几类数列通项的矩阵求法

本利用矩阵给出了几类数列的通项公式的求法，把数列通项公式的求法转化为矩阵幂的计算，思路简单、计算简便，并能判别其敛散性。     

THE ASYMPTOTIC SOLUTION FOR A CLASS OF SINGULARLY PERTURBED PROBLEM FOR SEMILINEAR SINGULAR EQUATION

The singularly perturbed boundary value problem for a class of semilinearsingular equation is considered. Using a simple and special method the asym-ptotic behavior of solution is studied.     

123 Phases in CeLa2Cu2MgO8 samples

A tetragonal 123 phase with the composition close to CeLa₂ { Cu ₂ ²⁺ } [Mg²⁺]O₈ (the braces indicate the Cu(2) positions; the brackets indicate the Cu(1) positions) with the parameters a = b = 0.3909(3) nm, c = 1.6591(8) nm was prepared at 860°C under an oxygen atmosphere with an elevated oxygen pressure. When the lanthanum-for-barium substitution was incomplete, the resulting 123 phase had the composition close to CeLa_1.7Ba_0.3{ Cu _1.7 ²⁺ } [Mg]O₈ with the unit cell parameters a = b = 0.3868(3) nm, c = 1.6578(8) nm that contains Cu³⁺ in the Cu(2) positions. The partial substitution of barium for lanthanum (the melting point of barium oxide is almost 500°C lower that of the lanthanum oxide) appreciably facilitated the synthesis: the 123 phase in this sample was more than 90%. The existence of Cu³⁺ in the Cu(2) positions enhanced the electrical conductivity of the sample.     

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.