弱双四元数矩阵方程AXAH+BYBH=C的反Hermite解

在本文中,我们讨论弱双四元数矩阵方程AXAH+BYBH=C的反Hermite解,其中矩阵A,B是已知的弱双四元数矩阵,C是已知的弱双四元数反Hermite矩阵,X,Y是未知的弱双四元数反Hermite方阵。本文的目标是建立解存在的充分必要条件和通解表达式。

Least Squares Hermitian Problem of Matrix Equation (<i>AXB</i>, <i>CXD</i>) = (<i>E</i>, <i>F</i>) Associated with Indeterminate Admittance Matrices

For A&#8712;Cm&#935;n, if the sum of the elements in each row and the sum of the elements in each column are both equal to 0, then A is called an indeterminate admittance matrix. If A is an indeterminate admittance matrix and a Hermitian matrix, then A is called a Hermitian indeterminate admittance matrix. In this paper, we provide two methods to study the least squares Hermitian indeterminate admittance problem of complex matrix equation (AXB,CXD)=(E,F), and give the explicit expressions of least squares Hermitian indeterminate admittance solution with the least norm in each method. We mainly adopt the Moore-Penrose generalized inverse and Kronecker product in Method I and a matrix-vector product in Method II, respectively.

同核双金属烯烃聚合催化剂

与单核金属配合物催化剂相比,双核金属配合物催化剂所具的双金属活性中心对烯烃聚合催化活性和所得聚合物的性能(包括聚合物微结构、分子量大小和分子量分布)产生了重要影响。本文综述了双金属配合物作为均相催化剂催化乙烯聚合及共聚合的最新研究,归纳思路包括不同的金属类型,即基于前过渡金属(Zr,Ti,Hf)和后过渡金属(Ni,Fe,Co)的双核金属组合;不同的配体化合物,即CGC配体、酚氧亚胺配体、氮杂环胺配体、α-二亚胺和亚胺吡啶配体等。这些研究表明,前过渡金属催化剂不仅解决了乙烯自聚还实现了乙烯与α-烯烃共聚;后过渡金属催化剂高效催化乙烯自聚合,其中铁和钴催化剂获得高度线性聚乙烯,镍催化剂则产生多支链聚乙烯。