Recent Papers

EPR spectra of $\gamma$-irradiated acetylene and its derivatives

This study examines the relationship between molecular structure and radical formation in acetylene and several acetylene derivatives subjected to gamma irradiation at 77 K, using electron paramagnetic resonance spectroscopy. Spectra were recorded for methylacetylene, deuterated methylacetylene, eth…

ON AN ESTIMATE OF THE MIXED DERIVATIVE IN \(L_p(G)\)

The paper studies estimates for generalized mixed derivatives of functions whose first derivatives and unmixed second derivatives belong to \(L_p\). It reviews known cases in which an interior estimate can be extended to the whole domain, then proves that for \(1<p<\infty\) the full-domain estimate …

A generating function for the Clebsch–Gordan coefficients

This note constructs a generating function for Clebsch-Gordan coefficients of the three-dimensional rotation group, using a realization of irreducible representations in polynomial spaces and the action of the associated infinitesimal operators. The canonical basis polynomials in the Kronecker produ…

Electroreduction of Anions and Polarographic Maxima of the Second Kind

This study examines the electroreduction of peroxydisulfate anions at a dropping mercury electrode under conditions producing polarographic maxima of the second kind, where tangential surface motion intensifies solution stirring. Polarization curves in potassium chloride backgrounds of varying conce…

Isotope exchange reaction of substituted benzylmercury bromides with mercuric bromide labeled with the radioactive isotope $\mathrm{Hg}^{203}$

The study examines isotope exchange between substituted benzylmercury bromides and mercuric bromide labeled with mercury 203 as a model for electrophilic substitution at saturated carbon. Kinetic measurements were carried out primarily in quinoline, the only tested solvent in which exchange proceede…

Cis-trans isomerization of 1,4-polybutadiene units under the influence of nitrogen dioxide

This study examines cis to trans isomerization of cis 1,4 polybutadiene units and cis butene 2 under the influence of nitrogen dioxide in benzene solution. Using sealed ampoule reactions under dry argon, infrared spectroscopy for polymer microstructure, chromatographic analysis for butenes, and nitr…

On the Frequency of Formation of Cavitation Cavities in Turbulent Boundary Layers and Wake Flows

This paper develops a statistical model for the frequency of cavitation cavity formation in turbulent boundary layers and wake flows, treating inception as the crossing of a critical pressure level by turbulent pressure fluctuations. By adapting Rice’s formula for level crossings of a normally distr…

On a New Sesquiterpene Hydrocarbon, Daucene

This paper reports the isolation and characterization of daucene, a new bicyclic sesquiterpene hydrocarbon of composition C15H24, from the sesquiterpene fraction of essential oil obtained from wild carrot fruits growing in Armenia. The compound was separated by repeated chromatography on alumina and…

Ketonization of $\mathrm{CH}_3\mathrm{COOH}$ over $\mathrm{CdO}$ and $\mathrm{MgO}$ and the kinetics of thermal decomposition of $\mathrm{Cd}(\mathrm{CH}_3\mathrm{COO})_2$ and $\mathrm{Mg}(\mathrm{CH}_3\mathrm{COO})_2$

This study examines vapor-phase ketonization of acetic acid over cadmium oxide and magnesium oxide in relation to the thermal decomposition of the corresponding acetates. Ketonization rates, thermogravimetric kinetics, Erofeev equation analysis, and X-ray phase data are compared to determine whether…

Molecular Compounds of Diphenylcyclopropenone, Tropone, and Benzophenone with Hydrogen Chloride

Infrared absorption spectroscopy was used to examine the interaction of hydrogen chloride with ketones lacking enol forms, chiefly diphenylcyclopropenone and tropone, with benzophenone as a comparison. The spectra show disappearance or strong lowering of carbonyl bands, new bands attributed to pertu…

Corrections to the Article Equilibrium of Isomerization of Bromopropanes (DAN, Vol. 135, No. 2, 1960)

Synthesis of $K$-strophanthin-$\beta$

This paper reports preliminary work on the partial synthesis of the cardiac glycoside K-strophanthin-beta from the more accessible natural monoside cymarin. The authors adapt the Koenigs-Knorr glycosylation of cymarin with acetobromoglucose, addressing the lability of the glycosidic bond and poor re…

