Recent Papers

From the History of the Struggle to Protect Workers’ Health in 1917

Depolarizations and intensities in the Raman spectra of benzene and hexadeuterobenzene

This paper applies a previously developed method for calculating Raman depolarizations and intensities to benzene and hexadeuterobenzene, treating totally symmetric, nonplanar degenerate, and planar degenerate vibrations. Using normal-coordinate data and experimental depolarization and intensity rat…

On Interval Logging of Acoustic Waves

This paper describes an interval acoustic logging method intended to improve the determination of formation velocities in boreholes. The proposed installation places both an electromagnetic elastic-wave source and a piezoelectric receiver in the borehole, uses intervals of 5 to 10 m, and records rep…

First Boundary Value Problem for a Fourth-Order Elliptic-Type Equation Degenerating on the Boundary of the Domain

This note studies the first boundary value problem for a general fourth order elliptic equation in two variables whose principal part degenerates on a portion of the boundary lying on the x-axis. It formulates weighted function spaces and boundary conditions appropriate to different rates of degener…

On the Quasiclassical Interpretation of Quantum Effects in the Theory of the Luminous Electron

This paper gives a quasiclassical interpretation of quantum effects in the motion of an ultrarelativistic radiating electron in a synchrotron magnetic field. Starting from classical equations for betatron and synchrotron oscillations with radiation reaction, it derives the associated damping terms a…

Transformations of $\beta$-Chloro Ethers in the Presence of Metals

The study examines transformations of β-chloro ethers in the presence of sodium, copper, aluminum, and magnesium, using chiefly the methyl ether of amylene chlorohydrin. Metallic sodium, contrary to an expected coupling reaction, cleaves the ether with formation of amylene, sodium methoxide, and sod…

ON POLYNOMIALS ORTHOGONAL ON A SMOOTH CONTOUR WITH A DIFFERENTIABLE WEIGHT

This paper studies polynomials orthogonal on the boundary of a bounded plane domain with a differentiable positive weight, relating their behavior to the smoothness of the contour and the differential properties of the weight. Using conformal mapping of the exterior domain, Szego-type factorization,…

Polymerization of Styrene Under the Influence of Diazoamino Compounds and Activators

This paper examines how organic acids and acid anhydrides affect the bulk polymerization of styrene initiated by diazoamino compounds, especially diazoaminobenzene, at 70 degrees Celsius. Kinetic measurements of polymer yield, initiator decomposition, and nitrogen evolution show that hydrocarbon-sol…

X-ray study of the effect of uniaxial pressure on the structure of polycrystalline barium titanate

This paper investigates how uniaxial pressure affects the crystal structure of polycrystalline barium titanate at room temperature, motivated by known pressure-dependent changes in its dielectric behavior and Curie temperature. Using an ionization X-ray diffraction method with a specially constructe…

Geometric Properties of Solutions to Nonlinear Systems of Partial Differential Equations

The paper studies geometric properties of differentiable solutions to nonlinear first-order systems of partial differential equations under a strong ellipticity condition formulated in terms of the local affine geometry of the associated mapping. Using methods from quasiconformal mapping theory and …

ON THE QUESTION OF THE GEOGRAPHICAL DISTRIBUTION OF MAGNETIC DISTURBANCES IN ANTARCTICA

This paper examines whether a previously identified Arctic pattern in the timing of morning magnetic disturbance maxima also applies in Antarctica. Using theoretical expectations from Birkeland’s terrella experiments and Størmer’s analysis of charged particle motion in a dipole field, the author ref…

Dependence of the Shape of the Stationary Brightness Distribution Diagram on the Ratio of Absorption and Scattering Coefficients

This paper experimentally investigates how the directional brightness distribution of limiting diffuse light in turbid absorbing media depends on the ratio of absorption to scattering coefficients, excluding the influence of the scattering indicatrix. Using colored milk and rosin media, light filter…

Dependence of cation adsorption on the potential of a platinum electrode

This study examines how adsorption of cesium, strontium, and lanthanum cations depends on the potential of a platinized platinum electrode in acid perchloric and sulfuric acid solutions. Using radioactive tracer isotopes, the authors measured changes in solution activity while varying electrode pote…

