Recent Papers

On Elementary Theories of Locally Free Universal Algebras

The paper studies first-order formulas over locally free universal algebras of a fixed finite type, where local freeness is characterized by separation and injectivity conditions for the fundamental operations. It presents an algorithm that transforms any formula into an equivalent normal form on al…

Synthesis of Silicon-, Germanium-, and Tin-Containing para-Substituted Styrenes and $\alpha$-Methylstyrenes

This paper examines the synthesis of para-substituted styrenes and alpha-methylstyrenes containing silicon, germanium, and tin, compounds of interest as monomers for heat-resistant polymers. The authors apply the organomagnesium, Normant-Ramsden, route to prepare known trimethylsilyl and trimethylst…

A Note on the Schrödinger Equation with a Singular Potential

This note gives a mathematical interpretation of the three-dimensional Schrödinger equation with a Dirac delta potential, whose formal Hamiltonian is not an operator in Hilbert space. The authors compare a cutoff regularization of the singular interaction, with a coupling constant depending on the c…

Continuum integrals associated with some differential equations and systems

This note extends a method for representing solutions of differential equations by continual integrals to operator equations and systems associated with semigroups in Hilbert spaces. It defines matrix-valued set functions on path spaces, gives criteria for when they have bounded variation, and deriv…

The applicability of Allen's model to the radiolysis of aqueous solutions

This paper examines the applicability of Allen’s model of aqueous radiolysis, particularly the approximation that primary radiolysis products may be treated as uniformly distributed and described by homogeneous chemical kinetics. The authors use predicted intensity scaling relations, in which concen…

Boundary properties of functions of the class $W_p^{(l)}$ on domains with corner points

This note studies boundary values of Sobolev functions in classes W_p^{(l)} on bounded plane domains whose piecewise smooth boundaries may have corner points. It first establishes matching criteria for fractional Sobolev classes across a point, then uses these results to characterize the traces of n…

Reactions of Polyfluorinated Nitrosoalkanes with Amines

This study examines reactions of polyfluorinated nitrosoalkanes with compounds containing nucleophilic amino functions. It shows that primary aliphatic, alicyclic, and aromatic amines generally form polyfluorinated azo compounds under low-temperature or acidic conditions, while halogenated nitrosoal…

On the phenomenon of “scattering” of charged quasiparticles at singular points in $\mathbf{p}$-space

This paper analyzes a form of apparent scattering of charged quasiparticles in metals and semiconductors that arises from singular points of the dispersion relation in momentum space rather than from force centers in real space. Using the semiclassical equations of motion in weakly varying electroma…

On the Summation of the Product of Two Numerical Series

This note studies conditions under which the Cauchy product of two numerical series is summable or absolutely summable when the factors are summable by complex normal triangular methods. It defines several classes of summation methods according to how they preserve ordinary summability, boundedness,…

Thermal Conductivity and Viscosity of Zirconium and Hafnium Tetrachloride Vapors in the Temperature Range $300-700^\circ$

This study measures molecular transport properties of zirconium and hafnium tetrachloride vapors needed for developing separation methods for these compounds. Thermal conductivity was determined by a hot-wire method between 300 and 500 C, using hydrogen as a reference gas, and viscosity was measured…

Some Problems on the Behavior of Finite Automata

This paper studies finite automata operating in random environments that penalize actions with specified probabilities, formulating their behavior as Markov chains under ergodicity assumptions. It analyzes automata with a linear tactic, deriving the expected penalty and showing that in a stationary …

BIOPHYSICS

A New Route for the Synthesis of Quinolizidine Derivatives

This paper reports a simple synthetic route to quinolizidine derivatives, a class that includes several physiologically active alkaloids. The method starts from 2-methyl-2-(beta-cyanoethyl)dihydroresorcinol, which is hydrogenated over skeletal nickel in alkaline methanol and then treated with acetic…

On the equilibrium between the tetrazole and azide forms of benzothiazolotetrazole

This paper examines the equilibrium between tetrazole and azide forms of benzthiazolotetrazole using infrared spectroscopy in crystals, solutions, and melts. The spectra show that the crystalline compound has the tetrazole structure, while dissolution produces a reversible tetrazole to azide equilib…

