In this paper, we study the iterative algorithms for saddle point problems(SPP). Bai, Golub and Pan recently studied a class of preconditioned Hermitian and skew-Hermitian splitting methods(PHSS). By further accelerating it with another parameters, using the Hermitian/skew-Hermitian splitting iteration technique we present the generalized preconditioned Hermitian and skew-Hermitian splitting me...

We prove that the first positive eigenvalue, normalized by the volume, of the sub-Laplacian associated with a strictly pseudoconvex pseudo-Hermitian structure θ on the CR sphere S ⊂ C, achieves its maximum when θ is the standard contact form.

In this note we prove that if the fundamental 4-form of an almost-quaternionic Hermitian manifold (M,Q, g) of dimension 4n ≥ 8 satisfies the conformal-Killing equation, then (M,Q, g) is quaternionic-Kähler.

We consider the quotient of the Hermitian curve defined by the equation yq + y = xm over Fq2 where m > 2 is a divisor of q + 1. For 2 ≤ r ≤ q + 1, we determine the Weierstrass semigroup of any r-tuple of Fq2 rational points (P∞, P0b2 , . . . , P0br ) on this curve. Using these semigroups, we construct algebraic geometry codes with minimum distance exceeding the designed distance. In addition, w...

We address the problem of coupling non-Hermitian systems, treated as fundamental rather than effective theories, to the electromagnetic field. In such theories the observables are not the x and p appearing in the Hamiltonian, but quantities X and P constructed by means of the metric operator. Following the analogous procedure of gauging a global symmetry in Hermitian quantum mechanics we find t...

Closed-form formulas are derived for the rank and inertia of submatrices of the Moore–Penrose inverse of a Hermitian matrix. A variety of consequences on the nonsingularity, nullity and definiteness of the submatrices are also presented.

The Kobayashi indicatrix (infinitesimal unit ball) of a domain in IE n is known to be a biholomorphic invariant. In particular, if a domain is biholomorphic to a ball, then the indicatrix is the ball. Until the recent deep results of Lempert [4], it was not known to what extent the indicatrix characterizes the domain. Sibony had shown earlier that the indicatrix of any pseudoconvex circular dom...

in this paper‎, ‎we study the extremal‎ ‎ranks and inertias of the hermitian matrix expression $$‎ ‎f(x,y)=c_{4}-b_{4}y-(b_{4}y)^{*}-a_{4}xa_{4}^{*},$$ where $c_{4}$ is‎ ‎hermitian‎, ‎$*$ denotes the conjugate transpose‎, ‎$x$ and $y$ satisfy‎ ‎the following consistent system of matrix equations $a_{3}y=c_{3}‎, ‎a_{1}x=c_{1},xb_{1}=d_{1},a_{2}xa_{2}^{*}=c_{2},x=x^{*}.$ as‎ ‎consequences‎, ‎we g...

Recently, the present authors considered doubly warped product CR-submanifolds in a locally conformal Kaehler manifold and got some inequalities about the length of the second fundamental form ([14]). In this report, we obtain an inequality of the mean curvature of a doubly warped product CR-submanifold in a locally conformal Kaehler space form. Then, we consider the equality case of this inequ...

This paper concerns quadratic matrix functions of the form L(λ) = Mλ2 +Dλ+K where M,D,K are Hermitian n× n matrices with M > 0. It is shown how new systems of the same type can be generated with some eigenvalues and/or eigenvectors updated and this is accomplished without “spill-over” (i.e. other spectral data remain undisturbed). Furthermore, symmetry is preserved. The methods also apply for H...