Recent Papers

Mesh Method for Some Problems of Mathematical Physics

The paper develops a finite-difference grid method for second-order strongly elliptic equations, motivated by the need for convergence estimates that do not require continuous fourth derivatives of the solution. It constructs grid equations variationally by averaging the coefficients of the differen…

Reactivity of Noble Gases. A New Method for Preparing $\mathrm{XeF}_2$

This paper reports a simplified synthesis of xenon difluoride from xenon and fluorine under ordinary temperature and elevated pressure, in contrast to earlier methods requiring heating, irradiation, electric discharge, or specialized apparatus. The authors argue that severe conditions are unnecessar…

On the concept of a minimal scale of spaces

This paper develops the theory of scales of Banach spaces, focusing on minimal scales and their interpolation properties. It defines regular and reflexive continuous normal scales, proves that maximal scales constructed from normally embedded endpoint spaces are regular, and shows that a minimal sca…

Remarks on the Fisher–Welch–Wald Test

This note examines the Fisher, Welch, Wald test for equality of the means of two normal samples when variances are unknown and possibly unequal, focusing on whether a nonrandomized similar test of the usual boundary form can exist. Building on earlier nonexistence results under differentiability and…

One-sided inequalities of Chebyshev type

This paper develops one-sided versions of Chebyshev-type probability inequalities that require assumptions only on one tail of a distribution rather than on moments over the whole real line. It proves a general bound for probabilities of the form P(X ≥ t) and P(X ≤ -t) using monotone nonnegative fun…

Cathode sputtering of tungsten by potassium ions

This study examines cathode sputtering of polycrystalline tungsten by potassium ions, focusing on how adsorbed gases and alkali films alter measured sputtering yields. Using radioactive tracer measurements and collector biasing, the authors distinguish neutral sputtering from a negative-ion componen…

Regular Solutions of Monge–Ampère Equations

This paper studies the first boundary-value problem for two-dimensional Monge-Ampere equations in a convex domain, seeking solutions regular up to the boundary. It introduces boundary-dependent geometric quantities, lower and upper twisting of the prescribed boundary curve, and uses them to formulat…

Embedding Theorems for Banach Spaces of Measurable Functions

This note studies symmetric Banach spaces of measurable functions on the unit interval, defined by rearrangement invariance and monotonicity with respect to absolute value. It characterizes the possible fundamental functions of such spaces, proves continuous embeddings between every symmetric space …

ON A PROBLEM OF OPTIMAL DISCRETE CONTROL

This paper studies a finite-stage discrete optimal control problem in which a linear state recurrence with a nonlinear control term is optimized according to a convex terminal cost. By reformulating the reachable terminal states as a compact convex set and using duality from mathematical programming…

Involuted Semigroups of Full Binary Relations

This paper studies involuted semigroups representable by semigroups of complete binary relations, with multiplication and inversion of relations, and their ordered analogues under inclusion. It gives a necessary and sufficient condition for an ordered involuted semigroup to be represented by complet…

Regularity, product and spectra of proximity spaces

This paper studies regularity of proximity spaces, understood as possession of a greatest compatible uniform structure, and shows that not every proximity space is regular. It introduces a strong Cartesian product for proximity spaces, compares it with the earlier weak product, and derives criteria …

On the Theory of a Laminar Multicomponent Boundary Layer on a Chemically Active Surface

This paper formulates and approximates the problem of a laminar multicomponent boundary layer near a stagnation point or line on a chemically active burning surface of complex composition. Using effective diffusion coefficients, it derives governing equations and boundary conditions for momentum, sp…

Asymptotic formulas for the eigenvalues of the Laplace operator in the case of a polyhedron

The paper studies the high frequency asymptotics of eigenvalues of the Laplace operator in an m-dimensional polyhedron with either Dirichlet or Neumann boundary conditions. It proves that the standard Weyl remainder for a piecewise smooth domain can be sharpened in the polyhedral case from \(O(k^{m-…

Determination of Thermodynamic Constants of Molecular Compounds by Dielectrometric Titration

A dielectrometric titration method is developed for determining thermodynamic constants of molecular compound formation in nonpolar solutions. The approach measures changes in dielectric constant and density during stepwise addition of one component, uses deviations of titration curves from extrapol…

