Recent Papers

On the Problem of Optimal Control of a Mathematical Pendulum

Some plane problems of thermoelasticity under periodic thermal actions

This note treats quasistatic plane thermoelasticity problems for plates and cylinders subjected to periodic thermal actions, neglecting coupling between elasticity and heat conduction. Using Bessel-function representations of the periodic heat-conduction problem, it derives thermoelastic displacemen…

STUDY OF THE EXTRACTION PROPERTIES OF β—β′-DICHLORODIETHYL ETHER (CHLOREX)

This study examines the extraction behavior of beta,beta-prime-dichlorodiethyl ether, or Chlorex, as an industrially available solvent for separating metal ions from hydrochloric acid solutions. Using radioactive tracers, the authors measured distribution coefficients for twelve elements over varyin…

On fractional powers of elliptic operators

The paper studies mapping properties of fractional powers of positive linear operators in scales of Lebesgue, Lorentz, and Marcinkiewicz spaces, using the notion of an operator’s characteristic set in the unit square of integrability indices. It proves general theorems showing how the characteristic…

On the Relationship Between Thermodynamics and Kinetics of Some Solid-Phase Reactions

This paper examines the relation between thermodynamic and kinetic parameters in selected solid phase reactions, extending the Polanyi and Evans concept from reaction heat effects to changes in isobaric isothermal potential. Using literature thermochemical and activation energy data, the authors der…

THE ANALYTIC STRUCTURE AND FUNDAMENTAL PROPERTIES OF SOLUTIONS OF EQUATIONS WITH ALGEBROID RIGHT-HAND SIDES IN THE CASE OF A FOCUS AND GENERALIZATIONS

INTERACTION OF 1-VINYLCYCLOHEXENE-3 DIOXIDE WITH ALCOHOLS

This study examines the addition of several lower alcohols to 1-vinylcyclohexene-3 dioxide, a cycloolefin dioxide for which comparable reactions had not been experimentally characterized. The dioxide was prepared by epoxidation with acetyl hydroperoxide, and its reactions with ethyl, propyl, isoprop…

ON THE CONSTRUCTIVE THEORY OF THE RIEMANN INTEGRAL

This note develops the constructive theory of the Riemann integral for constructive functions on the unit segment. It compares an epsilon-delta style definition of constructive Riemann integrability with a sequential definition based on regularly contracting sequences of integral sums, proving their…

On the Behavior of a Temlyakov-Type Integral of the First Kind at Points of the Skeleton of a Domain $D$ of Type $A$

This paper studies the boundary behavior of functions represented by Temlyakov integrals of the first kind over domains of type A in two complex variables, focusing on approach to the skeleton points from the domain where the integral is not analytic. Under specified Lipschitz and Fourier-series con…

EPR SPECTRA OF ANION-RADICALS OF CERTAIN AROMATIC HYDROCARBONS

This study examines the electron paramagnetic resonance spectra of anion radicals formed by reducing diphenylmethane, diphenylethane, and 1,3-diphenylpropane with metallic potassium in 1,2-dimethoxyethane or tetrahydrofuran at low temperatures. The spectra indicate that the primary reduction product…

On New Compounds of Rare-Earth Element Oxides and Lithium

The study examines the formation of lithium compounds with rare earth oxides, focusing on systems for which little or no prior information was available, especially praseodymium and terbium sesquioxides. Rare earth oxides or nitrates were reacted with lithium compounds under controlled calcination c…

ON AN ANALYTIC THEORY OF SYSTEMS OF LINEAR DIFFERENTIAL EQUATIONS WITH AN IRREGULAR SINGULAR POINT

On Eigenvalues and Eigenfunctions of Integro-Differential Operators[^1]

POLYMERIZATION OF BUTADIENE BY CATALYSTS BASED ON CARBONYLS OF GROUP VIII METALS OF THE PERIODIC SYSTEM OF ELEMENTS

This study examines the polymerization of butadiene using catalyst systems formed from Group VIII metal carbonyls and Lewis acids, with particular attention to nickel and cobalt carbonyls. Experiments in hydrocarbon solvents at 50 degrees C show that the carbonyls alone are inactive, whereas their r…

