区间Bézier曲线和曲面的升阶

把Bézier曲线、曲面的升阶公式推广到区间Bézier曲线、曲面,证明了在不断升阶的过程中,区间控制顶点的并集收敛到原区间Bézier曲线、曲面.这里的升阶公式可用于将低次的区间Bézier曲线、曲面转换成高次形式,并且升阶可以增加控制顶点的数目,便于更加灵活地对这些区间曲线、曲面作形状控制.由升阶公式和升阶的收敛性可得到一种简洁有效的区间Bézier曲线、曲面的几何作图方法.     

带幂非线性项变系数非线性波动方程的李对称分类与等价性变换

从微分方程群理论分析角度,研究了一类含有3个任意函数和2个幂非线性项的变系数非线性波动方程.由于方程具有很强的任意性和非线性项,可通过等价性变换寻找方程的不变对称分类.首先给出了等价性变换的一般结果,其中包括一些包含任意元的非局部变换.然后对所研究的方程,利用广义扩展等价群和条件等价群给出了方程的完全对称分类.最后获得并分析了方程的特殊类相似解.     

Conservation laws for variable coefficient nonlinear wave equations with power nonlinearities

Conservation laws for a class of variable coefficient nonlinear wave equations with power nonlinearities are investigated.The usual equivalence group and the generalized extended one including transformations which are nonlocal with respect to arbitrary elements are introduced.Then,using the most direct method,we carry out a classification of local conservation laws with characteristics of zero order for the equation under consideration up to equivalence relations generated by the generalized extended equivalence group.The equivalence with respect to this group and the correct choice of gauge coefficients of the equations play the major roles for simple and clear formulation of the final results.