Characterization of simple K 4-groups

In this paper, we prove that a group G is isomorphic to M, where M is a simple K ₄-group, if and only if the following hold: (1) |G| = |M|, (2) nse(G) = nse(M).      

A simple method to construct soliton-like solution of the general KdV equation with external force

A simple and direct method is described to construct the soliton-like solution for the general KdV equation with external force. Crucial to the method is the assumption that the solution chosen is a special truncated expansion.     

Membranes of revolution under partially vanishing normal load

This paper investigates the existence and uniqueness of solutions of some boundary value problems modeling the deformation of a membrane of revolution under a partially vanishing normal load. The frame of the membrane models we deal with is the Reissner theory of thin shells of revolution, in which strain-displacement relations are nonlinear, although it assumes a linear stress-strain relation.     

一个特殊可重复排列数的算法

研究一类特殊的可重复排列性质,建立了一般情形下求这类排列数的递推公式,导出了一些特殊情形下的具体计算公式.     

THREE-POINT BOUNDARY VALUE PROBLEM FOR p-LAPLACIAN DIFFERENTIAL EQUATION AT RESONANCE

By topological degree theory,the three-point boundary value problem for p-Laplacian differential equation at resonance is studied. Some new results on the existence of solutions are obtained,which improve and extend some known ones in the previous literatures.     

一类二阶奇异微分方程正解的存在唯一性

利用上下解方法,不动点理论研究奇异微分方程u" f(t,u)=0,t∈(0,1)在边界条件au(0)-βu'(0)=0,γu(1) δu'(1)=0下C[0,1]正解和C1[0,1]正解的存在性与唯一性.其中非线性项f(t,u)关于u是减的,仅满足较弱的要求.     

A theorem on upper-lower solutions for nonlinear elliptic systems and its applications

We report on a result of upper-lower solutions for nonlinear elliptic systems without the assumption of quasi-monotonicity. An application is described involving the existence of positive steady states of a certain interaction system arising in biology and medical sciences.     

Earth surface effects on active faults: An eigenvalue asymptotic analysis

We study in this paper an eigenvalue problem (of Steklov type), modeling slow slip events (such as silent earthquakes, or earthquake nucleation phases) occurring on geological faults. We focus here on a half space formulation with traction free boundary condition: this simulates the earth surface where displacements take place and can be picked up by GPS measurements. We construct an appropriate functional framework attached to a formulation suitable for the half space setting. We perform an asymptotic analysis of the solution with respect to the depth of the fault. Starting from an integral representation for the displacement field, we prove that the differences between the eigenvalues and eigenfunctions attached to the half space problem and those attached to the free space problem, is of the order of d^-2, where d is a depth parameter: intuitively, this was expected as this is also the order of decay of the derivative of the Green's function for our problem. We actually prove faster decay in case of symmetric faults. For all faults, we rigorously obtain a very useful asymptotic formula for the surface displacement, whose dominant part involves a so called seismic moment. We also provide results pertaining to the analysis of the multiplicity of the first eigenvalue in the line segment fault case. Finally we explain how we derived our numerical method for solving for dislocations on faults in the half plane. It involves integral equations combining regular and Hadamard's hypersingular integration kernels.     

A difference scheme for solving the Timoshenko beam equations with tip body

In this article, a Timoshenko beam with tip body and boundary damping is considered. A linearized three-level difference scheme of the Timoshenko beam equations on uniform meshes is derived by the method of reduction of order. The unique solvability, unconditional stability and convergence of the difference scheme are proved. The convergence order in maximum norm is of order two in both space and time. A numerical example is presented to demonstrate the theoretical results.     

Filler effect on photopolymerization of a medical oligoester composition

The effect of an inorganic filler (aerosil) on photopolymerization of an oligoester composition is investigated by means of IR spectroscopy. It is shown that the filler, depending on its concentration, is capable of enhancing or hindering the main process, or inducing side reactions. Institute for Surface Chemistry, National Academy of Sciences of Ukraine, 31, Nauka Ave., Kiev, 252022, Ukraine. Translated from Zhurnal Prikladnoi Spektroskopii, Vol. 66, No. 1, pp. 119–124 January–February, 1999.