Comparative Study of the Kinetics of Transformations of Benzene and Its $\mathrm{C}_7$–$\mathrm{C}_8$ Homologues under the Action of Steam on a Nickel-Chromium Catalyst

The study compares the kinetics of steam-induced transformations of benzene, toluene, ethylbenzene, xylenes, and m-cresol over an industrial nickel chromium catalyst at 360 to 400°C. Using a flow catalytic apparatus with chromatographic analysis, the authors examine monodealkylation, further demethy…

$\mathrm{O}$-Esters of trinitromethane in the 1,3-dipolar cycloaddition reaction

This study examines whether O-alkyl esters of trinitromethane can be generated and trapped through 1,3-dipolar cycloaddition. The authors prepared methyl and ethyl trinitromethane O-esters in solution by diazomethane methylation or oxonium-salt alkylation, then reacted them with methyl acrylate and …

On a property of alternative quasigroups with an invariant finite measure

This paper studies alternative quasigroups equipped with a finite invariant measure, including compact groups with Haar measure and finite quasigroups with normalized counting measure. It proves a covering or translation property: if a measurable subset has measure greater than \((k-1)/k\), then for…

Study of the Oxidation of Methyl Ether of o-Amino- $n$ -tert.-Butylphenol by EPR

This study examines the stepwise oxidation of the methyl ether of o-amino-p-tert-butylphenol by benzoyl peroxide using electron paramagnetic resonance spectroscopy. By varying the molar ratio of substrate to oxidant in dry benzene under evacuated conditions, the authors followed changes in hyperfine…

Kinetic Current Instability of Alfvén Waves in Plasma with Finite Ion Larmor Radius

This paper analyzes a kinetic current instability of Alfvén waves in a homogeneous low pressure plasma carrying an electric current along an external magnetic field, with emphasis on effects of a finite ion Larmor radius. Using a kinetic dispersion relation for nearly transverse low frequency oscill…

On Certain Hankel Transformations

Integration of Analytic Functionals with Respect to Sign-Changing Distributions

The paper studies continual integration of analytic functionals on the space of continuous paths starting at zero with respect to a sign-alternating distribution associated with a higher-order heat-type equation. It defines the distribution through finite-dimensional quasi-intervals using the Green …

On an Algorithm for Minimizing Convex Functions

The paper proposes an algorithm of centered sections for approximate minimization of Lipschitz convex functions on convex polyhedra, using gradient direction evaluations to cut away regions that cannot contain a minimizer. It develops the method first in two dimensions, where centroid cuts give geom…

Mechanism of the Catalytic Decomposition of Hydroperoxides under the Influence of Copper Stearate

This paper examines the catalytic decomposition of n-decyl hydroperoxide by copper stearate in liquid phase at 80 degrees C, with attention to radical and nonradical pathways relevant to hydrocarbon oxidation. Using inhibitor consumption by N-phenyl-beta-naphthylamine to measure radical formation, t…

Synthesis and Reactions of Trimethylsilylketene–Trimethylsiloxyacetylene

Thermal decomposition of trimethylsilylalkoxyacetylenes is examined as a route to trimethylsilylketene, and the resulting product is characterized by NMR and infrared spectroscopy. The spectral data indicate that the substance exists as an equilibrium mixture of the ketene form and trimethylsiloxyac…

The Nature of Crystalline Elastic Ethylene Copolymers

This paper examines how crystallization and supramolecular morphology affect the elastic properties of ethylene vinyl acetate copolymers with varying vinyl acetate content. Using electron microscopy, X-ray data, and mechanical testing, the authors trace the transition from polyethylene-like spheruli…

Study of the decay of $\mathrm{Pd}^{101}$, $\mathrm{Rh}^{101^*}$, $\mathrm{Rh}^{101}$

