In complete analogy with the classical situation (which is briefly reviewed) it is possible to define bi-Hamiltonian descriptions for Quantum systems. We also analyze compatible Hermitian structures in full analogy with compatible Poisson structures.

We study balanced Hermitian structures on almost abelian Lie algebras, i.e. algebras with a codimension-one ideal. In particular, we classify six-dimensional which carry structure. It has been conjectured in [1] that compact complex manifold admitting both metric and an SKT necessarily Kähler metric: prove this conjecture for solvmanifolds left-invariant structures. Moreover, investigate the be...

Abstract This paper presents a frequency domain solution to the delay-type Nehari problem. The solvability condition is formulated in terms of nonsingularities of three matrices. The optimal value is the maximal value such that one of the three matrices becomes singular when decreases from to . The all sub-optimal compensators are parameterized in a transparent structure with a modified Smith p...

It is shown that the Hermitian-symmetric space CP1 × CP1 × CP1 and the flag manifold F1,2 endowed with any left invariant metric admit no compatible integrable almost complex structures (even locally) different from the invariant ones. As an application it is proved that any stable harmonic immersion from F1,2 equipped with an invariant metric into an irreducible Hermitian symmetric space of co...

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.

We investigate an N-particle Bose-Hubbard dimer with an additional effective decay term in one of the sites. A mean-field approximation for this non-Hermitian many-particle system is derived, based on a coherent state approximation. The resulting nonlinear, non-Hermitian two-level dynamics, in particular, the fixed point structures showing characteristic modifications of the self-trapping trans...

We present a characterization, in terms of torsion-free generalized connections, for the integrability various structures (generalized almost complex structures, hypercomplex Hermitian and hyper-Hermitian structures) defined on Courant algebroids. develop new, self-contained, approach theory Dirac generating operators regular algebroids with scalar product neutral signature. As an application w...