Recent Papers

Corrections to the Article Nonlocal Solvability of Boundary Value Problems for Quasilinear Partial Differential Equations of Hyperbolic Type (DAN, Vol. 176, No. 2, 1967)

RESULTS OF OBSERVATIONS OF 560 RADIO SOURCES AT A FREQUENCY OF 86 MHz

This paper reports 86 MHz observations of 560 radio sources from the 3C and 3CR catalogs made between 1965 and 1967 with the East West array of the DKR-1000 radio telescope. The authors describe the determination of right ascensions and relative flux densities, using primary and secondary calibratio…

ON DIFFERENCE APPROXIMATIONS OF DIFFERENTIAL OPERATORS OF MATHEMATICAL PHYSICS

The paper proposes a combinatorial-topological framework for constructing finite difference approximations to linear equations of mathematical physics expressed through the exterior derivative and its adjoint on a Riemannian manifold. Using cellular decompositions, cochains, the coboundary operator,…

On the Behavior of $Pi1$ Micropulsations at Magnetically Conjugate Points

This paper examines Pi1 micropulsation bursts observed at the magnetically conjugate stations Cogra and Kerguelen, with attention to their occurrence, spectral structure, and relation to other geomagnetic disturbances. Using magnetogram comparisons, sonographic analysis, and autocorrelation function…

ON EXTENSIONS, CHARACTERISTIC FUNCTIONS, AND GENERALIZED RESOLVENTS OF SYMMETRIC OPERATORS

This paper studies closed symmetric operators in a Hilbert space whose domains need not be dense, focusing on extensions, characteristic functions, and generalized resolvents. It introduces and uses an isometric operator associated with the defect subspaces to parametrize dissipative, accumulative, …

ON SOME STRUCTURAL PROPERTIES OF SUBSEMIGROUPS IN A GROUP

This note studies subsemigroups of torsion-free groups through the lattice-like structure of all subsemigroups of a group. Using the notions of S-products, S-elements, and singly covering elements, it establishes necessary and sufficient structural conditions on the ideal generated by a subsemigroup…

ON PROBLEMS OF MATHEMATICAL PROGRAMMING HAVING A MINIMAL POINT

This note studies mathematical programming problems in partially ordered Banach spaces with regular minihedral cones, where the feasible set is defined by inequalities involving an operator and the objective is any monotone functional. It shows that, for continuous monotone operators, nonemptiness o…

ON THE ADMISSIBLE ORDER OF GROWTH OF THE CHARACTERISTIC OF QUASICONFORMALITY IN THE THEOREM OF M. A. LAVRENT’EV

This note refines Lavrent’ev’s theorem on locally homeomorphic quasiconformal mappings of Euclidean space in dimensions at least three by allowing the quasiconformality characteristic to grow with radius. Using modulus estimates for curve families and Grötzsch principles, it proves that if the local…

SIMULATION OF THE EARTH’S MAGNETIC FIELD

This paper reports a limited laboratory simulation of the interaction between the solar wind and the Earth’s magnetic field, with experimental parameters chosen to preserve the relevant dimensionless conditions for magnetic Reynolds number, Mach number, Alfvén Mach number, collisionless dissipation,…

SOLUTION OF THE KINETIC EQUATION

This paper solves the kinetic equation for charge carriers in semiconductors with a narrow conduction band under strong electric fields, motivated by organic molecular crystals whose band widths may be comparable with thermal energy. Using a nearest-neighbor one-dimensional band spectrum, acoustic p…

Experimental detection of an electromotive force along an external magnetic field induced by liquid metal flow ( $\alpha$ -effect)

An experiment is reported on the electromotive force induced along an external magnetic field by a liquid sodium flow whose velocity field lacks mirror symmetry, corresponding to the predicted magnetohydrodynamic alpha effect. The apparatus used interlacing perpendicular channels to create a stepwis…

GENERALIZED BOGOLIUBOV FUNCTIONS AND ELEMENTS OF THE CAUSAL \(S\)-MATRIX

The paper reformulates the Bogoliubov, Medvedev, and Polivanov axiomatic S-matrix approach in terms of vacuum expectation values of chronological operators, called generalized B-functions. It specifies the required linear properties of these generalized functions, including distributional structure,…

ON SOME CLASSES OF TOPOLOGICAL SPACES AND THEIR BICOMPACT EXTENSIONS

This note refines earlier results on semiregular topological spaces, finite spectra, and Urysohn, Ponomarev bicompact extensions. It identifies bicompact \(T_\lambda\)-spaces with bicompact \(T_\xi\)-spaces, proves that precisely \(T_\lambda\)-spaces admit bicompact \(T_\lambda\)-extensions, and int…

