双Z-连续格和双Z-Scott拓扑的性质

在完备格上定义了双Z-连续格和双Z-Scott拓扑,讨论了双Z-Scott拓扑的格序性质.得到了当P是Z-拟连续时,双Z-Scott拓扑是T2的;证明了双Z-连续格在保Z-双小于关系和对偶Z-双小于关系的双Z-Scott连续映射下的像仍是双Z-连续格.

关于两个Cartesian闭范畴交的一点注记

讨论了关于双Scott拓扑的一些性质.证明了范畴B ICONT(即以双连续格为对象,以双Scott连续映射为态射的范畴)作为两个Cartesian闭范畴B ICONTS(即以双连续格为对象,以Scott连续映射为态射的范畴)和B ICONTSop(即以双连续格为对象,以对偶Scott连续映射为态射的范畴)的交范畴不是Cartesian闭范畴.

Solutions and Continuum Limits of Two Semi-Discrete Lattice Potential Korteweg-de Vries Equations

We derive bilinear forms and Casoratian solutions for two semi-discrete potential Korteweg-de Vries equations. Their continuum limits go to the counterparts of the continuous potential Korteweg-de Vries equation.