Triterpene glycosides of Astragalus and their genins XXXIV. Cycloaraloside E from Astragalus amarus

Five compounds of glycosidic nature, designated 5–9 have been isolated from the roots of the plantAstragalus amarus Pall. (Leguminosae). The structure of substance 8, which has been called cycloaraloside E, has been shown on the basis of chemical transformations and spectral characteristics. Cycloaraloside E is 20R, 24S-epoxycycloartane-3β,6α,16β,25-tetraol 3,25-di-0-β-D-glucopyranoside.     

Functional equations for transfer-matrix operators in open Hecke chain models

We consider integrable open chain models formulated in terms of the generators of affine Hecke algebras. We use the fusion procedure to construct the hierarchy of commutative elements, which are analogues of the commutative transfer matrices. These elements satisfy a set of functional relations generalizing functional relations for a family of transfer matrices in solvable spin chain models of the U_q(gl(n|m)) type. __________ Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 150, No. 2, pp. 219–236, February, 2007.     

Reduction of the error of hydrophone calibration with respect to the field in a hydroacoustic tank by the reciprocity method

A hydrophone calibration procedure that considerably reduces the error caused by the acoustic field distortions in a hydroacoustic tank is proposed. The procedure is based on the definition of the reduced electric transfer impedances of transducers (i.e., the electric transfer impedances reduced to the spherical wave propagation law) and consists in measuring the electric transfer impedances for different distances between hydroacoustic transducers. The sensitivity of the hydrophone under calibration is calculated from the far-field values of the reduced electric transfer impedances. The latter are determined using a mathematical model of the hydrophone in the form of a system that contains a point sensing element and a finite number of point sources of acoustic signals (point reflectors). A method of determining the number and coordinates of the point reflectors from the analysis of the acoustic “images” of the hydrophone’s reflecting surface is proposed. The measuring technique, the algorithms of mathematical processing, and the results of experimental studies are considered. A comparative analysis of the results of the hydrophone calibration with respect to the field by the reciprocity method is performed for the cases of using the conventional technique and the proposed method.     

Paragrassmann differential calculus

This paper significantly extends and generalizes the paragrassmann calculus of our previous paper [1]. Here we discuss explicit general constructions for paragrassmann calculus with one and many variables. For one variable, nondegenerate differentiation algebras are identified and shown to be equivalent to the algebra of (p+1)×(p+1) complex matrices. If (p+1) is a prime integer, the algebra is nondegenerate and so unique. We then give a general construction of many-variable diffeentiation algebras. Some particular examples are related to multi-parametric quantum deformations of the harmonic oscillators.Dedication This paper is in memory of Mikhail Constantinovich Polivanov. One of the authors (A.T.F.) had a privilege to be a friend of him for many and many years. He was not only a distinguished scientist but a true Russian intellectual having deep roots in Russian culture. It is a deep sorrow that we can no more have a talk with him on science, poetry, religion ...Laboratory of Theoretical Physics, JINR, Dubna. SU-101 000 Moscow, Russia. Published in Teoreticheskaya i Matematicheskaya Fizika, Vol. 94, No. 2, pp. 213–231, February, 1993.     

Numerical Simulation of the Unsteady Laminar Flow Past a Circular Cylinder with a Perforated Sheath

The unsteady two-dimensional laminar flow past a circular cylinder encased in a perforated sheath is numerically simulated. On the basis of the calculated results a technique for controlling the wake flow by diverting a portion of the flow from the forward stagnation point through internal ducts to orifices in the sheath located in the separation zone, is analyzed.     

GLq(N)-covariant braided differential bialgebras

We study the possibility of defining the (braided) comultiplication for the GL _q (N)-covariant differential complexes on some quantum spaces. We discover suchdifferential bialgebras (and Hopf algebras) on the bosonic and fermionic quantum hyperplanes (with additive coproduct) and on the braided matrix algebra BM _q (N) with both multiplicative and additive coproducts. The latter case is related (forN = 2) to theq-Minkowski space andq-Poincaré algebra.     

Collective Acceleration of Ions in a Pulsed Magnetic Field of a Conical Spiral

The collective acceleration of laser plasma ions in a magnetic field generated by a powerful fast-growing current pulse in a low-inductive conical spiral is studied. The velocity of ions for a number of elements which significantly differ in atomic weight are obtained on the basis of collector measurements. The maximum velocity of both light (lithium) and heavy (lead) ions exceed the value of 108 cm/s; for ions of lead, the corresponding energy amounts to a value of ∼1 MeV. A mathematical model of ion acceleration is proposed and simulation results are compared with the experiment.     

Formation of singular (001) terraces on the surface of single-crystal HPHT diamond substrates

Methods of the experimental diagnostics and control of the misorientation angle for single-crystal HPHT (High Pressure High Temperature) diamond substrates are discussed. Such substrates are used for the homoepitaxial growth of doped and undoped CVD diamond layers. The formation of singular (001) terraces on the surface of HPHT diamond after microwave-discharge-plasma etching in pure hydrogen or a hydrogen–oxygen mixture is observed. This phenomenon can be used for rapid determination of the substrate misorientation and to improve the control precision of the deviation angle during substrate polishing, or for obtaining large singular (001) areas of single-crystal diamond substrates.