Showing 50 of 25357 papers

ON THE PROBLEM OF CLOSURE IN THE THEORY OF TURBULENCE

B. Ya. Lyubimov, F. R. Ulinich
1970 SovietRxiv: ru-197001.59771

The paper addresses closure in turbulence theory for chains of equations governing joint probability distributions of velocity and related random variables. It proposes a closure approach based on an exact cumulant expansion of joint characteristic and probability distributions, in which approximate…

ON THE ASYMPTOTIC BEHAVIOR OF GENERALIZED BAYES ESTIMATES

I. A. Ibragimov, R. Z. Khas'minskii
1970 SovietRxiv: ru-197001.59657

This paper studies the asymptotic behavior of generalized Bayes posterior densities and posterior mean estimates for independent samples from parametric families, allowing the prior factor to be a measurable function rather than necessarily a probability density. It identifies normalizing factors an…

ON THE ORDER OF APPROXIMATION OF A CONTINUOUS \(2\pi\)-PERIODIC FUNCTION BY PARTIAL SUMS OF ITS FOURIER SERIES

V. V. Zhuk
1970 SovietRxiv: ru-197001.59384

This note studies the rate of uniform approximation of continuous periodic functions by partial sums of their Fourier series, using best trigonometric approximation and quantities measuring the tails of Fourier coefficients or remainders in related \(L_q\) metrics. It proves an estimate for \(\|f-S_…

ON FINDING POSITIONS OF THE REDUCTION LINK THAT ARE EXTREMAL FOR THE CHARACTERISTIC CRITERION OF THE PERIODIC REGIME OF MOTION OF A MACHINE UNIT

I. I. Artobolevsky, V. S. Loshchinin
1970 SovietRxiv: ru-197001.59268

This paper addresses how to determine positions of a machine unit’s reduction link at which the characteristic criterion of a periodic limiting regime reaches extrema, indicating where inertia forces due to nonuniform initial motion are most significant relative to steady motion. Under standard assu…

ON THE STABILITY OF THREE-LEVEL DIFFERENCE SCHEMES

A. A. Samarskii
1970 SovietRxiv: ru-197001.59161

The paper studies stability of abstract three-level operator difference schemes in a Hilbert space, extending earlier stability results expressed in compound norms to estimates in standard energy norms associated with the scheme operators. Under positivity, Lipschitz continuity in time, and the cond…

AN OPTRON WITH DIRECT OPTICAL COUPLING AS A FOUR-TERMINAL NETWORK

È. I. Adirovich, D. A. Aronov, N. Yunusov
1970 SovietRxiv: ru-197001.58850

This paper develops a four-terminal network representation for an optocoupler with direct optical coupling, specifically an injection light-emitting diode coupled to a photoresistor. It derives the conductance, impedance, and hybrid parameter matrices in terms of differential device characteristics,…

A CARBON DIOXIDE LASER IN THE SINGLE-PULSE MODE

A. V. Eletskii, B. M. Smirnov
1970 SovietRxiv: ru-197001.58571

This paper analyzes the feasibility and optimal operating conditions of a single-pulse carbon dioxide laser intended to extract high pulse energy from a large gas volume. The authors argue that uniform electron production, preferably by photoionization of a small cesium additive, can overcome limita…

EQUIMORPHISMS AND QUASICONFORMAL MAPPINGS OF THE ABSOLUTE

D. A. De Spiller
1970 SovietRxiv: ru-197001.58077

This paper addresses Efremovich’s problem of characterizing which boundary homeomorphisms of the absolute spheres of two \(n\)-dimensional Lobachevsky spaces are induced by equimorphisms of the spaces. It proves that, for \(n \geq 2\), such an equimorphism exists if and only if the given boundary ma…

SOLUTION OF SPATIAL PROBLEMS OF THE THEORY OF ELASTICITY BY MEANS OF ANALYTIC FUNCTIONS AND CONTOUR INTEGRALS FOR CERTAIN NON-AXISYMMETRIC BODIES

A. Ya. Aleksandrov
1970 SovietRxiv: ru-197001.57871

This paper extends analytic function and contour integral methods for three-dimensional elasticity from bodies of revolution to certain non-axisymmetric bodies whose surfaces can be represented as envelopes of a moving cylindrical surface. The method superposes plane strain and antiplane deformation…

SPACES GENERATED BY GENFUNCTIONS

Unknown
1970 SovietRxiv: ru-197001.57843

This paper studies function spaces generated by measurable modular functions, called genfunctions, on sigma-finite measure spaces, extending earlier Musielak and Orlicz constructions under weaker hypotheses. It gives necessary and sufficient conditions for the associated space to admit a normal F-no…