On the Rate of Physicochemical Transformations of $\mathrm{CO}_2$ Molecules Behind a Shock Wave at Temperatures of 2000–4000 $^\circ$ K

This study examines the rate of vibrational excitation and dissociation of carbon dioxide molecules behind shock waves at temperatures corresponding to Mach numbers 6 to 11. The authors compare calculated flow parameters for different nonequilibrium states with shock tube measurements obtained by To…

Mass Spectrometric Study of Methylthiohydantoins of Amino Acids

This study addresses the difficulty of identifying amino acid derivatives released during peptide sequencing by Edman-type procedures, where phenylthiohydantoins may give weak or non-diagnostic molecular and fragment peaks. The authors examine methylthiohydantoins of amino acids as alternative deriv…

Chromium chalcogenosulfides

This study investigates mixed-anion chromium compounds formed from divalent chromium sulfide, motivated by the covalent character of Cr-S bonding and the expected oxidation behavior of chromium in such systems. Chromium sulfide was synthesized from the elements, then reacted with selenium or telluri…

HYDROTHERMAL SYNTHESIS OF GARNETS CONTAINING $\mathrm{V}^{3+}$, $\mathrm{In}^{3+}$, AND $\mathrm{Sc}^{3+}$

This paper reports the hydrothermal synthesis and characterization of new garnet-type compounds in which octahedral positions are occupied by vanadium, indium, or scandium ions. Using chloride solutions as solvents at about 550°C and 1300 atm, the author prepared several calcium, cadmium, and mangan…

Linear control problem in a Banach space

This paper studies a linear optimal control problem in a real Banach space ordered by a cone, with controls constrained by pointwise bounds and an integral inequality. Using generalized Riemann Stieltjes integrals and the evolution operator for a linear Cauchy problem under Kato type assumptions, th…

Solving the Dirichlet and Neumann Problems for Irregular Domains by Potential Theory Methods

This note extends Radon-type potential theory for irregular domains in three-dimensional space from double-layer to single-layer potentials and applies it to Dirichlet and Neumann boundary problems. Under a bounded-variation condition on the solid angle, it defines interior and exterior boundary flu…

Majorants for the Derivative of a Polynomial

The paper studies majorants for the kth derivative of algebraic polynomials of degree at most n, comparing the classical Markov majorant under a uniform bound on the interval with a discrete majorant defined by bounds at n plus 1 interpolation nodes. It proves an exact formula for the discrete major…

Preparation of organozinc compounds of the $\mathrm{R}_2\mathrm{Zn}$ type in the aromatic heterocyclic and aliphatic-aromatic series via the Grignard reagent

This paper describes the preparation of organozinc compounds of the type R2Zn in aromatic, heterocyclic, araliphatic, and aliphatic series using Grignard reagents and zinc chloride. The authors isolate several products as dioxanates by precipitating magnesium salts with dioxane, obtaining diphenylzi…

Synthesis of substituted methyltropilidenes by the reaction of alkylbenzenes with chlorocarbene and methyllithium

The study investigates the reaction of chlorocarbene, generated from methylene chloride and methyllithium, with benzene and several alkylbenzenes as a route to substituted methyltropylidenes. Experiments varying temperature, reagent ratios, and addition rate showed optimal formation near 30 to 40 °C…

Preparation of polymers with dibenzoborimidazoline units in the main chain

This paper reports the synthesis of polymers containing dibenzborimidazoline units in the main chain as part of a study of heat-resistant polymers with rigid heterocyclic structures. Polycondensation of 3,3-diaminobenzidine with either the tetrabutyl ester of p-phenylenediboronic acid or tetraacetyl…

Study of the 4197 cm $^{-1}$ Absorption Band of Potassium Ferricyanide under High Pressure

This study examines the infrared absorption spectrum of crystalline potassium ferricyanide under high pressure, focusing on the 4197 cm−1 band assigned to an overtone vibration of the ferricyanide complex. Spectra recorded during compression show a pressure induced shift of this band toward higher f…

Study of the Structure of the Electrical Double Layer on Gallium by Differential Capacitance Measurements