On the Polymorphism of Thallium Bisulfate

This study examines the polymorphism of thallium bisulfate, whose needle and plate crystal forms had suggested dimorphism, and seeks to determine the temperatures and stability conditions of its solid-state transformations. Single crystals of the alpha and beta modifications were analyzed by thermog…

BENDING OF A PRISMATIC BAR WEAKENED BY A CIRCULAR CAVITY

This paper treats the elastic bending of a homogeneous isotropic prismatic bar of square-like cross section weakened by a circular cavity, under a concentrated force applied along a minor axis. Using complex-variable methods in elasticity, the boundary-value problem is reduced to the construction of…

STUDIES OF SHORT-WAVELENGTH ULTRAVIOLET RADIATION FROM THE SUN

This review briefly presents new results of experimental and theoretical studies of short-wavelength solar radiation published since the first review on this topic, and also describes experiments planned to be carried out using artificial Earth satellites.

Study of the Conditions of Formation and Stability of Oxalate Complex Compounds of $\mathrm{Pu}$ $(\mathrm{III})$ in Aqueous Solutions

This study examines the formation and stability of oxalate complex compounds of plutonium(III) in aqueous solution, with attention to preventing oxidation by atmospheric oxygen. Spectrophotometric observations showed that Pu(III) complexes retain characteristic Pu(III) spectra only under nitrogen or…

Synthesis of Acetyl-2-chlorocycloallenes

The study examines the reaction of cycloalkanones with acetyl chloride in the presence of aluminum chloride as a route to alicyclic chlorovinyl ketone related compounds. Detailed analysis of the cyclohexanone reaction shows that the product is mainly acetyl-2-chlorocyclohexene-2, with a minor isomer…

On the Number of Limit Cycles of the Equation $\frac{dy}{dx}=\frac{P(x,y)}{Q(x,y)}$ , Where $P$ and $Q$ Are Polynomials of Degree $n$

This note studies upper bounds for the number of limit cycles of the differential equation dy/dx = P(x,y)/Q(x,y), where P and Q are real polynomials of degree n. The authors reduce the problem to counting nontrivial, nonhomologous cycles on integral curves of the corresponding complex projective equ…

Ferrocenesulfonic acids

This paper examines the sulfonation of ferrocene and the preparation of free mono and disulfonic ferrocenesulfonic acids and their derivatives. Ferrocene was treated with pyridine sulfur trioxide or dioxane sulfur trioxide under varied conditions, and products were isolated as free acids or as bariu…

INTERNAL STRESSES AROUND UNIT DISLOCATIONS

This paper examines whether the theory of dislocations can be tested as a theory of internal stresses around individual, unit edge dislocations, rather than only through macroscopic lattice distortions. The authors derive stress discontinuities for a horizontal row of edge dislocations, including fo…

Study of the $\mathrm{Zn}\rightleftarrows\mathrm{Zn}^{++}$ Exchange Process on the Faces of a Zinc Single Crystal by the Radioactive Tracer Method

This paper examines how crystallographic orientation affects the zinc atom to ion exchange process on single crystal zinc surfaces. Using zinc single crystals prepared by a Bridgman method, the authors compared basal and prism faces after electropolishing by exposing them to zinc sulfate solution la…

ON TWO DIRECTIONS OF THE DEHYDROCHLORINATION REACTION OF LOWER ALKYLENE CHLOROHYDRINS

This paper examines the dual course of dehydrochlorination of lower alkylene chlorohydrins, focusing on whether aldehydes arise by isomerization of initially formed epoxides or by an independent reaction pathway. Experiments compare ethylene chlorohydrin and mixtures of propylene chlorohydrin isomer…

On Some Applications of a Theorem of F. Riesz

This paper applies F. Riesz’s representation theorem to functional equations defined by linear operators on Hilbert and Banach function spaces. It argues that when the equation has a unique solution and the value of the solution at a point is bounded by the norm of the data, this point value can be …