Metric properties of endomorphisms of the $n$-dimensional torus

This paper studies metric properties of group endomorphisms of the n-dimensional torus by representing them through integral linear transformations of Euclidean space. It proves a decomposition theorem that splits an arbitrary torus endomorphism into invariant toral factors corresponding to irreduci…

On the EPR Spectrum of Irradiated Frozen Benzene

This paper examines the electron paramagnetic resonance spectrum of frozen benzene irradiated at low temperature, focusing on the assignment of its hyperfine structure to specific radiolysis radicals. The authors improve spectral resolution by slowly warming irradiated samples to 220 K, which reduce…

On the Rotation of a Deformable Body

This paper develops a finite-dimensional mechanical model for the rotation of a homogeneously deformable body whose center of mass is fixed. Using nine generalized coordinates describing a linear finite deformation, it derives the kinetic energy, Lagrange equations, and possible forms of elastic, vi…

ON SOME PROPERTIES OF SUMMATION METHODS

This paper studies inclusion and boundedness properties of summability, boundedness, and absolute summability fields associated with matrix and integral summation methods. It gives necessary and sufficient lacunarity conditions under which subsequences of the Cesàro, Euler, Abel, and integral Borel …

On Some Families of Extensions of a Symmetric Operator

This note studies families of intermediate extensions of a closed symmetric operator that are induced by self-adjoint extensions in a larger Hilbert space, with emphasis on their relation to generalized resolvents and projected eigenvectors. It characterizes such families for non-real spectral param…

Infrared Absorption Spectra of Some $\mathrm{R}$ – $\mathrm{O}$ – $\mathrm{Li}$ Compounds

This study examines the infrared absorption spectra of several lithium alcoholates with branched aliphatic radicals, together with isotopically substituted lithium methoxide derivatives, in order to clarify the spectral signatures of associated O-Li groups. Spectra were recorded for sublimed crystal…

Radiochromatography of organomercury compounds

A radiochromatographic method is described for separating organomercury compounds from inorganic mercury salts and from related organomercury salts, developed to support kinetic studies of isotope exchange reactions. Paper chromatography on ethylene glycol impregnated paper with an octane, benzene m…

On Some Well-Posed Problems for the Ultrahyperbolic and Wave Equations with Data on a Characteristic Cone

The paper studies an integral-geometric equation in which weighted integrals over spheres through the origin are prescribed, and uses Radon transform methods to establish inversion and uniqueness results, including unitarity properties of associated operators in odd dimensions with analogous stateme…

The Problem of Propagation of Long and Superlong Radio Waves Around the Earth and the Lower Ionospheric Layers ( $C$ , $D$ and $E$ ) in Light of Information Theory

The paper formulates long and superlong radio-wave propagation around the Earth and the lower ionosphere as an information-theoretic boundary-value and inverse problem, relating observed normal-wave parameters and reflection coefficients to essential parameters of the medium. Using an approximate me…

On the Temperature Distribution in a Piecewise Homogeneous Semi-Infinite Plate

The paper studies a boundary value problem for heat conduction in a semi-infinite plate composed of two homogeneous media separated along an interface, with different thermal diffusivities and conductivity constants. Under specified growth, continuity, and Hölder-type assumptions on the initial and …

On Dislocation Pile-Ups in Crystals Containing Impurities

This paper examines dislocation pile-ups in crystals containing impurities, addressing discrepancies between observed dislocation distributions and theories that assume freely gliding dislocations stopped by strong barriers. The authors propose a model in which an initial obstacle starts the pile-up…

Microdetermination of Carbon and Hydrogen in Organic Compounds by Gas Chromatography

A gas chromatographic method is proposed for microdetermination of carbon and hydrogen in organic compounds, intended to simplify and accelerate conventional combustion analysis. Samples of 2 to 5 mg are oxidized with copper oxide in a closed evacuated quartz tube, after which the combustion product…

Some Problems in the Theory of Homogeneous Markov Processes with Discrete Time

This paper studies homogeneous Markov processes with discrete time on an abstract measurable space under recurrence and minorization conditions formulated on a measurable subset. It introduces return kernels to this subset and uses them to derive criteria for the existence of a limiting stationary d…

