Jianzhou Liu

Energetics of charged domain walls in ferroelectric crystals

We calculated the energy variation due to the emergence of a new domain in barium titanate single crystal using equivalent inclusion method, and energy minimizing domain morphology and orientations have been identified. It is found that the energy difference between the charged and uncharged domain walls is relatively small, and the charged domain wall is metastable. It is also concluded that the compatibility of transformation strain plays a more important role in ferroelectric domain configurations than polarization compatibility, and the incompatibility of piezoelectric strain is insignificant.

The extension of Roth's theorem for matrix equations over a ring

Abstract This paper extends Roths similarity theorem as follows: Let R be a ring with identity, B(λ) = Σki = 0 Biλi ϵ Rm × q[λ]. If either R is a division ring and A ϵ Rn × n is algebraic, or R is finitely generated as a module over its center, then the matrix equation Σki = 0 AiXBi = C over R has a solution if and only if

Some inequalities for singular values and eigenvalues of generalized Schur complements of products of matrices

Abstract In this paper, using transformation of Schur complements of matrices and some estimates of eigenvalues of positive semidefinite Hermitian matrices, we obtain some inequalities of singular values for Schur complements of products of matrices.

A minimum principle and estimates of the eigenvalues for schur complements positive semidefinite hermitian matrices

Abstract We give a minimum principle for Schur complements of positive definite Hermitian matrices. Further, we obtain some inequalities for the eigenvalues of Schur complements of products and sums of positive definite Hermitian matrices.

Some inequalities for Schur complements

Abstract We shall obtain some inequalities for Schur complements of products and sums of matrices.

Some Löwner partial orders of Schur complements and Kronecker products of matrices

Abstract In this paper, we define generalized Schur complements of matrices. Further, combining Schur complements of matrices with Kronecker products of matrices, we study their Lowner partial order and obtain some important inequalities, that improve recent results.

A structural characterization of real k-potent matrices

Some well-known characterizations of nonnegative k-potent matrices have been obtained by Flor [P. Flor, On groups of nonnegative matrices, Compositio Math. 21 (1969), pp. 376–382.] and Jeter and Pye [M. Jeter and W. Pye, Nonnegative (s, t)-potent matrices, Linear Algebra Appl. 45 (1982), pp. 109–121.]. In this article, we obtain a structural characterization of a real k-potent matrix A, provided that (sgn(A)) k+1 is unambiguously defined, regardless of whether A is nonnegative or not.