Abstract It is shown that for a given hermitian Hamiltonian possessing supersymmetry, there is always a non-hermitian Jaynes-Cummings-type Hamiltonian(JCTH) admitting entirely real spectra. The parent supersymmetric Hamiltonian and the corresponding non-hermitian JCTH are simultaneously diagonalizable. The exact eigenstates of these non-hermitian Hamiltonians are constructed algebraically for c...

we state several conditions under which comultiplication and weak comultiplication modulesare cyclic and study strong comultiplication modules and comultiplication rings. in particular,we will show that every faithful weak comultiplication module having a maximal submoduleover a reduced ring with a finite indecomposable decomposition is cyclic. also we show that if m is an strong comultiplicati...

in this paper, we show that every element of a discrete module is a sum of two units if and only if its endomorphism ring has no factor ring isomorphic to $z_{2}$. we also characterize unit sum number equal to two for the endomorphism ring of quasi-discrete modules with finite exchange property.

Let  be a commutative ring and  be a unitary  module. We define a semi prime sub module of a module and consider various properties of it. Also we define semi-radical of a sub module of a module and give a number of its properties. We define modules which satisfy the semi-radical formula and present the existence of such a module.

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...

The purpose of this paper is to lay the foundations for a quantitative theory of relations among discriminants of hermitian RG-modules which are induced by character relations. This is accomplished by introducing an invariant δ(M) attached to an RG-module M which plays the role of a correction term in such relations and to study its functorial properties such as localization and induction theor...

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.

Most learning systems applied to problem solving have the goal of learning knowledge for solving problems more eeciently. However, very few systems have focused on the acquisition of planning operator descriptions. In this paper, we present a system that learns operator deenitions from the interaction with a completely unknown environment. In order to achieve better learning convergence, severa...