Effect of Caustic Soda Solutions on the Absorption Band of Surface Hydroxyls in Some Silicates

This study examines how caustic soda treatment affects surface hydroxyl absorption bands in fine particles of zircon and beryl, with attention to implications for flotation activation of silicate minerals. Natural mineral powders smaller than 5 microns were treated with sodium hydroxide, washed, dri…

Detection of the Inner Radiation Belt at an Altitude of 320 km in the Region of the South Atlantic Magnetic Anomaly

This paper reports satellite measurements of enhanced radiation at an altitude of about 320 km over the South Atlantic, where the geomagnetic field is unusually weak. Using gas discharge and scintillation counters aboard the second Soviet spacecraft satellite, the authors compare detector readings a…

SIMPLE SUBGROUPS OF SIMPLY CONNECTED REAL SIMPLE LIE GROUPS

The paper studies connected subgroups of simply connected real simple Lie groups that correspond to simple subalgebras of real forms of classical Lie algebras. It develops methods for computing the kernel of the homomorphism from the simply connected group with a given subalgebra to its image, compa…

Motion of twinning dislocations in calcite

This study investigates the mechanical stress required to initiate motion of twinning dislocations in calcite, a key microscopic parameter in crystal twinning. Using repeated etching and localized loading with a diamond pyramid, the authors directly observed dislocation displacement along twin bound…

The explosion method and the heats of formation of $\mathrm{CF}_4$ , $\mathrm{CF}_3\mathrm{Cl}$ , $\mathrm{CFCl}_3$ and $\mathrm{CCl}_4$

This paper develops an improved use of the explosion method for thermochemical measurements by proposing a way to calculate explosion temperatures while accounting for energy losses in a spherical bomb. The author argues that losses arise both from heat transfer to the vessel walls and from incomple…

Isotopic Exchange between $\mathrm{O}_2^{18}$ and Molten $\mathrm{Na}_2\mathrm{WO}_4^{16}$

This study examines oxygen isotopic exchange between oxygen gas enriched in O-18 and molten sodium tungstate of normal isotopic composition at 720, 745, and 764°C. Experiments used different melt layer thicknesses, with gas-phase isotopic composition measured over time by mass spectrometry to calcul…

On the Strong Law of Large Numbers for Nonhomogeneous Markov Chains

This note studies strong laws of large numbers for random variables forming nonhomogeneous Markov chains, using Dobrushin ergodicity coefficients to measure dependence. It gives sufficient variance summability conditions, including the uniformly ergodic case where the classical Kolmogorov condition …

Effect of Adsorbed Halogens on the Electron Work Function of Iron

This study examines how chemisorbed chlorine and iodine affect the electron work function of spectrally pure iron under varied gas pressures and interaction temperatures. Contact potential differences were measured by the vibrating capacitor method after exposing reduced and degassed iron to halide …

Addition of Hydridosilanes to Allylamine

This study examines the hydrosilylation of allylamine, an unsaturated amine containing a free amino group, with a series of alkyl, aryl, and alkoxy hydridosilanes. Reactions were carried out in the presence of chloroplatinic acid, and the resulting gamma-propylaminosilanes were characterized by boil…

On S. L. Sobolev’s embedding theorems for abstract functions

This paper extends Sobolev’s embedding theory for classes of abstract additive set functions with values in a Banach space. It proves a limiting exponent embedding theorem for the classes under consideration, establishes a stability theorem for composite abstract functions satisfying a specified reg…

On the geometric theory of the simplest singular variational problem for a $(n-1)$-fold integral

This note develops a geometric framework for a singular parametric variational problem defined by an invariant hypersurface hyperarea integral. It focuses on the case of singularity class one, interpreting the indicatrices as singular hypersurfaces in a centro-affine setting and deriving the associa…

On the weight and cardinality of $H$-closed spaces

This paper extends known results on the weight of compact Hausdorff spaces to broader classes of H-closed and noncompactifiable spaces. It proves that a continuous mapping from an H-closed space onto a canonical, equivalently noncompactifiable, space does not increase weight, and that the weight of …