OBTAINING DENSE MODIFICATIONS OF BORON NITRIDE AT HIGH PRESSURES AND SHEAR STRESSES

This paper investigates whether shear stresses can facilitate the high-pressure transformation of hexagonal boron nitride into denser phases, following evidence that shear affects polymorphic transition kinetics in other materials. Hexagonal boron nitride mixed with antimony was compressed to about …

ON THE DEVELOPMENT OF THE WESTERN INTENSIFICATION OF OCEAN CURRENTS. A NUMERICAL EXPERIMENT

This paper investigates the time development of western intensification in wind-driven ocean currents, using a linear homogeneous ocean model with vertical turbulent viscosity, variable Coriolis parameter, and a closed rectangular basin outside the equator. A numerical experiment is performed for an…

Study of a Nonlinear Singular Integral Equation with a Special Cauchy Kernel in the Class $H^k_{\alpha-\delta,\delta}(a,b)$

This note studies a nonlinear singular integral equation with a special Cauchy kernel on an interval in the weighted Hölder-type class \(H^k_{\alpha-\delta,\delta}(a,b)\), for \(0<\delta<\alpha<1\). It establishes mapping and continuity properties of the associated integral operator under Hölder and…

ON THE CAUCHY PROBLEM FOR A SECOND-ORDER HYPERBOLIC EQUATION DEGENERATING ON THE INITIAL HYPERPLANE

This paper studies the Cauchy problem for multidimensional second-order hyperbolic equations that degenerate on the initial hyperplane. For equations whose coefficients depend only on time, the problem is reduced by the Radon transform to a family of plane degenerate hyperbolic problems, allowing pr…

COMPLETENESS UP TO ENCODING OF SYSTEMS OF FUNCTIONS OF \(K\)-VALUED LOGIC AND THE COMPLEXITY OF RECOGNIZING IT

The paper studies completeness of systems of functions in k-valued logic under encodings of arguments and values, generalizing paired-line computation in logical networks. It defines completeness under a fixed encoding and completeness up to encoding, proves the existence of a universal encoding for…

MULTIVALUED MAPPINGS AND BOREL SETS

This paper studies selection problems for multivalued mappings into spaces of closed subsets, with emphasis on semicontinuity, canonical graph representations, and Borel measurability properties of selections. It establishes equivalences between upper or lower semicontinuity and openness or perfecti…

TURBULENT HEATING OF PLASMA IN A TORUS

This paper investigates whether plasma heated turbulently by a strong circumferential electric current can remain confined in a toroidal magnetic configuration after the heating current is switched off. Experiments on the Vikhr-2 device used titanium-hydride plasma injection, a strongly corrugated q…

APPLICATION OF THE NEWTON DIAGRAM TO THE PROBLEM OF STABILITY OF PERIODIC SOLUTIONS

The paper studies Lyapunov stability of periodic solutions of nonautonomous quasilinear systems with a small parameter, without imposing special restrictions on the constant matrix in the linear part. After shifting a periodic solution to the origin, the stability problem is reduced to the analysis …

GENERAL SOLUTIONS IN THE THEORY OF MAGNETOHYDRODYNAMIC FLOWS IN THE HYPERSONIC APPROXIMATION

This paper derives general solutions for hypersonic magnetohydrodynamic flows of an anisotropically conducting inviscid gas in a magnetic field, under the assumption that pressure gradients can be neglected. With constant interaction frequency, load parameters, and Hall-related anisotropy parameters…

GEOTHERMAL FEATURES OF ONE AREA OF THE YENISEI SECTOR OF THE ARCTIC

This paper examines geothermal conditions in a permafrost area of the Yenisei sector of the Arctic, based on temperature logging in 96 abandoned boreholes to depths of up to 500 m in the upper Pyasina River basin. The study documents strong spatial variability in rock temperatures, geothermal gradie…

ON BOUNDED SOLUTIONS OF THE RIEMANN BOUNDARY-VALUE PROBLEM WITH AN INFINITE INDEX OF POWER ORDER

The paper studies bounded analytic solutions of a Riemann boundary-value problem on the complex plane cut along a ray, in the case of a plus-infinite index of power order. Under Hölder-type assumptions on the argument and modulus of the coefficient, it derives explicit representations for all bounde…

Measurement of Turbulence in Gas Flows by an Optical Method

This paper applies an optical correlation method to measure the longitudinal turbulence component in a cold air jet, extending an approach previously used for plasma flows. A schlieren system observes density-marked flow produced by a heated wire, and signals from two nearby image points are recorde…

