We assume that each valence quark in a nucleon is in a phenomenological modified harmonic oscillator potential of the form: ( l+yo) (ar +br+cr +dr ), where a, b, c and d are constants and ? is one of the Dirac matrices. Then by making use of a suitable ansatz, the Dirac equation has a very simple solution which is exact. We then have calculated the static properties of the nucleon in the ...

We present the exact solution of the Osp(1|2) invariant magnet by the Bethe ansatz approach. The associated Bethe ansatz equation exhibit a new feature by presenting an explicit and distinct phase behaviour in even and odd sectors of the theory. The ground state, the low-lying excitations and the critical properties are discussed by exploiting the Bethe ansatz solution.

This paper is the rst of a series of two, where we study the asymp-totics of the displacement in a thin clamped plate made of a rigid \monoclinic" material , as the thickness of the plate tends to 0. The combination of a polynomial Ansatz (outer expansion) and of a boundary layer Ansatz (inner expansion) yields a complete multi-scale asymptotics of the displacement and leads to optimal error es...

Abstract The Finite Cell Method (FCM) allows for an efficient and accurate simulation of complex geometries by utilizing unfitted discretization based on rectangular elements equipped with higher-order shape functions. Since the mesh is not aligned to geometric features, cut arise that are intersected domain boundaries or internal material interfaces. Hence, multi-material problems, several cha...

We consider level crossing in the background of the sphaleron barrier for nondegenerate fermions. The mass splitting within the fermion doublets allows only for an axially symmetric ansatz for the fermion fields. In the background of the sphaleron we solve the partial differential equations for the fermion functions. We find little angular dependence for our choice of ansatz. We therefore propo...

The large-system performance of maximum-a-posterior estimation is studied considering a general distortion function when the observation vector is received through a linear system with additive white Gaussian noise. The analysis considers the system matrix to be chosen from a large class of random ensembles. We take a statistical mechanical approach by introducing a spin glass corresponding to ...

The purpose of this paper is to test the applicability of a fast boundary element method in the context of geoid computations of the gravity. The fast multipole method is the method of choice due to the its advantageous property of a fast evaluation in the post-processing. Several sets of trianglar meshes for the approximation of the unit sphere and several modifications of the prediscribed dat...

Bei der Funktionsmodellierung ist die Veränderung und Erweiterung der Struktur eines Modells eine häufig durchgeführte Aktivität. Während es bereits Refactoring-Ansätze für textuelle Programmiersprachen wie Java, C# usw. gibt, fehlt ein vergleichbarer, integraler und durchgehender Ansatz für Simulink-Modelle. Wir haben einen automatisierten Refactoring-Ansatz (im Folgenden SLRefactor-Ansatz gen...

Many problems concerning lattice paths, especially on the square lattice have been accurately solved. For a single path, many methods exist that allow exact calculation regardless of whether the path inhabits a strip, a semi-infinite space or infinite space, or perhaps interacts with the walls themselves. It has been shown that a transfer matrix method using the Bethe Ansatz allows for the calc...