One-Dimensional Unsteady Flows of a Barotropic Fluid

A. V. Gurevich, A. B. Shvartsburg
1970 SovietRxiv: ru-197001.57742

This paper studies one-dimensional nonstationary flows of a barotropic fluid with adiabatic index gamma equal to 2, a model relevant to several plasma, shallow-water, and nonlinear optical problems. Starting from the Euler equations, the authors show that this special case possesses an infinite sequ…

ON THE COMPLETENESS OF A SYSTEM OF ANALYTIC FUNCTIONS

I. I. Ibragimov
1970 SovietRxiv: ru-197001.57590

The paper studies completeness of systems of analytic functions of the form F(z, a_n), where F is generated by a power series with coefficients forming a complete analytic system and {a_n} is a sequence of complex numbers. Using a criterion that reduces completeness to uniform approximation of the g…

AN EXPERIMENT IN THERMAL SOUNDING OF THE ATMOSPHERE FROM SATELLITES

K. Ya. Kondrat'ev, V. Nordberg, O. M. Pokrovskii, Yu. M. Timofeev, R. Khanel
1970 SovietRxiv: ru-197001.57531

This paper examines satellite thermal sounding of the atmosphere, in which vertical temperature profiles are inferred from measurements of outgoing thermal radiation. Using Nimbus III interference spectrometer data for Brownsville, Texas, the authors compare two inversion approaches for the resultin…

SOME APPROXIMATE METHODS FOR SOLVING TIME-OPTIMAL PROBLEMS IN BANACH SPACES IN THE PRESENCE OF PHASE CONSTRAINTS

Unknown
1970 SovietRxiv: ru-197001.57231

The paper studies time-optimal control problems in Banach spaces with phase constraints, where admissible controls generate trajectories that must satisfy set-valued and functional restrictions. Using separation-type functionals defined on reachable and target sets, it establishes criteria for contr…

ON THE EXISTENCE OF WEIGHTED FINITE INCIDENCE STRUCTURES

A. Ya. Petrenyuk
1970 SovietRxiv: ru-197001.57183

This paper introduces a weight function for finite incidence structures with block multiplicities and uses it to study structures whose block sizes belong to a prescribed finite set and whose weights on all subsets of fixed size are specified. By double counting incidences within each equiblock comp…

On the triangular representation of operators close to unitary operators and the multiplicative factorization of their characteristic functions

V. M. BRODSKII
1970 SovietRxiv: ru-197001.56919

The paper extends triangular representation and characteristic function factorization results for bounded operators close to unitary operators, allowing invertible operators whose spectra need not lie on the unit circle. For operators T on a separable Hilbert space with I minus T*T in a symmetricall…

On Weighted Approximation by Polynomials on the Real Axis

Unknown
1970 SovietRxiv: ru-197001.56750

This paper studies weighted approximation of functions on the real line by algebraic polynomials with the Gaussian weight exp(-x²/2), using weighted Lp norms. It proves an inverse-type estimate for an antiderivative F of a function f, showing that the best weighted polynomial approximation error of …

High-Velocity Impact of a Body on Rocks

V. M. Titov, Yu. I. Fadeenko, G. A. Shvetsov
1970 SovietRxiv: ru-197001.56676

This paper investigates crater formation produced by millimeter-scale balls impacting strong rocks, porous rocks, pumice, and sand at velocities of 3 to 11.5 km/sec. Experiments measuring crater volume, shape, penetration behavior, and fragment ejection show that a simple proportionality between eje…

SCATTERING OF SOUND BY SPIN WAVES

N. I. Pushkina, R. V. Khokhlov
1970 SovietRxiv: ru-197001.56612

This paper develops a theoretical treatment of combination scattering of sound by spin waves in cubic ferromagnets, including both magnetostrictive interactions and the intrinsic magnetoelastic effect. For a longitudinal incident sound wave propagating perpendicular to a constant internal magnetic f…

SECULAR CHANGES IN GRAVITY IN UKRAINE

A. Sh. Faitelson, E. A. Azarkina
1970 SovietRxiv: ru-197001.56465

This paper examines possible secular changes in gravity across Ukraine using repeated gravity measurements made in 1962 and 1969 at 36 uniformly distributed points. Differences relative to a reference point in Kiev ranged from about +0.4 to −0.5 mGal, with estimated errors of approximately ±0.08 mGa…

On a Peculiarity of Shock Compressibility of Quartzite

A. M. PODURETS, R. F. TRUNIN
1970 SovietRxiv: ru-197001.56370

This paper examines the anomalous shock compressibility of quartzite, specifically the observed constancy of shock wave velocity over a broad pressure range from about 120 to 330 kbar. The authors argue that the effect is associated with the shock induced quartz to stishovite transformation, but dif…

