Recent Papers

Synthesis and Physicomechanical Properties of Polymer Films with a Regular Structure

ON QUASIANALYTIC FUNCTIONS IN \(L(-\infty,\infty)\)

This note introduces a function-level notion of quasianalyticity in the space of integrable functions on the real line, defined through the behavior of continuous linear functionals on translates of a single function. It proves that any function satisfying this definition is infinitely differentiabl…

On the Influence of the Steric Factor on the Viscometric Properties and Polydispersity of Polyarylates

This study examines how steric effects from side substituents influence the viscometric behavior and molecular weight distribution of polyarylates based on isophthalic acid and several dihydric phenols. Polyarylates prepared by equilibrium and interfacial polycondensation were fractionated, their mo…

Relaxation Method for Solving Systems of Inequalities with Convex Functions in the Left-Hand Sides

The paper develops a relaxation method for finding a solution, or a nonnegative solution, of a consistent finite system of inequalities whose left hand sides are smooth convex functions on Euclidean space. The argument is based on Fejér monotonicity with respect to convex sets and on supporting half…

Spaces of universal disposition

The paper introduces spaces and subspaces of universal, almost universal, and a-universal disposition for classes of Banach spaces, especially finite-dimensional and separable spaces. Using an extension construction for isomorphisms between embedded pairs of Banach spaces, together with compactness …

On Singular Integral Operators on a Group

The paper develops a theory of singular integral operators on nondiscrete commutative locally compact groups, defining them through Fourier multipliers with homogeneous degree zero symbols and establishing analogues of classical Mikhlin and Gohberg results. It proves compactness of commutators with …

Mass spectra of water upon its ionization by a strong electric field

Water vapor was ionized in strong electric fields on tungsten, molybdenum, platinum, gold, and nichrome emitters, and the resulting ions were analyzed with a magnetic mass spectrometer. The spectra on tungsten, molybdenum, and nichrome were dominated by oxonium ion hydrates of the form protonated wa…

Synthesis and Some Properties of Phosphacyclopentene Derivatives

This study reports the synthesis and preliminary biological evaluation of a series of phosphacyclopentene and oxaphosphacyclopentene derivatives, motivated by earlier indications of physiological activity in related organophosphorus compounds. Esters, acids, a sodium salt, and phosphine oxide deriva…

Commutative Systems as Generalized Semigroups

This note introduces commutative systems, or k-systems, consisting of two mutually centralizing systems of transformations on a set, as a generalization of semigroups with left and right translations. It characterizes when such systems arise from semigroups or groups, develops analogues of Green-typ…

Asymptotic Representation of the Spectral Matrix of a Fourth-Order Differential Operator

The paper studies the spectral matrix of a self-adjoint fourth-order differential operator on the half-axis with an integrable nonnegative potential and two boundary conditions at the origin. The argument first treats the corresponding problem on a finite interval, constructs asymptotic fundamental …

One Estimate of the Deviation of the Distribution of the Sum of Independent Random Variables from the Normal Law

The paper proves a general estimate for the uniform deviation between the distribution of a normalized sum of independent, not necessarily identically distributed, mean zero random variables and the standard normal distribution. Using a truncation argument and Esseen’s Berry, Esseen bound for variab…

TRANSFORMATION OF TIME IN PROBLEMS OF STABILITY WITH RESPECT TO THE FIRST APPROXIMATION

Spectroscopic Study of the Tautomerism of 4-Carbomethoxy-3-ketothiophane, 2-Carbomethoxy-3-ketothiophane, and 4-Methyl-2-carbomethoxy-3-ketothiophane

ON THE SPREADING OF QUANTUM AND CLASSICAL PROBABILITY PACKETS

This paper compares the temporal spreading of quantum wave packets and classical probability packets in one-dimensional motion under arbitrary potential fields. Using the Schrödinger and Liouville equations, and approximating the potential to second order about the packet center, it derives a common…

ON THE MORPHOLOGY OF CRYSTALS OF CUBIC BORON NITRIDE

This paper examines the crystal morphology of synthesized cubic boron nitride, motivated by earlier discrepancies between reported tetrahedral or octahedral habits and the sphalerite-type structure indicated by X-ray data. More than 100 improved crystals, together with polished sections and reflecte…

Study of etherates of trihalogermanes by NMR spectroscopy

This study examines etherate complexes of trichlorogermane and related Group IVB trihalides with simple ethers using proton NMR spectroscopy, with supporting elemental, material-balance, and infrared observations. The spectra indicate that diethyl ether forms a complex of composition 2 ether to 1 tr…

On Continuous Measures

This paper studies the sequential order topology on the Boolean ring of all subsets of a set and records its basic topological and algebraic properties. It shows that translations are homeomorphisms, the space is Hausdorff and totally disconnected, is noncompact for uncountable underlying sets, has …