Measurement of the Density of Structurally Modified Water Droplets

This paper investigates the density of droplets of structurally modified water, whose previously reported anomalous properties suggested that its density might differ from that of ordinary water. Because only minute quantities were available, the authors used hydrostatic weighing in density-gradient…

SOME CONSEQUENCES OF THE HYPOTHESIS ON THE UNCOUNTABILITY OF THE SET OF CONSTRUCTIVE REAL NUMBERS

The paper derives consequences, in descriptive set theory and foundations, of hypotheses concerning the cardinality and measure-theoretic size of the set of constructive real numbers. Working within naive set theory but noting formalizability in systems such as ZF, it uses Gödel’s function on counta…

A NEW SILICON–OXYGEN RADICAL \([Si_3O_{10}]\) IN THE STRUCTURE OF \(Na_4Cd_2[Si_3O_{10}]\)

The paper reports an X-ray crystallographic determination of the hydrothermally synthesized sodium cadmium silicate Na4Cd2[Si3O10], including its monoclinic cell, space group C2/c, atomic coordinates, and interatomic distances. Patterson and Fourier methods followed by least-squares refinement of 16…

A GENERALIZATION OF LYAPUNOV’S FIRST STABILITY THEOREM FOR CERTAIN CLASSES OF DIFFERENTIAL EQUATIONS IN BANACH SPACES

The paper extends Lyapunov’s first stability theorem to nonlinear differential equations in complex Banach spaces of the form given by a linear generator and an analytic perturbation. It treats both bounded operators with spectrum in the left half-plane and certain unbounded operators generating str…

IRREGULAR SURFACES OF BOUNDED EXTERNAL CURVATURE AND INEQUALITIES OF ISOPERIMETRIC TYPE

This note studies two-dimensional Fréchet surfaces in Euclidean space whose external positive curvature, defined through multiplicities of supporting caps, is finite and whose boundary has finite length. The authors introduce the class of such surfaces and prove an isoperimetric-type area estimate i…

SOME DATA ON THE CHARACTER OF THE GEOMAGNETIC FIELD DURING REVERSALS

This paper examines the character of the geomagnetic field during polarity reversals using paleomagnetic data from terrigenous red beds of the Evenki suite exposed near Krasnyi Yar on the middle Angara River. The study evaluates the origin and stability of natural remanent magnetization through mine…

BOUNDARY-VALUE PROBLEMS FOR SECOND-ORDER DIFFERENTIAL EQUATIONS IN A HILBERT SPACE WITH A VARIABLE SELF-ADJOINT OPERATOR

This note studies boundary-value problems for second-order differential equations in a Hilbert space with a variable unbounded self-adjoint uniformly positive operator. It establishes an a priori estimate implying uniqueness for several homogeneous boundary conditions, then constructs Green function…

ON THE POSSIBILITY OF CONSTRUCTING A THIN-LAYER MODEL OF THE TRANSITION REGION FROM THE MANTLE TO THE EARTH’S CORE

This paper examines whether discrepancies between observed and theoretical dynamic characteristics of seismic waves reflected from the mantle, core boundary can be explained by a thin-layer transition region rather than by a simple boundary between two half-spaces. Using published observations of Pc…

ON THE SPECTRAL PROPERTIES OF INDECOMPOSABLE OPERATORS

The paper studies spectral properties of indecomposable positive linear operators in semi-ordered Banach spaces with normal reproducing cones. It gives variational characterizations of the spectral radius under several hypotheses, derives comparison results for ordered operators, and formulates inco…

ON FRACTIONAL INTEGRATION BY PARTS

The paper studies solvability and regularity for the abstract Cauchy problem \(v'(t)+Av(t)=f(t)\) in a Hilbert space, where \(A\) is a positive definite self-adjoint operator. It proves fractional integration by parts estimates in Slobodetskii spaces, including the limiting \(W_2^{1/2}\) case with b…

On a formulation of an inverse problem for the generalized wave equation

This paper formulates an inverse problem for a generalized wave equation with a point impulse source, asking whether the coefficient multiplying the unknown function can be reconstructed from boundary observations of the regular part of the solution at the travel time between two boundary points. Us…

APPLICATION OF THE FOCK EXPANSION IN THE THEORY OF VAN DER WAALS FORCES

This paper examines the use of Fock expansions in the direct variational calculation of van der Waals dispersion forces, taking the interaction of two hydrogen atoms as the basic test case. By transforming the first-order perturbation equation to hyperspherical variables, the author shows that an ex…

PARTITIONS OF LEBESGUE SPACE INTO TRAJECTORIES DETERMINED BY ERGODIC AUTOMORPHISMS

The paper studies nonmeasurable partitions of a Lebesgue space into trajectories of measure-preserving automorphisms, asking which properties of an automorphism are determined by the trajectory partition alone. Using derived automorphisms, compatible maps along orbits, and Vershik’s theorem on decre…