This study examines the structure of the electrical double layer on high-purity gallium, testing whether regularities established for mercury electrodes also apply to another liquid metal. Differential capacitance was measured on a dropping gallium electrode in 1 N solutions containing various catio…

Underdetermined and overdetermined systems of differential equations with constant coefficients

This note studies general linear systems of partial differential equations with constant coefficients, including underdetermined and overdetermined cases not covered by square nonsingular matrices. Using syzygy chains over the polynomial ring of differential operators and associated Ext modules, it …

On the Thermodynamics of Complex Carbides $(\mathrm{Fe}_x\mathrm{Mo}_y)_2\mathrm{C}$

This paper investigates the thermodynamics of complex iron, molybdenum carbides of the type (Fe x Mo y)2C, a class for which data were limited compared with simple transition metal carbides. Carbides with several iron contents were synthesized, structurally identified as having the Mo2C structure, a…

Thermodynamics of Heterogeneous Catalysis Processes. Recombination of Gas Atoms on the Surface of Solids

This paper applies the thermodynamics of irreversible processes to heterogeneous catalysis, focusing on the recombination of gas atoms on solid surfaces. The authors model an open two-phase system consisting of a gaseous atomic-molecular mixture and a solid catalyst, derive entropy production and li…

Undecidability of the Theories of Symmetric and Simple Finite Groups

This paper proves undecidability results for the elementary theories of the classes of finite symmetric groups, finite alternating groups, and finite simple groups. The argument reduces from the theory of two equivalence relations, using an effective translation of formulas into the group signature …

Linear Pyrolysis of Condensed Substances

This paper examines stationary one-dimensional linear pyrolysis of condensed substances, focusing on polymethyl methacrylate, and addresses whether the decomposition rate can be related directly to surface or heater temperature. The authors combine experimental measurements of decomposition rate, pl…

Passage of a Nonequilibrium Gas Through the Critical Section of a Nozzle

The paper analyzes steady quasi-one-dimensional flow of a nonequilibrium gas near the critical section of a nozzle, neglecting ordinary viscosity and thermal conductivity while retaining relaxation effects. Using expansions of the hydrodynamic and thermodynamic equations to cubic order, it derives f…

ON THE QUESTION OF UNIQUENESS OF THE SOLUTION OF AN INTEGRAL EQUATION

The paper studies uniqueness for systems of nonlinear integral equations and points out limitations of standard majorant estimates based on a single Banach norm, especially their inability to reflect componentwise behavior and the role of the free term. It develops refined comparison criteria using …

Spectral sensitization of the internal photoelectric effect of copper phenylacetylide by dyes

This study examines spectral sensitization of the internal photovoltaic effect in the organic semiconductor copper phenylacetylide by adsorbed organic dyes. Using transverse photoconductivity and diffusion photo-emf measurements, the authors compare undyed samples with samples treated mainly with ch…

Viscosity, Raman Scattering Spectra, and Thermodynamic Parameters of the Homologous Series of Normal Paraffins $\mathrm{C}_5$–$\mathrm{C}_{18}$

This paper examines relationships among viscosity, low-frequency Raman spectra, and thermodynamic parameters in the homologous series of normal paraffins from C5 to C18. Activation energies derived from the temperature dependence of viscosity are compared with Raman frequencies below 500 cm-1 in liq…

Metrization of Lipschitz Spaces

Structure of spectral absorption bands of $\mathrm{Co}(\mathrm{H}_2\mathrm{O})^{2+}_6$ and $\mathrm{Co}(\mathrm{OR}_1\mathrm{R}_2)^{2+}_6$ complexes in solutions in the 25 000–13 000 cm $^{-1}$ region

This paper examines the structure of electronic absorption bands of hexaaquocobalt(II) and cobalt(II) complexes with oxygen-containing organic ligands in solution, focusing on the 25,000 to 13,000 cm⁻¹ region used to infer coordination symmetry. Using recording spectrophotometry and graphical differ…

Estimation of the Mass of a Superstar

This paper estimates the mass and physical conditions of a “superstar” of the 3C 273 type by balancing gravity against radiation pressure in its ionized atmosphere. Using the observed luminosity and treating Compton scattering by electrons as the dominant coupling between radiation and matter over m…

