in this paper, we derive the necessary and sufficient conditions for the quaternion matrix equation xa=b to have the least-square bisymmetric solution and give the expression of such solution when the solvability conditions are met. futhermore, we consider the maximal and minimal inertias of the least-square bisymmetric solution to this equation. as applications, we derive sufficient and necess...

In this paper we construct families of homology spheres which bound 4-manifolds with intersection forms isomorphic to $-E_8$. We show that these have arbitrary large correction terms. This result says among spheres, the difference maximal rank minimal sub-lattice definite filling and even is arbitrarily large.

We consider positive definite (semidefinite) extension problems for matrices with structure determined via a Stein equation. Some related extremal problems (maximal and minimal rank extensions, maximal determinant extension) are also considered. Connections with interpolation problems for a certain class of analytic contractive valued functions on the unit ball of Cd are discussed. © 2003 Publi...

Let R(A) denote the rank (also called bilinear complexity) of a finite dimensional associative algebra A. A fundamental lower bound for R(A) is the so-called Alder– Strassen boundR(A) 2 dimA t, where t is the number of maximal twosided ideals of A. The class of algebras for which the Alder–Strassen bound is sharp, the so-called algebras of minimal rank, has received a wide attention in algebrai...

A topological space (X, T) with property R is maximal R (minimal R) if T is a maximal (minimal) element in the set R(X) of all topologies on the set X having property R with the partial ordering of set inclusions. The properties of maximal topologies for compactness, countable compactness, sequential compactness, Bolzano-Weierstrass compactness, and Lindelöf are investigated and the relations b...