STUDY OF ARTIFICIAL MIARGYRITE (AgSbS$_2$) BY THE METHOD OF NUCLEAR QUADRUPOLE RESONANCE

Artificial monoclinic miargyrite, AgSbS2, synthesized from high-purity elements through the cubic modification and prolonged annealing, is examined by nuclear quadrupole resonance of Sb121 and Sb123 nuclei, with supporting microscopic, thermal, and X-ray powder characterization. The observed low-tem…

ON THE BUBNOV–GALERKIN METHOD FOR PARABOLIC EQUATIONS IN A HILBERT SPACE

The paper studies the Bubnov-Galerkin approximation for abstract parabolic equations in a Hilbert space with time-dependent positive self-adjoint operators and fixed domains. It develops uniform operator estimates, using logarithmic convexity and Heinz-type inequalities, for projected evolution oper…

ON THE STRUCTURE OF THE FIELD OF FRACTIONS OF THE ENVELOPING ALGEBRA OF A SEMISIMPLE LIE ALGEBRA

The paper studies the field of fractions of the universal enveloping algebra of an arbitrary complex semisimple Lie algebra, extending earlier work on a structural hypothesis for such fields. It realizes the enveloping algebra as differential operators on the basic affine space and enlarges it by vi…

Test spaces for cohomological dimensions of paracompact spaces

This note constructs test spaces for the cohomological dimension of paracompact spaces, extending earlier results for compact spaces. Using sheaf cohomology, product spectral sequences, and a large-base argument, it proves that for each prime p and integer N there is a compactum Y such that every pa…

INFINITE HERMITIAN MATRICES WITH OPERATOR COEFFICIENTS

This paper studies deficiency indices and self-adjointness for symmetric operators in direct sums of Hilbert spaces generated by finite infinite Hermitian matrices with operator coefficients. It proves a perturbation-type sufficient condition for self-adjointness, gives criteria for nonzero deficien…

ON THE UNIFORM CONVERGENCE OF FREQUENCIES OF THE APPEARANCE OF EVENTS TO THEIR PROBABILITIES

This paper studies when empirical frequencies of all events in a class converge uniformly to their probabilities for independent samples, a question motivated in part by learning algorithms. It introduces the index and growth function of a class of measurable sets, proves that the growth function is…

Corrections to the article “Basic Boundary Value Problems of Potential Theory for a Space with an Elliptic Slit. Pressure of an Elliptic Punch on an Elastic Half-Space” (Reports of the Academy of Sciences of the USSR, Vol. 176, No. 1, 1967)

FORMATION OF AN INTRAGRAIN DISLOCATION SUBSTRUCTURE DURING THE GROWTH OF NaCl SINGLE CRYSTALS FROM THE MELT

This study examines the origin of intragrain dislocation structures in NaCl single crystals grown from the melt, focusing on whether observed dislocation patterns reflect growth processes or subsequent thermal treatment. NaCl crystals grown by Czochralski and related methods, together with annealed …

GAS HYDRATES IN CAPILLARIES

This paper examines whether gas hydrates can be stabilized in capillaries under conditions where ordinary bulk hydrate formation would not be expected, motivated by Pauling’s hypothesis relating anesthesia to hydrate formation in nerve capillaries. Using chlorine hydrate as an example, it argues tha…

MUTUAL RESTRICTIONS ON CURVATURE AND AREA FOR SURFACES LYING IN A COMPACT PART OF SPACE

This paper studies quantitative restrictions relating the area of a surface in Euclidean space to its diameter and curvature variation. For closed \(C^2\) surfaces contained in a ball, it proves an upper bound for area in terms of the integral of absolute Gaussian curvature and the square of the enc…

SECOND EXPERIMENT ON THE INVESTIGATION OF THE CONSTANTS OF ION–MOLECULE REACTIONS DIRECTLY IN THE IONOSPHERE

This paper reports a second rocket experiment designed to estimate the relative rate constants of the ionospheric ion molecule reactions of O+ with N2 and O2 directly in the upper atmosphere. During a 1967 daytime midlatitude flight, air was released near a radio frequency mass spectrometer at about…

ON EXTENDING THE RANGE OF APPLICATION OF SPECIAL ALGORITHMS OF LINEAR PROGRAMMING

This paper addresses linear programming problems in which special algorithms are available when all constraint vectors belong to a set permitting simplified solution of associated linear systems, but only part of the vectors satisfy this condition. It proposes a general device for applying such spec…