A class η-weak-pseudo-Hermiticity generators for spherically symmetric non-Hermitian Hamiltonians are presented. An operators-based procedure is introduced so that the results for the 1D Schrödinger Hamiltonian may very well be reproduced. A generalization beyond the nodeless states is proposed. Our illustrative examples include η-weak-pseudo-Hermiticity generators for the non-Hermitian weakly ...

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...

Exact solvability of some non-Hermitian η-weak-pseudo-Hermitian Hamiltonians is explored as a byproduct of η-weak-pseudo-Hermiticity generators. A class of Veff (x) = V (x) + iW (x) potentials is considered, where the imaginary part W (x) is used as an η-weak-pseudo-Hermiticity generator to obtain exactly solvable η-weak-pseudo-Hermitian Hamiltonian models. PACS numbers: 03.65.Ge, 03.65.Fd,03.6...

A class η-weak-pseudo-Hermiticity generators for spherically symmetric non-Hermitian Hamiltonians are presented. An operators-based procedure is introduced so that the results for the 1D Schrödinger Hamiltonian may very well be reproduced. A generalization beyond the nodeless states is proposed. Our illustrative examples include η-weak-pseudo-Hermiticity generators for the non-Hermitian weakly ...

We explain why the main conclusion of Bender et al, J. Phys. A 39, 1657 (2006), regarding the practical superiority of the non-Hermitian description of PT -symmetric quantum systems over their Hermitian description is not valid. Recalling the essential role played by the Hermitian description in the characterization and interpretation of the physical observables, we maintain that as far as the ...

$r$-module. in this paper, we explore more properties of $max$-injective modules and we study some conditions under which the maximal spectrum of $m$ is a $max$-spectral space for its zariski topology.

An upper bound on the minimal state complexity of codes from the Hermitian function field and some of its subfields is derived. Coordinate orderings under which the state complexity of the codes is not above the bound are specified. For the self-dual Hermitian code it is proved that the bound coincides with the minimal state complexity of the code. Finally, it is shown that Hermitian codes over...

Notions of numerical ranges and joint numerical ranges of octonion matrices are introduced. Various properties of hermitian octonion matrices related to eigenvalues and convex cones, such as the convex cone of positive semidefinite matrices, are described. As an application, convexity of joint numerical ranges of 2×2 hermitian matrices is characterized. Another application involves existence of...