On bounded solutions of a certain quasilinear system

The paper studies bounded solutions of a quasilinear system of differential equations with a rapidly varying forcing term, extending results on forced harmonic oscillations in weakly nonlinear systems. It introduces an exponential dichotomy type condition for the associated linear system, constructs…

On the Structural Properties of Semigroups

This note studies structural properties of semigroups through the ordered set, and extended lattice, of their subsemigroups, focusing on structural characterizability and structural determinability. It gives lattice-theoretic criteria for several classes, including periodic semigroups, semigroups wi…

Radical Polymerization as an Energy Chain Process Carried Out by Means of an Exciton

This paper develops a quantum mechanical interpretation of radical polymerization at low temperatures, addressing why chain growth can proceed when repeated thermal activation of monomer addition would be inefficient. It compares ordinary energy-chain propagation, in which reaction heat is localized…

Thermodynamic Characteristics of Niobium Oxides. (Equilibrium with Hydrogen and Electrochemical Measurements)

This study determines thermodynamic characteristics of niobium oxides in the niobium oxygen system, focusing on equilibria among Nb2O5, NbO2, NbO, and metallic niobium. Hydrogen reduction equilibria were measured by a circulation method at 1200 to 1550 °C, and electromotive force measurements were m…

Motion with Plane Waves of an Incompressible Conducting Fluid Taking into Account Electromagnetic Radiation

This paper analyzes one-dimensional oscillations of a finite plane layer of incompressible, perfectly conducting fluid after an initial release of energy, with external pressure, magnetic pressure, and electromagnetic radiation from the free surface included. Using Lagrangian variables, the author d…

Heat Capacity $c_v$ of Water and Steam at High Temperatures and High Pressures

This study reports direct calorimetric measurements of the constant-volume heat capacity of water and water vapor at temperatures up to 500 degrees Celsius and pressures up to 800 atmospheres, extending earlier work with improved stirring and reduced heat-loss effects. Measurements along several iso…

On Some Estimates of a Differentiable Function

This note establishes two sharp estimates for a real function differentiable n times on an interval under prescribed zeros of the function and its successive derivatives at possibly different points. The first bound involves constants from the expansion of tan t plus sec t, while the second gives an…

Investigation of Higher Oxides and Peroxides of Uranium by the Isotope Method

This study examines the poorly characterized low temperature region of the uranium oxygen system, especially the structures and decomposition behavior of uranium peroxide hydrate and uranium heptoxide. Using oxygen 18 labels placed selectively in peroxide oxygen or hydration water, the authors follo…

On the Distribution of Electron Density in Indium Arsenide

This paper investigates the distribution of electron density in indium arsenide with the sphalerite structure, motivated by the relation between bonding and the semiconductor properties of III,V compounds. Powder X-ray diffraction data obtained with Cu K alpha radiation were used to calculate struct…

Conditions for well-posedness of one-dimensional mixed problems

This note studies well-posedness for a class of one-dimensional mixed initial-boundary value problems for systems of linear partial differential equations on several non-overlapping intervals with coupled boundary conditions. Using asymptotic fundamental solutions for the associated ordinary differe…

Study of phase equilibrium in the quasi-ternary system $\mathrm{Ti}$ – $\mathrm{Ti}_3\mathrm{Sn}$ – $\mathrm{Zr}$

This study examines phase equilibria in the titanium rich region of the titanium, zirconium, tin system, treated as the quasi-ternary system Ti, Ti3Sn, Zr. Seventy four alloys were prepared by crucibleless induction melting in purified helium, annealed at selected temperatures from 500 to 1560°C, qu…

A NEW ISOTOPE Ir$^{183}$

This paper reports evidence for a new neutron-deficient isotope, Ir-183, produced among the spallation products of gold irradiated with 660 MeV protons. The authors radiochemically separated iridium from irradiated gold, periodically isolated daughter osmium, and measured osmium decay activities to …

Atomic scattering factors and electron density distribution in gallium antimonide

