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Volumen 9, Ausgabe 1 (2018)

Forschungsartikel

Factorial Unitary Representations of Compact Lie Groups, Wigner Sets and Locally Invariant Quantum Fields

Moffat J and Wang C

The fibre bundle construct defined in our previous work continues to be the context for this paper; quantum fields composed of fibre algebras become liftings of; or sections through; a fibre bundle with base space a subset of curved space-time. We consider a compact Lie group such as SU(n) acting as a local gauge group of automorphisms of each fibre algebra A(x). Compact Lie groups, represented as gauge groups acting locally on quantum fields, are key elements in electroweak and strong force unification. In our recent joint work we have focused on the translational subgroup of the Poincare group as the generator of local diffeomorphism invariant quantum states. Here we extend those algebraic non-perturbative approaches to address the other half of unification by considering the existence of quantum states of the fibre algebra A(x) invariant to the action of compact non-abelian Lie groups. Wigner sets are complementary to little groups and we prove they have the finite intersection property. Exploiting this then allows us to show that invariant states are common in the sense that the weakly closed convex hull of every normal (density matrix) state contains such an invariant state. From these results and our related research emerges the existence of a locally invariant density matrix quantum state of the field.

Forschungsartikel

The Homotopy Analysis Method for a Fourth-Order Initial Value Problems

Massoun Y and Benzine R

In this paper, we apply the homotopy analysis method for solving the fourth-order initial value problems by reformulating them as an equivalent system of first-order differential equations. The analytical results of the differential equations have been obtained in terms of convergent series with easily computable components. Several examples are given to illustrate the efficiency and implementation of the homotopy analysis method.

Forschungsartikel

New Exact Solutions for the Maccari System

Abdelrahman MAE and Hassan SZ

In this article we apply three mathematical methods for solving the Maccari system, namely, the exp(-ϕ(ξ))- expansion method, the sine-cosine approach and the Riccati-Bernoulli sub-ODE method. These methods are used to construct new and general exact periodic and soliton solutions of the Maccari system. This nonlinear system can be turned into another nonlinear ordinary differential equation by suitable transformation. It is shown that the exp(-ϕ(ξ))-expansion method, the sine-cosine method and the Riccati-Bernoulli sub-ODE method provide a powerful mathematical tool for solving a great many systems of nonlinear partial differential equations in mathematical physics.

Kurze Kommunikation

Relations of Infinite Spaces in Full Voids and Constitution of Total Energies and Their Effect on Matter

Daris M

The work and specifically this project to make a simple argument to show there is something else behind the light is its new speed input has it Energy and bring out a new relationship of light and that this new relationship will Change all the old settings that exists and has a ratio of approach need for the community Because the community is always looking for the science and new relationship and our project will improve the approach by providing the needs of the community and ca has a consequence Positive total return and hence global performance level Physical and especially in the Field of the speed of light everybody knowing Search the reality around any relationships exist and settings that are either hardware Equipment or not and our effort is based on the hardware side for a light and Calculation that will give us the truth that is behind the light and there is something else that Are hidden that the experience will give us. All that man will find it or go get it is found in our brain just Point the finger on the right path to find the result.

Forschungsartikel

Bound State Solutions of the Klein-Gordon Equation for the More General Exponential Screened Coulomb Potential Plus Yukawa (MGESCY) Potential Using Nikiforov-Uvarov Method

Hitler L, Iserom IB, Tchoua P and Ettah AA

There has been a growing interest in investigating the approximate solutions of the Klein-Gordon equation and relativistic wave equations for some physical potential models. This is due to the fact that the analytical solutions contain all the necessary information for the quantum system under consideration. In this paper, we obtained the solutions of the Klein-Gordon equation with more general exponential screened coulomb (MGESC), Yukawa potential (YP) and the sum of the mixed potential (MGESCY) using the Parametric Nikiforov-Uvarov Method (PNUM). The bound state energy eigenvalues and the corresponding un-normalized eigenfunctions expressed in terms of hypergeometric functions are obtained.

Forschungsartikel

Fractional and High Order Asymptotic Results of the MFPT

Bar-Haim A

This work discusses the Mean First Passage Time (MFPT) and Mean Residence Time (MRT) of continuous-time nearest-neighbor random walks in a finite one-dimensional system with a trap at the origin and a reflecting barrier at the other end. The asymptotic results of the MFPT for random walks that start, for example, at the reflecting point, have a variety of dependencies with respect to its size N. For example, for the case of birth and death processes the MFPT~N; for the case of symmetric random walks the MFPT~N2 and for the case of biased random walks the MFPT~αN where α is a constant that depends on the system’s rates. In this work a transition matrix is derived in such a way that the MRT of the system is equal to (m+1)d where m is the site number, and d is any arbitrary number satisfying the condition d>0. Since the MFPT is the sum of MRTs then the corresponding MFPT for such a transition matrix is MFPT~N(1+d). Thus, one can determine the asymptotic result of the MFPT to be N1+d for any arbitrary d>0, and based on it, obtain the corresponding transition matrix. Several examples of fractional and high order asymptotic results of the MFPT such as N3.5, N5, N6, are presented.

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