ALMOST-PERIODIC SOLUTIONS OF DIFFERENTIAL EQUATIONS IN HILBERT SPACE

This paper studies the existence of almost-periodic solutions for differential equations in Hilbert space. It formulates multiplier problems for equations with commuting self-adjoint operators, proves a solvability criterion for the bounded strong case, and notes a special hyperbolic case in which a…

ON THE RIEMANN—HILBERT PROBLEM FOR A HOLOMORPHIC VECTOR

This note studies a Riemann, Hilbert type boundary value problem for a holomorphic vector in a three dimensional domain, with two real linear boundary conditions on the vector components. It first derives an integral representation of such vectors using a Cauchy type integral and the Green function …

On a case of the existence of a countable set of periodic motions

This paper studies a three-dimensional analytic differential system with a saddle-focus equilibrium whose one-dimensional separatrix returns to the equilibrium, forming a homoclinic trajectory. Using local coordinates near the saddle-focus and a Poincare point transformation decomposed into a local …

Spatial Heat-Conduction Problems for Certain Bodies Consisting of Inhomogeneous Material

Study of Photochemical Reactions in Complex Oxalates by EPR

This study examines photochemical transformations in frozen solutions of transition metal complex oxalates under ultraviolet irradiation using electron paramagnetic resonance at 77 K. Solutions containing trioxalate complexes of cobalt, iron, chromium, and manganese, as well as simple oxalate salts,…

Metric properties of mappings of class $BL^{3/2}$

The paper studies metric properties of homeomorphic mappings in three-dimensional domains belonging to the class BL^{3/2}, with bounded Dirichlet integral for the mapping and, in the principal class considered, for its inverse. An example shows that an earlier notion of relative distance does not al…

New Data on the Conditions of Fallout of Czechoslovak Tektites (Moldavites)

This paper reexamines the occurrence and post-depositional history of Czechoslovak tektites, or vltavins, using recent geological mapping and expeditionary observations from the South Bohemian and Moravian parts of the European tektite field. It argues that the original fall area was substantially l…

Radiolysis of solid solutions of stable radicals in isopropyl alcohol

The study investigates how stable nitroxide radicals are destroyed during electron irradiation of frozen solid solutions in isopropyl alcohol at 100 K, using electron paramagnetic resonance to follow both the stable radical and radicals formed in the solvent. Solutions of 2,2,6,6-tetramethylpiperidi…

Kinetics of Oxygen Adsorption on Silver at Low Pressures

The paper examines the kinetics of oxygen chemisorption on powdered silver at low oxygen pressure, with simultaneous measurements of adsorption and electron work function from contact potential differences. Experiments at approximately 2.5 x 10^-2 mm Hg and 23 to 200°C show an initial kinetic region…

On the Question of the Čaplygin Method for the Cauchy Problem

On the Perturbation Method in the Theory of Dynamic Stability of Distributed-Parameter Systems

The paper studies dynamic stability problems for systems with distributed parameters that reduce to a linear Hamiltonian equation in a separable Hilbert space with periodic perturbation. It proves a structural representation of the solution operator as a unitary operator plus a completely continuous…

A NEW APPROACH TO THE CALCULATION OF INTENSITIES IN THE VIBRATIONAL SPECTRA OF MOLECULES

This paper proposes a general method for calculating intensities in molecular vibrational spectra within the harmonic approximation, addressing limitations of additive bond dipole and polarizability models. The authors formulate the molecular dipole moment, and by extension the polarizability, as fu…

On Artificial Crystallization Nuclei for Crystallizing Polymers

This paper examines the use of salts of organic acids, especially heavy metal salts with melting points above those of the polymers studied, as artificial crystallization nuclei for crystallizing polymers. The authors introduced small amounts of these salts into polyethylene, polypropylene, and poly…

Determination of the Charge Sign of Photocurrent Carriers by the Capacitive Method

This paper examines whether the capacitor method can reliably determine the sign of photocurrent carriers in semiconductors, despite reported polarity reversals in photo-emf spectra. The authors compare competing interpretations of these reversals and present experimental evidence from photo-Hall, p…

The Invariant Meaning of Riemann Invariants

This paper examines the group-theoretic meaning of the Riemann invariants for one-dimensional gas flow with plane waves. Using Cartan’s method of exterior forms, the governing gas-dynamic equations are rewritten as a Pfaffian system and transformed by canonization into basic invariant forms of a fin…

On Some Regularities of the Liquid-Phase Direct Photooxidation of Trichloroethylene

This paper examines the direct, nonsensitized liquid-phase photooxidation of trichloroethylene by oxygen to form dichloroacetyl chloride, with further oxidation products including phosgene, carbon monoxide, and hydrogen chloride. Experiments varied temperature, irradiation intensity and wavelength, …

ON THE UNIQUE SOLVABILITY OF PLANE PROBLEMS OF GAS DYNAMICS WITH FREE BOUNDARIES

The paper studies the existence and uniqueness of plane subsonic potential gas flows with free boundaries, including Kirchhoff-type separated flows past obstacles or in channels and inverse or mixed problems for determining airfoil profiles from prescribed velocity data. The method transforms the ga…

