The eigenproblems of the rank-one updates of the matrices have lots of applications in scientific computation and engineering such as the symmetric tridiagonal eigenproblems by the divide-andconquer method and Web search engine. Many researchers have well studied the algorithms for computing eigenvalues of Hermitian matrices updated by a rank-one matrix [1–6]. Recently, Ding and Zhou studied a ...

Three types of Riemannian submersions whose total space is an almost Hermitian almost contact metric manifold are studied. The study is focused on fundamental properties and the transference of structures. 1. Introduction. In this paper, we discuss some geometric properties of Riemannian submersions whose total space is an almost Hermitian almost contact metric manifold. If the base space is an...

We introduce a nonsymmetric real matrix which contains all the information that the usual Hermitian density matrix does, and which has exactly the same tensor product structure. The properties of this matrix are analyzed in detail in the case of multi-qubit (e.g. spin = 1/2) systems, where the transformation between the real and Hermitian density matrices is given explicitly as an operator sum,...

We study the functional codes of second order defined by G. Lachaud on X ⊂ P(Fq) a quadric of rank(X )=3,4,5 or a non-degenerate hermitian variety. We give some bounds for the number of points of quadratic sections of X , which are the best possible and show that codes defined on non-degenerate quadrics are better than those defined on degenerate quadrics. We also show the geometric structure o...

We emphasize the crucial rôle played by non-factorizable phases in the analysis of the Yukawa flavour structure performed in weak bases with Her-mitian mass matrices and with vanishing (1, 1) entries. We show that non-factorizable phases are important in order to generate a sufficiently large sin 2β. A method is suggested to reconstruct the flavour structure of Yukawa couplings from input exper...

In this talk we investigate some classes of structures that are preserved by applying a QR step on a matrix A. We will handle two classes of such structures: the first we call polynomial structures, for example a matrix being Hermitian or Hermitian up to a rank one correction, and the second we call rank structures, which are encountered for example in all kinds of what we could call Hessenberg...

We show that distinct topological phases of the band structure of a non-Hermitian Hamiltonian can be classified with elements of the braid group. As the proof of principle, we consider the non-Hermitian evolution of the statistics of nonequilibrium stochastic currents. We show that topologically nontrivial phases have detectable properties, including the emergence of decaying oscillations of pa...

We develop an intersection theory for a singular hermitian line bundle with positive curvature current on a smooth projective variety and irreducible curves on the variety. And we prove the existence of a natural rational fibration structure associated with the singular hermitian line bundle. Also for any pseudoeffective line bundle on a smooth projective variety, we prove the existence of a na...

A slant immersion is an isometric immersion from a Riemannian manifold into an almost Hermitian manifold with constant Wirtinger angle (1~ . In this article we study and characterize slant surfaces in the complex 2-plane ~2 via the Gauss map. We also prove that every surface without complex tangent points in a 4-dimensional almost Hermitian manifold M is slant with respect to a suitably chosen ...

The development of strong linearizations preserving whatever structure a matrix polynomial might possess has been a very active area of research in the last years, since such linearizations are the starting point of numerical algorithms for computing eigenvalues of structured matrix polynomials with the properties imposed by the considered structure. In this context, Hermitian matrix polynomial...