论广义量词的对称性及相关性质

首先介绍相关的概念;其次,笔者证明了类型为〈1,1〉的广义量词的对称性与单调性的关系定理;然后,笔者给出了该类量词的余对称性、余相交性和余驻留性的定义;接着,笔者提出并证明了关于这三个性质的四个定理;最后,证明了余对称性与单调性的关系定理。

Lie Symmetries and Conserved Quantities of Holonomic Systems with Remainder Coordinates

Aim To study the Lie symmetries and the consered quantities of the holonomic systems with remainder coordinates. Methods Using the invariance of the ordinary differential equations under the infinitesimal transformations to establish the determining equations and the restriction equations of the Lie symmetries of the systems. Results and Conclusion the structure equation and the form of conserved quantities were obtained. An example was given to illustrate the application of the result.

Some Growth Rates of Certain Holomorphic Maps

In this paper we discuss some properties of h olomorphic maps between Kahler manifolds with certain curvature restrictions.

CTE Solvability, Nonlocal Symmetry and Explicit Solutions of Modified Boussinesq System

A consistent tanh expansion(CTE) method is used to study the modified Boussinesq equation. It i proved that the modified Boussinesq equation is CTE solvable. The soliton-cnoidal periodic wave is explicitly given by a nonanto-BT theorem. Furthermore, the nonlocal symmetry for the modified Boussinesq equation is obtained by th Painlev′e analysis. The nonlocal symmetry is localized to the Lie point symmetry by introducing one auxiliary dependen variable. The finite symmetry transformation related with the nonlocal symemtry is obtained by solving the initia value problem of the prolonged systems. Thanks to the localization process, many interaction solutions among soliton and other complicated waves are computed through similarity reductions. Some special concrete soliton-cnoidal wav interaction behaviors are studied both in analytical and graphical ways.

Nonlocal Symmetries and Explicit Solutions of the Boussinesq Equation

The nonlocal symmetry of the Boussinesq equation is obtained from the known Lax pair. The explicit analytic interaction solutions between solitary waves and cnoidal waves are obtained through the localization procedure of nonlocal symmetry. Some other types of solutions, such as rational solutions and error function solutions, are given by using the fourth Painlev~ equation with special values of the parameters. For some interesting solutions, the figures are given out to show their properties.

Residual-based a posteriori error estimates for symmetric conforming mixed finite elements for linear elasticity problems

A posteriori error estimators for the symmetric mixed finite element methods for linear elasticity problems with Dirichlet and mixed boundary conditions are proposed. Reliability and efficiency of the estimators are proved. Numerical examples are presented to verify the theoretical results.

Nonlocal Symmetry,CTE Solvability and Interaction Solutions of Whitham–Broer–Kaup Equations

Whitham–Broer–Kaup(WBK) equations in the shallow water small-amplitude regime is hereby under investigation. Nonlocal symmetry and Bcklund transformation are presented via the truncated Painlevé expansion.This residual symmetry is localised to Lie point symmetry by the properly enlarged system. The finite symmetry transformation of the prolonged system is computed. Based on the CTE method, WBK equations are linearized and new analytic interaction solutions between solitary waves and cnoidal waves are given with the aid of solutions for the linear equation.