W-Gleitgleitkinematik

The following gives some starting elements of a theory, which the author calls glide-glide-kinematics and which goes far beyond the kinematics of helical motion in ℝ ⁿ , which was studied up to now. We are mainly concerned here with “angle-preservering glide-glide-kinematics”, generalising (and giving as well some idea of) the distance-preservering glide-glide-kinematics, which we develop in a forthcoming book ([5]) in detail.      

Quality properties of solutions of diffenetial inequalities of a special form

Volgograd. Translated from Sibirskii Matematicheskii Zhurnal, Vol. 33, No. 3, pp. 78–90, May–June, 1992.     

Reflectionless potentials and soliton series of the KDV equation

Potentials of the Schrödinger equation, slowly decreasing at infinity, generate an infinite discrete spectrum converging to zero. The inverse scattering problem in the class of such potentials is solved in a constructive way similarly to the classical soliton theory. An infinite-dimensional system arising from Backlund transformations over soliton solutions plays the role of a determinant representation of the potential. The asymptotics at infinity is derived by use of the Poisson summation formula. An application to the long-time asymptotics of the solution of the Korteweg-de Vries equation is considered.In Memory of Prof. M. C. PolivanovInstitute of Mathematics, Urals Branch, Russian Academy of Sciences, 450000, Chernyshevsky str. 112, Ufa, Russia. Published in Teoreticheskaya i Matematicheskaya Fizika, Vol. 93, No. 2, pp. 286–301, November, 1992.     

Sets of pairs of values omitted by univalent functions

This article proves covering theorems for classes of univalent functions that omit given pairs of values. In particular, a problem posed by D. A. Brannan [R. Zh. Mat. 1978, 2B63] is solved.Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova Akademii Nauk SSSR, Vol. 185, pp. 140–145, 1990.     

Polynomial approximation inL p (0<p<1)

We prove that forf∈L _p , 0<p<1, andk a positive integer, there exists an algebraic polynomialP _n of degree ≤n such that $$\left\| {f - P_n } \right\|_p \leqslant C\omega _k^\varphi \left( {f,\frac{1}{n}} \right)_p $$ whereω _k ^? (f,t)p is the Ditzian-Totik modulus of smoothness off inL _p , andC is a constant depending only onk andp. Moreover, iff is nondecreasing andk≤2, then the polynomialP _n can also be taken to be nondecreasing.     

Statistical theory of the crystal state

A theory of the crystalline state of matter is constructed in the framework of the method of distribution functions. The system of two exact equations for the single- and two-particle distribution functions is solved by a series expansion in powers of the small parameter =(n-n _o)/n ₀, wheren is the density of the crystal andn ₀ is the density of the liquid at its crystallization point. In the zeroth order in , the theory leads to the Ornstein-Zernike equation, which determines all the properties of the molten state; in the first order, it leads to equations that determine the symmetry type of the crystal and the main lattice periods. Finally, in the second order in the theory makes it possible to calculate the jump in the density on crystallization of the molten state. The proposed method of solution is valid only at temperatures above the triple point, i.e., in the region in which the crystal can be in equilibrium with the molten matter.Institute of Physical Chemistry, USSR Academy of Sciences. Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 90, No. 1, pp. 113–127, January, 1992.     

ICP－AES法测定钨合金中镍、钴、铁、锰时酸度的影响

本文研究了用电感耦合等离子体发射光谱技术测定钨合金中镍、钴、铁、锰含量的方法及酸度对测量结果的影响。用氢氟酸及硝酸处理试样，并加入适量盐酸。实验研究了测量值随氯离子浓度增大而下降的变化曲线，找出了测量不同元素的最佳测定条件，测量结果同标准值比较，误差较小。