in this paper we introduce the concept of dirac structures on (hermitian) modules and vectorbundles and deduce some of their properties. among other things we prove that there is a one to onecorrespondence between the set of all dirac structures on a (hermitian) module and the group of allautomorphisms of the module. this correspondence enables us to represent dirac structures on (hermitian)mod...

In this article we consider the system of operator equations T_iX=U_i for i=1,2,...,n and give necessary and suffcient conditions for the existence of common Hermitian solutions to this system of operator equations for arbitrary operators without the closedness condition. Also we study the Moore-penrose inverse of a ncross 1 block operator matrix and. then gi...

for solving large sparse non-hermitian positive definite linear equations, bai et al. proposed the hermitian and skew-hermitian splitting methods (hss). they recently generalized this technique to the normal and skew-hermitian splitting methods (nss). in this paper, we present an accelerated normal and skew-hermitian splitting methods (anss) which involve two parameters for the nss iteration. w...

We study 2-incompressible Grassmannians of isotropic subspaces of a quadratic form, of a hermitian form over a quadratic extension of the base field, and of a hermitian form over a quaternion algebra.

We extend the Siegel-Weil formula to all quaternion dual pairs. Applications include the classification problem of skew hermitian forms over a quaternion algebra over a number field and a product formula for the weighted average of the representation numbers of a skew hermitian form by another skew hermitian form.

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 are concerned with classical polar spaces, i. e. with the set of points and lines of some vector space W on which a non–degenerate (σ, )-hermitian form or pseudo-quadratic form vanishes. To state the Main Theorem we introduce some notation. Let L be a division ring and W be a (left–)vector space over L endowed with a (σ, )–hermitian form or a pseudo–quadratic form q (with assoc...

For the non-Hermitian and positive semidefinite systems of linear equations, we derive sufficient and necessary conditions for guaranteeing the unconditional convergence of the preconditioned Hermitian and skew-Hermitian splitting iteration methods. These result is specifically applied to linear systems of block tridiagonal form to obtain convergence conditions for the corresponding block varia...

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...