The aim of the present paper is to study a Bochner Ricci semi-symmetric quasi-Einstein Hermitian manifold (QEH)n, a Bochner Ricci semi-symmetric generalised quasi-Einstein Hermitian manifold G(QEH)n and a Bochner Ricci semisymmetric pseudo generalised quasi-Einstein Hermitian manifold P (GQEH)n.

We construct, analyze and implement SSOR-like preconditioners for non-Hermitian positive definite system of linear equations when its coefficient matrix possesses either a dominant Hermitian part or a dominant skew-Hermitian part. We derive tight bounds for eigenvalues of the preconditioned matrices and obtain convergence rates of the corresponding SSOR-like iteration methods as well as the cor...

In this paper, we further investigate the local Hermitian and skew-Hermitian splitting (LHSS) iteration method and the modified LHSS (MLHSS) iteration method for solving generalized nonsymmetric saddle point problems with nonzero (2,2) blocks. When A is non-symmetric positive definite, the convergence conditions are obtained, which generalize some results of Jiang and Cao [M.-Q. Jiang and Y. Ca...

For a non-Hermitian Hamiltonian H possessing a real spectrum, we introduce a canonical orthonormal basis in which a previously introduced unitary mapping of H to a Hermitian Hamiltonian h takes a simple form. We use this basis to construct the observables Oα of the quantum mechanics based on H. In particular, we introduce pseudo-Hermitian position and momentum operators and a pseudo-Hermitian q...

Let H be any complex inner product space with inner product < ·, · >. We say that f : | C → | C is Hermitian positive definite on H if the matrix ( f(< z,z >) )n r,s=1 (∗) is Hermitian positive definite for all choice of z, . . . ,z in H, all n. It is strictly Hermitian positive definite if the matrix (∗) is also non-singular for any choice of distinct z, . . . ,z in H. In this article we prove...

Let M be an n-dimensional projective algebraic manifold in certain projective space CP . The hyperplane line bundle of CP restricts to an ample line bundle L on M , which is called a polarization of M . A Kähler metric g is called a polarized metric, if the corresponding Kähler form represents the first Chern class c1(L) of L in H (M,Z). Given any polarized Kähler metric g, there is a Hermitian...

We will use the variational approach to (0.1) as described in [2] and we will stick to the notations of that paper. Given the complex n-dimensional Hermitian space (C, 〈·, ·〉), for any m ∈ N let H m := H(J,C) be the Sobolev space of all H-maps from J := [0, 1] into C. A derivative dependent Hermitian form is the form Ω(x)[u] = Pm i,j=0〈D u(x), ωi,j(x)D u(x)〉, where, each ωi,j is a smooth path o...

in this paper, we nd the relationships between module contractibility of abanach algebra and its ideals. we also prove that module contractibility ofa banach algebra is equivalent to module contractibility of its module uniti-zation. finally, we show that when a maximal group homomorphic image ofan inverse semigroup s with the set of idempotents e is nite, the moduleprojective tensor product ...

We investigate the following two problems on a hermitian form Φ over an algebraic number field: (1) classification of Φ over the ring of algebraic integers; (2) hermitian Diophantine equations. The same types of problems for quadratic forms were treated in the author’s previous articles. Here we discuss the hermitian case. Problem (2) concerns an equation ξΦ · ξ = Ψ , where Φ and Ψ represent he...