There are several kinds of hyperrings, for example, Krasnerhyperrings, multiplicative hyperring, general hyperrings and$H_v$-rings. In a multiplicative hyperring, the multiplication isa hyperoperation, while the addition is a binary operation. In this paper, the notion of derivation on multiplicative hyperrings is introduced and some related properties are investigated. {bf Keywords:} multiplic...

In this supplemental article, we introduce some useful results in spectral theory and perturbation theory. Some of the results are well-established. We briefly review them for the purpose of easy reference. For example, the results for eigenvalues have become quite standard for decades (see, e.g. Dunford and Schwartz, 1988, Chapter VII.6). We derive a bound for the perturbation of eigenprojecti...

The pseudo-perturbative shifted l expansion technique PSLET is shown applicable in the non-Hermitian PT symmetric context. The construction of bound states for several PT symmetric potentials is presented, with special attention paid to V (r) = ir3 − α √ ir oscillators.

We point out that an unorthodox way to describe the production of rapid-ity gaps in deep inelastic scattering, recently proposed by Buchm uller and Hebecker, suggests a description of the production of heavy quark bound states which is in agreement with data. The approach questions the conventional treatment of the color quantum number in perturbative QCD.

We exploit theoretical results on the meson spectrum within the framework of a Bethe-Salpeter (BS) formalism adjusted for QCD, in order to extract an “experimental” coupling α s (Q) below 1 GeV by comparison with the data. The relativistic BS potential follows from a proper ansatz on the Wilson loop to encode confinement. The experimental points α s (Q) exhibit a reasonable agreement with the i...

We address the question of whether atomic bound states begin to stabilize in the short ultra-intense field limit. We provide a general theory of ionization probability and investigate its gauge invariance. For a wide range of potentials we find an upper and lower bound by non-perturbative methods, which clearly exclude the possibility that the ultra intense field might have a stabilizing effect...

In this note, we numerically investigate a stochastic nonlinear Schrödinger equation derived as a perturbation of the deterministic NLS equation. The classical NLS equation with focusing nonlinearity of power law type is perturbed by a random term ; it is a strong perturbation since we consider a space-time white noise. It acts either as a forcing term (additive noise) or as a potential (multip...

We study the part of the renormalized, cutoff QED light-front Hamiltonian that does not change particle number. The Hamiltonian contains interactions that must be treated in second-order bound state perturbation theory to obtain hyperfine structure. We show that a simple unitary transformation leads directly to the familiar Breit-Fermi spin-spin and tensor interactions, which can be treated in ...