We call a positive definite integral quadratic form universal if it represents all positive integers. Then Lagrange’s Four Square Theorem means that the sum of four squares is universal. In 1930, Mordell [M] generalized this notion to a 2-universal quadratic form: a positive definite integral quadratic form that represents all binary positive definite integral quadratic forms, and showed that t...

in this paper we consider the solutions of linear systems of saddle point problems‎. ‎by using the spectrum of a quadratic matrix polynomial‎, ‎we study the eigenvalues of the iterative matrix of the hermitian and skew hermitian splitting method‎.

Let (M, θ) be a strictly pseudoconvex pseudo-Hermitian compact hypersurface in C in the sense of Webster [34] with a pseudo-Hermitian real oneform θ on M . Let Rθ be the Webster pseudo scalar curvature for M with respect to θ. By the solution of the CR Yamabe problem given by Jerison and Lee [18], Gamara and Yacoub [10] and Gamara [9] (for n = 1), there is a pseudo-Hermitian real one-form θ so ...

This paper is concerned with a generalization of the Hermitian and skew-Hermitian (HSS) splitting iteration for solving positive definite, non-Hermitian linear systems. It is shown that the new scheme can outperform the standard HSS method in some situations and can be used as an effective preconditioner for certain linear systems in saddle point form. Numerical experiments using discretization...

This paper is concerned with a generalization of the Hermitian and skew-Hermitian splitting iteration for solving positive definite, non-Hermitian linear systems. It is shown that the new scheme has some advantages over the standard HSS method, and can be used as an effective preconditioner for certain linear systems in saddle point form. Numerical experiments using discretizations of incompres...

We study almost Hermitian structures admitting a Hermitian connexion with totally skew-symmetric torsion or equivalently, those almost Hermitian structures with totally skewsymmetric Nijenhuis tensor. We investigate up to what extent the Nijenhuis tensor fails to be parallel with respect to the characteristic connexion. This is naturally described by means of an extension of the notion of Killi...

In Schrödinger picture the unitarity of evolution is usually guaranteed by Hermiticity Hamiltonian operator h=h† in a conventional Hilbert space Htextbook. After Dyson-inspired operator-transformation (OT) non-unitary preconditioning ?:h?H simplified H is, its manifestly unphysical Hauxiliary, non-Hermitian. Besides natural OT-based physical interpretation it can also be “Hermitized” (i.e., mad...

This paper deals with the Hermitian H(A) and skew-Hermitian part S(A) of a complex matrix A. We characterize all complex matrices A such that H(A), respectively S(A), is a potent matrix. Two approaches are used: characterizations of idempotent and tripotent Hermitian matrices of the form [ X Y ∗ Y 0 ] , and a singular value decomposition of A. In addition, a relation between the potency of H(A)...

We investigate differential geometric aspects of moduli spaces parametrizing solutions of coupled vortex equations over a compact Kähler manifold X . These solutions are known to be related to polystable triples via a Kobayashi–Hitchin type correspondence. Using a characterization of infinitesimal deformations in terms of the cohomology of a certain elliptic double complex, we construct a Hermi...