Casimir Energy of the Laplacian on a Riemannian Manifold| Chapter 6 | Research Highlights in Mathematics and Computer Science Vol. 4

 Special principles of spectral zeta function on Riemannian repeat have been computed utilizing various mathematical approximation schemes. The acts of some of those principles are of fundamental importance in quantity field theory. A particular profit of interest in this member is the Casimir energy delimited, mathematically, via the spectral zeta function as a function on the set of versification on the manifold by (−12) [1,2] and [3]. In this unit, a general arrangement for computing the Casimir strength of the Laplacian on the unit n-spatial sphere, Sn by present image of the spectral zeta function through the Riemann zeta function is addressed. The ghostly zeta function of the Laplacian can be computed utilizing this method on a sort of different Riemannian repeat.

Author(s) Details:

Louis Omenyi,
Department of Mathematics and Statistics, Alex Ekwueme Federal University, Ndufu-Alike, Nigeria.

Please see the link here: https://stm.bookpi.org/RHMCS-V4/article/view/9160

Casimir Energy of the Laplacian on a Riemannian Manifold| Chapter 6 | Research Highlights in Mathematics and Computer Science Vol. 4

 In this affiliate, we analyze the Magic Polygons of order 3 (P(n, 2)) and present sure properties that were advantageous in the implementation of an invention to determine the number of magic polygons for balanced polygons up to 24 hands. First, is made an similarity between Magic Polygons and pieces of the Symmetric Group, such similarity is clear once the Magic Polygons is a fixed arrangement of numbers. Made aforementioned equivalence, it's incidental that in order to find all Magic Polygons for a regular shape of n sides, it's enough to produce all permutations of the set {1,2. . . 2n+1} and verify that ones answer the definition. But this is not high-quality way, cause the same change would be restored many times, due the action of the Dihedral Group in the formal polygon. Therefore, a analytical approach is needed in consideration of simplify the computational process. This habit, we reach the concept of Equivalents Magic Polygons, and located in some features here began, we avoid few of them. Yet, is introduced the idea of Derivatives Magic Polygons because a Magic Polygon maybe built from some Arithmetic Progression, and is not restricted to the open sequence.

Author(s) Details:

Louis Omenyi,
Department of Mathematics and Statistics, Alex Ekwueme Federal University, Ndufu-Alike, Nigeria.

Please see the link here: https://stm.bookpi.org/RHMCS-V4/article/view/9160