This study examines the distribution of electron density in gallium antimonide as part of an investigation of bonding in group III antimonide semiconductor compounds. Using X-ray powder diffraction with Cu K alpha radiation, the authors determined structure amplitudes, calculated atomic scattering f…

Obtaining High-Purity Hydrocarbons by Thermal Displacement Chromatography

This paper examines thermal-displacement chromatography as a preparative method for deep purification of organic gases, using propylene isolation as the main example. Mixtures containing propylene and impurities such as ethane, propane, ethylene, acetylene, sulfur compounds, water, and heavier hydro…

On the Dirichlet and Neumann Problems on Triangular and Hexagonal Lattices

This note studies finite difference approximations to Dirichlet and Neumann boundary value problems for harmonic conjugate functions on paired triangular and hexagonal grids. It shows that although the local four point approximation of the Laplace operator on a hexagonal grid has only first order re…

CATIONIC-TYPE SILVER SELENOCYANATE COMPLEXES

This study examines whether silver selenocyanate forms cationic complexes analogous to known silver halide complexes and whether nitrate and perchlorate counterions affect their formation. The authors measured the solubility of freshly prepared silver selenocyanate in concentrated aqueous silver nit…

On the Quantitative Assessment of Substituent Effects on the Polarographic Reduction of Certain Azomethine Compounds

This paper examines the quantitative influence of aromatic substituents on the polarographic reduction of azomethine compounds using the Hammett relationship. Phenylhydrazones, semicarbazones, and thiosemicarbazones of substituted aromatic aldehydes and acetophenones were studied in methanol water b…

Distribution of Heterocharge and Field in Photoelectrets

This paper analyzes the spatial distribution of heterocharge, electric field, potential, and carrier concentrations in photoelectrets using a band model with donor and acceptor levels under illumination and a polarizing field. Starting from stationary transport, trapping, and Poisson equations, it d…

Initiation of Polymerization by Electric Charges Arising at the Phase Interface

This paper examines whether electric charges and potential jumps arising at phase boundaries can initiate polymerization in systems lacking conventional initiators or catalysts. The authors develop a kinetic argument that interfacial potentials may alter both the pre-exponential factor and activatio…

Necessary and sufficient conditions for uniform embedding of a space into Euclidean space

This note gives necessary and sufficient conditions for a metric space of uniform dimension n to be uniformly embeddable in Euclidean space of dimension N at least 2n+1, and extends the formulation to uniform spaces with a countable base. The criterion combines a noncondensation condition, expressed…

On the Solvability of Nonlinear Ritz Systems

This note studies the solvability of finite nonlinear systems arising from the Ritz method, equivalently from the Bubnov-Galerkin approximation, for minimizing a functional that is the potential of a nonlinear operator in a Hilbert space. Following Davidenko’s continuation idea, the Ritz equations a…

ADDITION OF DIALKYL PHOSPHOROUS ACIDS TO 3,3′-DIMETHOXY-DIPHENYL-4,4′- AND DIPHENYLMETHANE-4,4′-DIISOCYANATES

This paper examines the addition of dialkyl phosphorous acids to 3,3′-dimethoxy-diphenyl-4,4′-diisocyanate and diphenylmethane-4,4′-diisocyanate, extending earlier work on related diisocyanates. The reactions were carried out in the presence of small amounts of sodium or sodium alcoholate, and the a…

On Steric Hindrance in Menshutkin Reactions

The study examines how steric hindrance affects pressure dependence in Menschutkin reactions, using nitrobenzene as a solvent to reduce solvation volume effects. Rate constants were measured under pressure for reactions of 2,6-lutidine with ethyl and isopropyl iodide, and of gamma-picoline with ethy…

New criteria for paracompactness and metrizability of an arbitrary $T_1$-space

The paper introduces an alpha-base, a strengthening of a countable complete system of open coverings, and uses it to formulate criteria for paracompactness and metrizability in general separation settings. It proves that a space is paracompact exactly when every open cover majorizes some sequence of…

