We propose a class of regularized Hermitian and skew-Hermitian splitting methods for the solution of large, sparse linear systems in saddle-point form. These methods can be used as stationary iterative solvers or as preconditioners for Krylov subspacemethods.We establish unconditional convergence of the stationary iterations and we examine the spectral properties of the corresponding preconditi...

Recently, Bender et al. have considered the quantum brachistochrone problem for the non-Hermitian PT -symmetric quantum system and have shown that the optimal time evolution required to transform a given initial state |ψi〉 into a specific final state |ψf 〉 can be made arbitrarily small. Additionally, it has been shown that finding the shortest possible time requires only the solution of the two...

A Hermitian Einstein-Weyl manifold is a complex manifold admitting a Ricci-flat Kähler covering M̃ , with the deck transform acting on M̃ by homotheties. If compact, it admits a canonical Vaisman metric, due to Gauduchon. We show that a Hermitian Einstein-Weyl structure on a compact complex manifold is determined by its volume form. This result is a conformal analogue of Calabi’s theorem stating ...

For arbitrary equally sized square complex matrices A and Q (Q Hermitian), the paper provides a complete algebraic test for verifying the existence of a Hermitian solution X of the nonstrict Lyapunov inequality A X + XA + Q 0: If existing, we exhibit how to construct a solution. Our approach involves the validation problem for the linear matrix inequality P k j=1 (A j X j B j + B j X j A j) + Q...

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 ...

The correlation functions of the multi-arc complex matrix model are shown to be universal for any finite number of arcs. The universality classes are characterized by the support of the eigenvalue density and are conjectured to fall into the same classes as the ones recently found for the hermitian model. This is explicitly shown to be true for the case of two arcs, apart from the known result ...

Difference equations of the form X ( t ) = F * ( t ) X ( t 1 ) F ( t ) F * ( t ) X ( t 1)G(t)[ l + G * ( t ) X ( t 1)G(t)]t G * ( t ) X ( t 1)F(t)+ Q(t ) and their associated Hermitian matrices H ( t ) = (0 v F* _C,C.)(t) are studied. Solution of different Riccati equations can be compared if the difference of their corresponding Hermitian matrices is semidefinite for all t. An application to t...

Currently secure communication is a very challenging task. Cryptography is providing solution to this challenge. But cryptography highly depends on invertible mathematical functions. Mathematical stuff embedded with computer model brings the unbreakable cryptosystem. Many algorithms are proposed in the literature and they are having their own limitations. In this paper, an algorithm based on He...

We establish necessary and sufficient conditions for the existence of and the expressions for the general real and complex Hermitian solutions to the classical system of quaternion matrix equationsA1X C1, XB1 C2, and A3XA3 C3. Moreover, formulas of the maximal andminimal ranks of four real matrices X1, X2, X3, and X4 in solution X X1 X2i X3j X4k to the system mentioned above are derived. As app...