This article contains a short summary of an oral presentation in the 2nd International Workshop on “Pseudo-Hermitian Hamiltonians in Quantum Physics” (14.-16.6.2004, Villa Lanna, Prague, Czech Republic). The purpose of the presentation has been to introduce a non-Hermitian generalization of pseudo-Hermitian Quantum Theory (QT) allowing to reconcile the orthogonal concepts of causality, Poincaré...

We investigate one-point algebraic geometric codes CL(D, G) associated to maximal curves recently characterized by Tafazolian and Torres given by the affine equation yl = f(x), where f(x) is a separable polynomial of degree r relatively prime to l. We mainly focus on the curve y4 = x3 +x and Picard curves given by the equations y3 = x4-x and y3 = x4 -1. As a result, we obtain exact value of min...

In this work we study the convergence properties of one-level parallel Schwarz method with Robin transmission conditions applied to one-dimensional and two-dimensional Helmholtz Maxwell's equations. One-level methods are not scalable in general. However, it has recently been proven that when impedance used case algorithm being equations absorption, then, under certain assumptions, scalability c...

Let J be a unitary almost complex structure on a Riemannian manifold (M, g). If x is a unit tangent vector, let π := Span{x, Jx} be the associated complex line in the tangent bundle of M . The complex Jacobi operator and the complex curvature operators are defined, respectively, by J (π) := J (x) + J (Jx) and R(π) := R(x, Jx). We show that if (M, g) is Hermitian or if (M,g) is nearly Kähler, th...

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...

Exact solvability of some non-Hermitian η-pseudo-Hermitian Hamiltonians is explored as a byproduct of η-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-pseudo-Hermiticity ”quasi-generator” to obtain quasiexactly solvable η-pseudo-Hermitian Hamiltonian models. PACS numbers: 03.65.Ge, 03.65.Fd,03.65.Ca

We call a positive definite Hermitian lattice regular if it represents all integers, which can be represented locally by the lattice. We investigate binary regular Hermitian lattices over imaginary quadratic fields Q( √ −m) and provide a complete list of the (normal) binary regular Hermitian lattices.

We consider light pulses in a circular array of $2N$ coupled nonlinear optical waveguides. The waveguides are either Hermitian or alternate gain and loss $\mathcal{PT}$-symmetric fashion. Simple patterns the include ring traveling abreast breather---a string where all even odd flash turn. In addition, structure displays solitons gyrating around necklace by switching from one waveguide to next. ...

We study complex potentials and related non-diagonalizable Hamiltonians with special emphasis on formal definitions of associated functions and Jordan cells. The non-linear SUSY for complex potentials is considered and the theorems characterizing its structure are presented. We define the class of complex potentials invariant under SUSY transformations for (non-)diagonalizable Hamiltonians and ...