On mechanical cubature formulas in $n$-dimensional space

This paper studies the error functional of mechanical cubature formulas in n-dimensional domains, focusing on the first part of the minimax problem: determining the maximal error for fixed coefficients and nodes. The analysis is carried out for unit balls in Sobolev-type spaces with square-integrabl…

Two Classes of Inequalities for Sufficiently Smooth Functions of $n$ Variables

This paper develops two related classes of interpolation inequalities for sufficiently smooth functions of several variables, emphasizing inequalities that are sharp both with respect to dimension and differential order. It proves new inequalities for anisotropic smoothness norms defined through fin…

Comparative Study of the Kinetics of the Conversion of Various Hydrocarbons to Acetylene in an Electric Discharge in a Static System

This study compares the kinetics and energetics of converting methane, ethane, propane, ethylene, and propylene to acetylene in glow and high-voltage arc discharges under static conditions. Experiments measured product composition, hydrocarbon conversion, apparent first-order decomposition constants…

Linear-Enveloping Coupler Curves of Mechanisms with a Prismatic Pair

This paper develops the theory of linearly enveloping coupler curves for planar mechanisms containing three revolute pairs and one prismatic pair. It derives parametric equations for the envelopes generated by arbitrary straight lines fixed in the connecting rod or slider of slider-crank type mechan…

Acyloxy Derivatives of Cobalt, Nickel, and Manganese

This study investigates the preparation of acyloxy derivatives of cobalt, nickel, and manganese by exchange reactions between metal acetylacetonates and carboxylic acids. Cobalt and nickel diacetylacetonates and manganese triacetylacetonate were reacted with saturated and unsaturated dibasic acids, …

Approximation of Functions by Generalized Linear Landau Operators

The paper studies approximation of functions by generalized linear Landau operators defined through kernels of the form \([1-(t-x)^{2k}]^n\), where \(k\) is a positive integer. It establishes pointwise and uniform convergence on subintervals of \((0,1)\), \(L^p\) convergence, estimates in terms of t…

Dependence of the limiting explosion pressure of gaseous hydrazoic acid on the power of the spark pulse

This study examines how the limiting explosion pressure of gaseous hydrazoic acid depends on the power of a spark pulse, addressing earlier views that the pressure reaches a lower boundary beyond which increased spark energy has no effect. Experiments in a spherical glass vessel with a central spark…

On the Cauchy Problem for a Class of Nonlinear Parabolic Systems

This note studies the Cauchy problem for nonlinear parabolic systems whose highest spatial differentiation orders may differ in different variables, extending earlier results for linear and near-linear systems. It defines a class of 2b-parabolic systems and proves local existence, uniqueness, contin…

Reflection spectra of polycrystalline cadmium sulfide films at a temperature of $77,3^\circ$ K

This study examines the reflection spectra of thin polycrystalline cadmium sulfide films at liquid nitrogen temperature in the 460 to 490 mµ region, with attention to how spectral structure depends on deposition conditions. Films were prepared by sublimation in vacuum, argon, or hydrogen sulfide on …

On the Mechanism of Formation of Carbonyl Compounds and Acids during Emulsion Oxidation of Isopropylbenzene

This study examines the formation of carbonyl compounds and acids during the emulsion oxidation of isopropylbenzene, with particular attention to the effects of inhibition by beta-naphthol. Oxidation experiments in a weakly alkaline emulsion showed that addition of the inhibitor stopped peroxide acc…

Synthesis of Phosphocyanine Dyes

This paper investigates synthetic routes to polymethine dyes in which phosphorus replaces one or both terminal nitrogen atoms of conventional cyanine chromophores. The authors show that phosphonium salts with active methylene groups condense with p-dimethylaminobenzaldehyde to give phosphostyryl dye…

DIVERGENT DIAGRAMS IN THE FORMAL PERTURBATION THEORY FOR A NONIDEAL FERMI–DIRAC SYSTEM AND THEIR MUTUAL COMPENSATION

This note examines formal divergences in the Brueckner-Goldstone perturbation expansion for the ground-state energy of a nonideal Fermi-Dirac system with regular interactions. It formulates a criterion for divergences caused by simultaneous vanishing of energy denominators at the Fermi surface, show…