广义仿拓扑群的若干性质研究

该文探讨广义仿拓扑群的广义邻域基、闭包运算、广义分离性、商群、同态映射、广义乘积、广义紧性等问题,建立了任意一个抽象群上的广义仿拓扑群化定理和广义仿拓扑群的一个广义拓扑同构定理,证明了每一广义仿拓扑群中单位元的广义开邻域生成的子群是广义开子群以及一族强广义仿拓扑群的广义乘积仍是广义仿拓扑群,并提出了一些问题.

Functional Variable Separation for Extended Nonlinear Elliptic Equations

This paper is devoted to the study of functional variable separation for extended nonlinear elliptic equations. By applying the functional variable separation approach to extended nonlinear elliptic equations via the generalized conditional symmetry, we obtain complete classification of those equations which admit functional separable solutions （FSSs） and construct some exact FSSs to the resulting equations.

Classification and Functional Separable Solutions to Extended Nonlinear Wave Equations

The generalized conditional symmetry approach is applied to study the variable separation of the extended wave equations. Complete classification of those equations admitting functional separable solutions is obtained and exact separable solutions to some of the resulting equations are constructed.

Variable Separation and Exact Separable Solutions for Equations of Type uxt=A（u,ux）uxx＋B（u,ux）

The generalized conditional symmetry is developed to study the variable separation for equations of type uxt = A（u,ux）uxx ＋ B（u, ux）. Complete classification of those equations which admit derivative-dependent functional separable solutions is obtained and some of their exact separable solutions are constructed.