SPECTRAL SYNTHESIS FOR THE SHIFT OPERATOR AND ZEROS IN CERTAIN CLASSES OF ANALYTIC FUNCTIONS, SMOOTH UP TO THE BOUNDARY

N. K. Nikol'skii
1970 SovietRxiv: ru-197001.55875

This note studies spectral synthesis for invariant subspaces of the shift operator in weighted sequence spaces and the corresponding classes of analytic functions in the unit disk. It relates synthesis to quasianalyticity and uniqueness theorems for functions smooth up to the boundary, formulating c…

On Spectral Expansions Corresponding to an Arbitrary Nonnegative Self-Adjoint Extension of the Laplace Operator

Unknown
1970 SovietRxiv: ru-197001.55271

The paper studies spectral expansions and Riesz means associated with arbitrary nonnegative self-adjoint extensions of the Laplace operator in arbitrary domains, including cases with point, continuous, or mixed spectrum. Combining earlier methods for spectral expansions with Gårding’s theorem, it es…

ON THE SPECULAR REFLECTION OF VAPOR MOLECULES AND SUPRAMOLECULAR FLOW IN NARROW CAPILLARIES

B. V. Deryagin, N. N. Fedyakin, A. V. Novikova
1970 SovietRxiv: ru-197001.54882

This paper examines how specular reflection of vapor molecules from capillary walls can alter gas transport in narrow capillaries, producing a flow regime distinct from ordinary Knudsen flow. The authors develop a model in which molecules reflected below a limiting angle have an increased transport …

SOME PROPERTIES OF A SOLID-STATE LASER WITH A LONG RESONATOR

L. S. Kornienko, N. V. Kravtsov, E. G. Lariontsev, A. M. Prokhorov
1970 SovietRxiv: ru-197001.54440

This paper examines theoretical properties of solid-state lasers with very long resonators, motivated by the increased coupling of longitudinal modes, changes in spectral behavior, and possible approach to nonresonant feedback when resonator mode bands overlap. It proposes using an optical delay lin…

ON SAMPLE MODELING OF THE GRAVITATIONAL FIELD OF THE SUN

A. Z. Petrov
1970 SovietRxiv: ru-197001.54244

This paper develops an approximate selective modeling of the Sun’s gravitational field in Einstein’s theory by replacing selected Schwarzschild geodesics with non-geodesic curves in a flat four-dimensional model space. Imposing spherical symmetry, staticity, and Lorentz-type equations of motion, the…

THE HYDROGEN ATOM AND THE CONFORMAL GROUP

Yu. B. Rumer
1970 SovietRxiv: ru-197001.53955

This note reformulates the nonrelativistic hydrogen atom in terms of generators of the conformal group. Starting from the conformal commutation relations, the author constructs Heisenberg-representation generators, applies a canonical transformation to a light-cone constrained basis, and identifies …

ON THE LOCAL STRUCTURE OF NORMAL FIELDS

E. I. Ostrovskii
1970 SovietRxiv: ru-197001.53905

This paper studies the local sample path structure of separable Gaussian fields on compact spaces with continuous covariance kernels. Using the Mercer, Hilbert-Schmidt expansion of the covariance operator, it establishes almost sure pointwise representation of the field by its spectral series, then …

DETERMINATION OF CERTAIN CLOUD PARAMETERS BY LASER LOCATOR

E. G. Shvidkovskii, O. K. Kostko
1970 SovietRxiv: ru-197001.53212

This paper presents a laser backscatter method for determining cloud microphysical parameters from lidar sounding data. The authors derive a layer by layer expression for the cloud scattering coefficient under the assumption of single scattering, then relate this coefficient to liquid water content …

SOME PROBLEMS IN MODELING ULTRALONG ATMOSPHERIC WAVES

G. P. Kurbatkin
1970 SovietRxiv: ru-197001.53131

This paper discusses theoretical and numerical issues in modeling ultralong atmospheric waves for possible medium range weather prediction over one to three weeks. It proposes using a two level Phillips type hydrodynamic model, augmented by effects of surface inhomogeneity, orography, boundary layer…

A NONLINEAR ANALOGUE OF THE NEWTONIAN POTENTIAL AND METRIC PROPERTIES OF \((p,l)\)-CAPACITY

V. G. Maz'ya, V. P. Havin
1970 SovietRxiv: ru-197001.53001

This paper develops a nonlinear analogue of the Newtonian, or Riesz, potential adapted to the study of \((p,l)\)-capacity in Euclidean space for \(p>1\), \(pl<n\). Using Fourier-defined Sobolev-type spaces and an associated energy for generalized functions and measures, it establishes potential-theo…

ON OPERATORS IN HÖLDER SPACES

M. Z. Berkolaiko, Ya. B. Rutitskii
1970 SovietRxiv: ru-197001.52745

This note studies linear, integral, convolution, and superposition operators in generalized Hölder spaces defined by a concave modulus function. It proves continuity of positive linear operators between such spaces, establishes automatic continuity for integral operators under mapping assumptions, a…