Corrections to the Article “Physical Properties of Titanium Carbide in the Homogeneity Region” (Doklady, Vol. 157, No. 2, 1964)

Exceptional Case of Convolution-Type Integral Equations in the Class of Generalized Functions

This paper studies exceptional convolution-type integral equations with two kernels and paired equations in spaces of generalized functions, allowing Fourier transforms of the kernels to have real zeros of integral multiplicity, including behavior at infinity. The equations are reduced by Fourier tr…

THERMOGRAPHIC AND DILATOMETRIC STUDY OF POLYPYROMELLITIMIDE

Polypyromellitimide films subjected to different degrees of heat treatment were examined by differential thermal analysis and vacuum dilatometry to clarify their phase and aggregate behavior between 20 and 400°C. Initial polyamic acid and partially imidized films showed irreversible endothermic effe…

FACILE HETEROLYTIC CLEAVAGE OF THE CARBON–CARBON BOND IN CYCLOHEPTATRIENE DERIVATIVES

Cycloheptatriene derivatives bearing electron-acceptor substituents in the side chain are examined for heterolytic cleavage of the cycloheptatrienyl carbon bond. Experiments with cycloheptatrienylmalonic acid, cycloheptatrienylacetylacetone, cycloheptatrienylacetaldehyde, and cycloheptatrienylacetoa…

ON THE FEATURES OF TRANSPORT AND RELAXATION PHENOMENA OF SMALL-RADIUS POLARONS

This paper examines high-temperature transport and relaxation phenomena of localized small-radius polarons in low-mobility ideal crystals. It develops a stochastic formulation in which phonon-field fluctuations drive polaron hopping, derives Kubo-type expansions for the mobility tensor, and identifi…

On the Relationship Between the Thermodynamic Properties of Austenite and Its Structure

This paper examines how the thermodynamic activity of carbon in austenite is related to the interstitial structure of the iron lattice. It reviews earlier activity equations and argues, using Pauling’s polyhedron method, that carbon can occupy only one quarter of the octahedral voids because adjacen…

General Scheme for Solving Boundary Value Problems in the Space of Generalized Functions

This note develops a general scheme for boundary value problems in spaces of generalized functions on a smooth closed contour. It treats the Riemann problem, linear conjugation with shift, Carleman type problems, and the Hilbert problem by reducing solvability and representation to corresponding adj…

ON THE STABILITY OF THE ZERO SOLUTION OF A CLASS OF DIFFERENTIAL EQUATIONS OF ORDER \(n\)

ON DUALITY PRINCIPLES

This paper develops duality principles for the existence problem of periodic solutions of nonlinear systems of higher-order ordinary differential equations with periodic coefficients. It compares the fixed-point formulation given by the shift operator on initial data with fixed-point formulations fo…

On a Limit Theorem for Determinants in the Class of Boolean Functions

This note studies the probability that a random system of n linear equations over Boolean functions has a unique solution, equivalently that its determinant over the two element field equals one. For independent but not necessarily identically distributed Boolean matrix entries with probabilities un…

STUDY BY THE METHOD OF NUCLEAR MAGNETIC RESONANCE OF THE POSITION OF HYDROGEN IONS IN CERTAIN HETEROPOLY COMPOUNDS

Proton nuclear magnetic resonance was used to examine the state and position of hydrogen ions and hydration water in silicotungstic, phosphotungstic, and phosphomolybdic heteropoly acids during dehydration. Measurements of absorption line intensity, width, and second moment at low temperature showed…

Liquid-Phase Hydrogenation of Some Mononuclear Aromatic Compounds in the Presence of Ruthenium Catalysts

This study examines the liquid phase hydrogenation of mononuclear aromatic compounds using ruthenium dioxide, ruthenium on activated carbon, and ruthenium on silica gel catalysts under elevated hydrogen pressure. Experiments in rotating autoclaves show that ruthenium dioxide is generally the most ac…

On the Order of Arrangement of Zones in Sedimentation Chromatograms

This paper derives general relations for predicting the sequence of precipitation and the resulting order of zones in precipitation chromatograms. Using solubility products, ion activities, supersaturation ratios, and initial ion concentrations, it shows that precipitation order can depend both on t…

SOME THEOREMS ON THE EXISTENCE OF A PERIODIC SOLUTION OF AN AUTONOMOUS SYSTEM OF SIX DIFFERENTIAL EQUATIONS

Corrections to the Article Properties and Structure of Dicyclopentad

On the Oxidation of a Series of Platinites by Sodium Vanadate

This study examines the kinetics of oxidation of several divalent platinum complexes by sodium vanadate in order to assess how ligands affect the oxidation rate of the central platinum atom. Using a sampling method at constant sulfuric acid acidity, the authors determined reaction orders, rate const…