quasi-stationary thermal regime in explosive reactions, in which heat accumulation is small compared with heat release and removal, so that the process may be treated as a sequence of near-stationary states. Starting from dimensionless nonstationary equations for thermal explosi…

ON THE SECOND MIXED DERIVATIVE

Unknown
1958 SovietRxiv: ru-195801.37663

The paper examines whether, for a continuous function on the two-dimensional torus, continuity of the pure second derivatives in a Banach function space implies continuity or membership of the mixed second derivative. It shows that although Bernstein had obtained affirmative results for certain spac…