On the Nature of the Chemical Bond in $\mathrm{A}^{\mathrm{III}}\mathrm{B}^{\mathrm{V}}$ Semiconductor Compounds

This paper examines the nature of chemical bonding in group III to group V semiconductor compounds, challenging the model of Mooser and Pearson that assumes electron transfer from the group V atom to the group III atom before tetrahedral covalent bonding. Using x-ray spectral analysis of the antimon…

Duality of Functors in the Category of Pointed Sets

The paper studies duality for covariant functors on the category of sets with a distinguished point, using the associated internal Hom and smash product constructions. It develops formulas for duals of functors built from products, bouquets, and specified unions, and analyzes a class of subfunctors …

Effect of Waves and Time on the Ability of a Monolayer to Reduce Water Evaporation

This study examines how wave motion and aging affect the ability of cetyl alcohol monolayers to reduce water evaporation. Using a controlled water bath, a mechanical wave generator, vapor absorption measurements, and surface pressure measurements, the authors compared clean and monolayer-covered sur…

On the triglycocollates of tetravalent platinum

The paper reports the synthesis and characterization of tetravalent platinum triglycocollate derivatives, especially the previously unobtained compound [Ptgl3]Cl. Oxidation of sodium diglycocollatoplatinate(II) with hydrogen peroxide gave a dihydroxo platinum(IV) intermediate, which was converted by…

Synthesis of Organotin Oxygen-Containing Compounds of the Acetylene Series

A method is described for synthesizing oxygen-containing organotin acetylene compounds in which the triple bond is in the alpha position relative to tin. The approach involves reacting acetylene derivatives containing an acetylenic hydrogen atom with hexaethylstannoxane, and is illustrated by the pr…

Structure and Reactivity of Fluorine-Containing $\beta$-Sultones

This paper examines the structure and reactivity of fluorine-containing beta-sultones formed from fluorinated olefins and sulfur trioxide, with emphasis on tetrafluoroethane-beta-sultone and related isomers. Using reactions of trifluorovinyl chlorosulfate, halogen exchange, thermal isomerization, an…

Coloration and Luminescence of Synthetic Ruby Irradiated with $\mathrm{Co}^{60}$ Gamma Rays

This paper examines how gamma irradiation from a Co60 source affects the optical absorption, coloration, thermoluminescence, and paramagnetic resonance of light pink synthetic ruby containing 0.2 to 0.4 percent Cr2O3. Using polarized absorption measurements, thermoluminescence recording during contr…

Some Cosmological Consequences of Galaxy Counts to Various Angular Diameters

This paper examines cosmological implications of galaxy counts by angular diameter using the homogeneous Palomar Atlas, arguing that angular diameters provide a more reliable statistical distance criterion than photographic magnitudes. It develops formulae for the expected number of galaxies above a…

ON THE CONVERGENCE OF THE PROJECTION METHOD IN EIGENVALUE PROBLEMS

This paper studies convergence of approximate eigenvectors produced by a projection method for holomorphic operator pencils between Hilbert spaces. Given projection-complete finite-dimensional subspaces, it first proves that the component of a normalized approximate eigenvector orthogonal to the eig…

Selective excitation of neon atoms upon addition of helium

This paper investigates selective excitation of neon atoms in helium neon discharges, motivated by the strong enhancement of the 6328 Å neon line when helium is added. Using a direct current discharge tube and spectrographic intensity measurements, the study compares line intensities in helium neon …

The thermochemistry of cerium $(\mathrm{IV})$ nitrate extraction with tributylphosphate

This paper examines the thermochemistry of extracting cerium(IV) nitrate from aqueous solution with tributyl phosphate, a system complicated by hydrolysis and possible transfer of basic salts into the organic phase. Using direct calorimetric measurements at 25 degrees, the authors determined heats o…

On the preparation of some compounds of $\mathrm{Pu}(\mathrm{V})$

This paper examines conditions for preparing concentrated nitric acid solutions of pentavalent plutonium and using them to synthesize Pu(V) compounds. Stability experiments over pH 2 to 6 and plutonium concentrations from 0.5 to 5 g/l indicate that Pu(V) is most stable at pH 3.5 to 4.5 and at concen…