The study investigates the radioactive decay chain involving Pd-101, Rh-101m, and Rh-101, with emphasis on gamma transitions, conversion electron spectra, and resulting nuclear level schemes. Activities obtained from proton-irradiated Ag or Cd targets were examined using a KETRON magnetic spectromet…

ON THE INTERACTION OF ESTERS OF PHOSPHOROUS ACID WITH 1,1-DIPHENYLETHANE HYDROPEROXIDE

This paper examines the kinetics of the reaction of 1,1-diphenylethane hydroperoxide with a range of phosphorous acid esters, including aliphatic and aromatic phosphites, mixed pyrocatechol phosphites, and diphosphites. The authors use polarographic measurement of hydroperoxide reduction at a droppi…

Multi-terminal networks containing make contacts of internal relays

This paper extends the characteristic function method for valve-contact multipoles to networks that include make contacts of internal relays, allowing feedback and multicycle transient operation while excluding break contacts of internal relays. It proves that, for fixed external relay states and ap…

SOME CASES OF UNIQUENESS OF THE SOLUTION OF THE INVERSE PROBLEM FOR STRINGS WITH A BOUNDARY CONDITION AT A SINGULAR END

The paper studies inverse spectral problems for strings in the class associated with nondecreasing mass functions on intervals with a possible singular endpoint and a boundary condition at the singular left end. It defines spectral, orthogonal, and positive spectral functions and formulates uniquene…

On the Structure of Copolymers of Acrolein with Vinyl Aryl Ethers

This paper investigates the structure of copolymers formed from acrolein and vinyl aryl ethers under cationic conditions, with emphasis on acrolein and vinyl phenyl ether. Fractionation, chemical tests, infrared spectroscopy, and comparison with independently synthesized 2-phenoxy-3,4-dihydropyran i…

EFFECTIVE TRANSFORMATION AND ASYMPTOTICS OF ONE CLASS OF NONLINEAR DIFFERENTIAL EQUATIONS

The paper studies an autonomous system of nonlinear differential equations with a small parameter, including a two-dimensional oscillatory component coupled to slow variables, and develops an effective transformation suited to averaging near a particular solution. After shifting to amplitude and pha…

Physical characterization of Einstein spaces of degenerate type II in the Petrov classification

This note examines four-dimensional Einstein spaces satisfying a generally covariant tensor wave equation for the Riemann curvature, interpreted as a criterion for gravitational waves, using Petrov’s algebraic classification. By expressing the curvature tensor in the associated six-dimensional bivec…

1,1'-Dialkylcobalticinium Salts

This paper addresses the limited availability of substituted cobalticinium salts, particularly those not readily accessible through electrophilic substitution or substituted cyclopentadienes. The authors propose using 1,1′-dialkylferrocenes as starting materials, cleaving them with lithium in ethyla…

INITIATED HETEROGENEOUS-CATALYTIC REACTIONS

This paper examines olefin hydropolymerization on cobalt catalysts as an initiated heterogeneous catalytic process, comparing reactions promoted by small additions of carbon monoxide or oxygen in the presence of hydrogen. The authors summarize experimental trends for ethylene, propylene, and butylen…

Anomalous Chemical Shifts and the Conformation of Cyclic Esters of Sulfurous and Selenious Acids

This paper examines anomalous proton chemical shifts in cyclic esters of sulfurous and selenious acids as evidence for their preferred conformations. Using experimental and calculated NMR spectra for propane-1,3-diol sulfite and selenite, dimethyl derivatives, and chlorinated sulfite isomers, the au…

On the Theory of Ordered Statistical Systems

A method is developed for solving Bogolyubov equations for correlation distribution functions of an inhomogeneous gas with small van der Waals number, without imposing molecular chaos. By separating macrospace and microspace scales, the equations are reduced in leading approximation to a hierarchy f…

OBSERVATION OF CASCADE TRANSITIONS

This paper reports an experimental observation of cascade population in cadmium atoms under electron excitation, motivated by its possible influence on optical excitation functions and lifetime measurements. Using a delayed-coincidence method with pulsed electron excitation, the authors measured the…