On the stability of nonlinear controlled systems

This note derives sufficient conditions for stability in the large of certain nonlinear automatic control systems governed by fifth and sixth order differential equations. Using Lur’e’s theorem, the stability problem is reduced to the existence of real solutions of associated quadratic resolving sys…

On the Potential Difference and Accumulation of Solution Components in the Diffusion Layer during Steady-State Electrolysis

This communication analyzes concentration and potential distributions in the diffusion layer during stationary electrolysis, emphasizing distinctions often obscured in treatments of concentration polarization. For binary electrolytes of arbitrary concentration, it shows that the experimentally acces…

On the mechanism of the E. Fischer reaction and its abnormal course

This paper examines the mechanism of the Fischer indole reaction and cases in which arylhydrazones undergo abnormal decomposition rather than normal cyclization. Using the generalized theory of conjugation, the authors argue that acid or complex-forming catalysts shift arylhydrazone tautomerism towa…

Solution by the Fourier Method of Non-Self-Adjoint Mixed Problems for Hyperbolic Systems in the Plane

The paper studies non-self-adjoint mixed problems for first-order hyperbolic systems in the plane with boundary conditions containing time derivatives at both endpoints. Using separation of variables and asymptotic analysis of the associated parameter-dependent boundary problem, it defines regular b…

Multistage Construction of Full-Availability Switching Systems

This paper develops a general method for constructing fully accessible switching systems, defined as discrete switching networks able to connect any input to any output regardless of existing connections, within the capacity limits set by the numbers of inputs and outputs. Extending Clos’s construct…

LETTER TO THE EDITOR

This letter clarifies the relation between the author’s earlier note on differential equations with pure mixed derivatives and prior work by Bianchi and Nicoletti. It acknowledges that several results in the note, including existence and uniqueness for characteristic boundary data and the Cauchy pro…

Study of the mechanism of alkylation of amines with $\mathrm{N}$-trimethyl-$\alpha$-phenethylammonium iodide

This paper examines the mechanism of amine alkylation by optically active N-trimethyl-alpha-phenethylammonium iodide, focusing on whether transfer of the alpha-phenethyl group occurs synchronously or through a free carbonium ion. Piperidine and morpholine were alkylated under nitrogen, and the optic…

THE FIRST BOUNDARY-VALUE PROBLEM FOR QUASILINEAR ELLIPTIC EQUATIONS

This paper studies the first boundary value problem with zero boundary data for a class of quasilinear elliptic equations in a bounded domain of arbitrary dimension. Under ellipticity, boundedness, differentiability, and monotonicity assumptions on the coefficients, it proves existence of solutions …

Equations of the Three-Dimensional Boundary Layer in a Compressible Gas for an Arbitrary Surface

This paper derives the equations of a three-dimensional boundary layer in a viscous compressible gas over an arbitrary smooth surface. Using orthogonal curvilinear coordinates based on the surface lines of curvature, the author applies boundary-layer scaling at large Reynolds number to the compressi…

Corrections to the Article “The Effect of Anelectrotonus on Inhibited Positive Conditioned Reflexes” (DAN, Vol. 112, No. 6, 1957)

On Estimating the Eigenvalues of Self-Adjoint Operators

This paper develops estimates for eigenvalues of self-adjoint operators with discrete spectrum in a Hilbert space, using moments generated by a chosen vector and its iterates under the operator. A lemma on weighted norms of functions of the spectrum is applied to polynomials to obtain computable int…

On the Forecasting of Atmospheric Pressure with the Aid of High-Speed Electronic Computing Machines

This paper presents a method for short-range forecasting of atmospheric pressure using high-speed electronic computing machines, based on simplified geostrophic and adiabatic equations for a flat Earth. The governing system is reduced to an elliptic equation for the geopotential tendency, solved thr…

Investigation of the Sensitization of Photooxidation of Organic Compounds by Anthraquinone Derivatives Using Infrared Absorption Spectra

This study examines the visible light sensitized photooxidation of benzaldehyde, tetralin, and isopropylbenzene by molecular oxygen in the presence of anthraquinone and several hydroxy and amino derivatives. Reaction progress was followed by near infrared absorption bands assigned to oxidation produ…