Effect of Acidity on the Yield of Radiation-Chemical Reactions

This paper examines how acidity affects yields in radiation chemical and related photochemical reactions, addressing inconsistencies in explanations based solely on rapid equilibrium between hydrogen atoms, protons, and molecular hydrogen ions. The authors propose that acceptor species compete with …

Effect of Temperature on the Optical Absorption of Polycrystalline Cadmium Sulfide Layers

This study examines how temperature affects optical absorption in polycrystalline cadmium sulfide films, with particular attention to the long-wavelength absorption region near 4600 to 5070 Å. CdS layers were prepared by vacuum sublimation in vacuum, argon, or hydrogen sulfide on substrates heated t…

ALGORITHMIC SOLVABILITY OF THE ISOMORPHISM PROBLEM FOR AUTOMATA

This paper studies algorithmic decision problems for automata presented by finite systems of generators, inputs, and defining relations, treating automata as algebraic systems. It shows that presentations can be transformed into closed systems of defining relations, yielding canonical word forms and…

On the Configuration of $H$-Congruences

This note studies pairs of line congruences characterized by the focality of their corresponding ruled surface submanifolds, with particular attention to the special class of congruences denoted H. Using the torsal frame formalism and differential relations for canonical frames, it identifies pairs …

On the Formation of Large Microscopic Structures in Crystalline Polypropylene

This paper investigates the microscopic crystalline structures formed in bulk isotactic polypropylene during cooling from the melt, a setting considered more relevant to polymer processing than dilute solutions or thin films. Polypropylene samples were cooled under controlled conditions, fractured a…

On the interaction of sulfur with rubber under the influence of $\gamma$-radiation

This study examines the interaction of sulfur with natural rubber under gamma irradiation using electron paramagnetic resonance over a range of low temperatures. Irradiation at room temperature produced similar long-lived radical spectra in pure rubber and rubber containing 2 percent sulfur, while i…

Condensation of Formaldehyde with Perfluoroolefins—Tetrafluoroethylene, Hexafluoropropylene, and Chlorotrifluoroethylene

This study examines the acid-catalyzed condensation of formaldehyde with fluorinated olefins, a Prins-type reaction that is generally hindered by the electrophilic character of fluoroolefin double bonds. Using chlorosulfonic acid as catalyst, paraformaldehyde was reacted with tetrafluoroethylene, he…

Dispersion Relations for the Compton Effect on Nucleons

The paper derives dispersion relations for invariant amplitudes describing Compton scattering of photons by nucleons. Using a gauge invariant decomposition into six scalar amplitudes, crossing symmetry, Cauchy’s theorem, and low energy constraints, it formulates relations whose subtraction constants…

On the Power of Circuits of Functional Elements

This paper studies the synthesis complexity of Boolean control systems represented as circuits of functional elements, using average and maximum numbers of excited elements, interpreted for example as circuit power, rather than total element count. It defines corresponding Shannon-type functions ove…

On the divisor class group of some algebraic curves

This note outlines a proof of finiteness for the degree zero divisor class groups of the function fields defined by curves \(y^l=x^k(1-x)\) over the cyclotomic field generated by an \(l\)-th root of unity, for specified small primes and values of \(k\). The argument uses complex multiplication on th…

On Thallium Polychromates

This study examines thallium chromates and polychromates through heterogeneous equilibria in the systems thallium chromate, chromic anhydride, and water, and in related systems containing sodium, potassium, and ammonium dichromates at 25°C. Phase diagrams and solubility isotherms show that monovalen…

On the Isotopic Exchange of Hydrogen in Primary and Secondary Alkyl Chlorides

This study examines isotopic hydrogen exchange in primary and secondary alkyl chlorides, extending earlier work on tertiary alkyl halides and testing whether exchange can be induced through ionization of the carbon chlorine bond. Alkyl chlorides were reacted with deuterium chloride in nitrobenzene i…

Effect of $\gamma$ Radiation from $\mathrm{Co}^{60}$ on Isotope Exchange Between Hydrocarbon Polymers and Gaseous Deuterium

This study examines radiation-induced isotopic exchange between gaseous deuterium and hydrocarbon polymers or liquid hydrocarbons under cobalt-60 gamma irradiation, a process not observed under ordinary nonirradiated conditions. Samples were sealed with deuterium at pressures up to about 150 atm, ir…