On Some Modifications of the Concept of Modulus of Smoothness and Their Applications

This paper develops modifications of the modulus of smoothness for periodic functions and Hilbert space elements, emphasizing moduli of primitives and an integrated \(\widetilde{L}\)-modulus. It derives criteria and estimates for absolute convergence of Fourier series in terms of best approximations…

General theorems on quadratic relaxation

The paper develops an abstract theory of quadratic relaxation processes for solving a linear equation with a positive definite bounded operator in a real Hilbert space, viewed equivalently as minimization of a quadratic potential. It introduces relaxation multipliers, relaxation angles, residual dis…

On the Ground-State Energy of a Molecule in the Adiabatic Approximation

This paper establishes a rigorous comparison between the exact ground state energy of a molecular Hamiltonian and its value in the adiabatic approximation. By decomposing the exact molecular wave function into electronic and nuclear factors and applying normalization identities, positivity of the nu…

Thermodynamic Analysis of Equilibrium During the Dissociation of Ferrites

This paper generalizes a thermodynamic scheme for calculating component activities during ferrite dissociation to cases in which both solid products, the spinel and wüstite phases, have variable composition. The authors formulate the equilibrium reaction, identify independent partial reactions by a …

On New Compounds of Oxides of Rare-Earth Elements, Strontium, and Barium

This paper investigates the formation of compounds between strontium or barium oxides and rare-earth oxides by calcining oxide or salt mixtures and analyzing the products by X-ray diffraction. Strontium oxide was found to form SrLn2O4 compounds with rare-earth elements from neodymium to lutetium, wh…

On the dependence of ion-electron emission from single crystals on target temperature

The paper examines how target temperature affects the angular dependence of ion electron emission from copper single crystals bombarded by 30 keV argon ions. Extending a prior model in which emission is proportional to the energy lost in the ion’s first collisions with surface atoms, the authors inc…

On the Planarity of Molecules of Diazoamino Compounds

This study examines the relationship between substitution pattern, molecular planarity, and visible absorption in aromatic diazoamino compounds. A series of chloro-, bromo-, and methyl-substituted diazoaminobenzenes was synthesized by several diazotization and coupling methods, and their electronic …

Deep magnetovariational soundings (MVS) in southern Central Siberia and Transbaikalia

This paper presents deep magnetovariational sounding results from southern Central Siberia, the Baikal region, and Transbaikalia, using geomagnetic bay variations with periods of 0.5 to 4 hours to infer apparent resistivity in the upper mantle. The authors argue that magnetic variation observations …

Estimation of Coefficients of Univalent Functions

This paper derives a new coefficient estimate for normalized univalent functions in the unit disk. Using functions associated with the exterior univalent class and a logarithmic expansion introduced in earlier work, it relates the coefficients of a function in the class to partial sums generated by …

Spectroscopic Study of Cool-Flame Luminescence in the Nitration of Propane with Nitrogen Dioxide

This study examines the luminescence of cold flames formed during vapor-phase nitration of propane with nitrogen dioxide, motivated by similarities between alkane nitration and cold-flame oxidation. Using a stabilized quartz jet reactor and a photoelectric grating spectrometer, the authors recorded …

Quasianalytic Classes of Functions in the Disk

This paper solves a quasianalyticity problem for functions analytic in the unit disk and infinitely differentiable up to the boundary, together with the corresponding class of boundary functions. For derivative bounds governed by a nondecreasing positive sequence, it proves that quasianalyticity is …

On the Laws of Development and Stabilization of Aerodynamic Disturbances

This paper examines nonlinear theories of the growth and stabilization of aerodynamic disturbances, focusing on whether they determine the direction of disturbance development beyond the linear regime. It reviews the amplitude equation associated with Landau and its subsequent derivations by Stuart,…

ISOCHRONISM OF THE CENTER OF CERTAIN SYSTEMS OF DIFFERENTIAL EQUATIONS