半线性椭圆方程正解的存在性及熄灭现象

本文在环形域上证明了带有奇异性的半线性椭圆方程边值问题(1)、(2·)在C~2(Ω)∩C~0(Ω)中正解的存在性,且这个解是径向对称的,解关于R_0(R_1)的连续单调性.还给出了解有熄灭现象的充分必要条件.     

Periodic solutions of second-order quasilinear hyperbolic equations

We study a periodic boundary-value problem for a quasilinear equation with the d'Alembert operator on the left-hand side and a nonlinear operator on the right-hand side and establish conditions under which the solution of the indicated problem is unique.Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 47, No. 10, pp. 1370–1375, October, 1995.     

Application of the variation principle for the problem of buckling of a nonlinearly elastic ring nonuniform along its thickness

There has been considerable recent attention given to the stressed and buckled states of items with complicated configuration made of different nonlinearly elastic materials joined by complete adhesion. However, effective analytical solutions for such problems have been hindered by mathematical difficulties. Approximate methods have thus been developed for such problems. A variational combined principle has been formulated in this communication. A nonlinear geometrical approach has been used for formulating a mixed-type functional with physical relationships given by Euler equations, nonlinear equilibrium equations, and nonlinear boundary conditions for a piecewise-nonuniform nonlinearly elastic body composed of finite elements (particles). As an example, buckling along the nonuniform thickness of nonlinearly elastic rings was analyzed hypothetically assuming plane cross-sections. Options for two-, three-, four-, five-, and six-layered rings in a periodical structure have been reviewed. The critical buckling forces for an even number of layers have been found to be equal to each other. The ratios of the critical forces, elasticity moduli, and proportionality levels were determined for all five variants by the Runge-Kutta method.Presented at the Ninth International Conference on the Mechanics of Composite Materials (Riga, October, 1995).Translated from Mekhanika Kompozitnykh Materialov, Vol. 31, No. 2, pp. 262–268, March–April, 1995.     

Investigation of natural compounds by the HPLC method II. HPLC fingerprint method for the epigeal organs of Ferula kuhistanica and F. tenuisecta

A microcolumn HPLC fingerprint method has been developed for the epigeal organs ofFerula kuhistanica andF. tenuisecta. The possibility has been shown of control by the microcolumn HPLC method of the qualitative and quantitative yields of ferutinin in the initial plant raw material and in preparations extracted from it, and also at each stage of the isolation of the desired product. The method is universal and does not depend on species and chemical composition of the plant. Institute of the Chemistry of Plant Substances, Uzbekistan Academy of Sciences, Tashkent. Translated from Khimiya Prirodnykh Soedinenii, No. 6, pp. 635–636, November–December, 1992.     

On the mechanism of phenol ozonolysis

The mechanisms of liquid-phase phenol ozonation are revised. A new mechanism in which a significant role is played by free-radical reactions is suggested for this process.     

Limit distribution of the number of consecutive records

A succinct series expression is derived for describing the limit distribution of the number of times r consecutive elements are all records (in a sequence of independent and identically distributed random variables with a common continuous distribution) for all r ≥ 2. Previously, only the limit distributions for r = 1, 2, and 3 were known. © 2005 Wiley Periodicals, Inc. Random Struct. Alg., 2005