CORRELATION THEORY OF ELECTRICAL FLUCTUATIONS AND THERMAL RADIATION

HEAT OF ADSORPTION OF BENZENE AND HEXANE VAPORS ON CALCINED AND HYDRATED SILICAS

This study examines how the hydration state of silica surfaces affects the adsorption of benzene and hexane vapors at 20 degrees C. Differential heats of adsorption and adsorption isotherms were measured for calcined silica and for the same material after prolonged hydration, with surface areas and …

Kinetic Equation for Steps on a Crystal Surface

This paper develops a statistical kinetic description of steps on a growing crystal surface, motivated by the coagulation of layers of different heights during crystal growth from vapor, solution, or melt. For a one-dimensional echelon of parallel steps with random heights, it formulates a nonlinear…

THE ALGEBRA OF MATRICES IN THE THEORY OF PARTICLES WITH SPIN \(3/2\)*

The paper develops an algebraic formulation for the 16-dimensional matrices appearing in the wave equation of a particle with definite spin 3/2 and positive total charge. It argues that relations following from the general minimal equation are insufficient to characterize this case, and proposes add…

A VARIATIONAL PROBLEM OF GAS DYNAMICS FOR AXISYMMETRIC SUPERSONIC FLOWS

The paper formulates a variational problem for determining the generator of a body of revolution with minimum wave drag in axisymmetric supersonic flow, and an analogous nozzle problem with minimal losses. Using a characteristic representation due to Nikolskii, the drag functional is optimized under…

Benzylidene derivatives of the hydrate form of $\alpha$-keto alcohols containing 1,3-dioxolane rings

This paper reports the synthesis of new 4-methoxy-1,3-dioxolane derivatives as cyclic ketal derivatives of the hydrated form of alpha-keto alcohols. The authors condense the methyl lactolide of dimethylbenzoylcarbinol with benzaldehyde, anisaldehyde, p-nitrobenzaldehyde, and benzophenone in carbon t…

MEMORIES OF PROFESSOR P. EHRENFEST\*)

Speech delivered by G. E. Uhlenbeck on February 2, 1956, at the American Association of Physics Teachers on the occasion of the presentation to him of the Oersted Medal for outstanding achievements in the teaching of physics.

Sturm-Type Theorems for Self-Adjoint Systems of Higher-Order Differential Equations

This paper studies self-adjoint systems of higher order differential equations with symmetric matrix coefficients and develops Sturm-type results for their conjugate points. It proves separation of distinct systems of conjugate points, comparison theorems under ordering of the coefficients, and spec…

Interaction of Intramolecular and Lattice Vibrations in Crystals According to Infrared Spectra

This paper examines how intramolecular vibrations interact with lattice vibrations in molecular crystals, using infrared absorption spectra of single crystals of barium nitrate and lead nitrate measured at room temperature and at low temperature. The authors analyze the observed absorption bands of …

Dynamic Method for Studying the Structure and Specific Surface Area of Adsorbents

A dynamic version of the molecular probe method is proposed for studying adsorbent structure and specific surface area from adsorption of phenol, benzyl alcohol, and thymol solutions in carbon tetrachloride passed through chromatographic columns. Breakthrough curves obtained under standardized flow …

On the Mechanism of Thermal Decomposition of Cellulose in Vacuum and the Formation of 1,6-Anhydro-1,5-glucopyranose—Levoglucosan

This study examines the mechanism by which levoglucosan forms during the thermal decomposition of cellulose in vacuum, testing the proposed pathway through cellulose hydrolysis to glucose followed by glucose dehydration. The authors compare decomposition products from cellulose, beta-d-glucose, levo…

On the Problem of Elastic Equilibrium of Bodies of Revolution

This paper develops a formulation for the elastic equilibrium of bodies of revolution under loads expanded in Fourier series with respect to the circumferential coordinate. Assuming harmonic forms for the displacement components, the equilibrium equations are reduced to auxiliary stress functions sa…

Errata to the Article “Nucleic Acids in Oogenesis and Fertilization of the Liver Fluke” (DAN, Vol. 110, No. 3, 1956)