The aim of this work is to investigate the role played by the fermion mass and that of an external field on the fermionic Casimir energy density under S1×R3 topology. Both twisted and untwisted spin connections are considered and the exact calculation is performed using a somewhat different approach based on the combination of the analytic regularization method through αrepresentation and the E...

A generalisation of the Faulhaber polynomials and Bernoulli numbers related to elliptic curves is introduced and investigated. This is applied to compute the density of states for the classical Lamé operators.

Euler Maclaurin formulas for a polytope express the sum of the values of a function over the lattice points in the polytope in terms of integrals of the function and its derivatives over faces of the polytope or its dilations. There are two kinds of Euler Maclaurin formulas: exact formulas, which apply to exponential or polynomial functions, and formulas with remainder, which apply to arbitrary...

There is a natural relationship to the post-Newtonian expansion scheme that is used to describe sources of gravity which are not too far from Newtonian, i.e, not too relativistic. Here the expantion can lead to the solutions for the exterior fields of such sources. Till now the post-Newtonian expansion known to high order, in some cases 8 th order. This paper has provided a high order expansion...

We give a formula for the Sn-equivariant Euler characteristics of the moduli spaces Mg,n of genus g curves with n marked points.

We observe that the classical Faulhaber’s theorem on sums of odd powers also holds for an arbitrary arithmetic progression, namely, the odd power sums of any arithmetic progression a+b, a+2b, . . . , a+nb is a polynomial in na+ n(n + 1)b/2. While this assertion can be deduced from the original Fauhalber’s theorem, we give an alternative formula in terms of the Bernoulli polynomials. Moreover, b...

A generalisation of the Faulhaber polynomials and Bernoulli numbers related to elliptic curves is introduced and investigated. This is applied to compute the density of states for the classical Lamé operators.

We have obtained the correct expression for the centrifugal force acting on a particle at the equatorial circumference of a rotating body in the locally non-rotating frame of the Kerr geometry. Using this expression for the equilibrium of an element on the surface of a slowly rotating Maclaurin spheroid, we obtain the expression for the ellipticity (as discussed earlier by Abramowicz and Miller...

In [14] Ozden-Simsek-Cangul constructed generating functions of higher-order twisted (h, q)-extension of Euler polynomials and numbers, by using p-adic q-deformed fermionic integral on Zp. By applying their generating functions, they derived the complete sums of products of the twisted (h, q)-extension of Euler polynomials and numbers, see[13, 14]. In this paper we cosider the new q-extension o...

Given a finite simplicial complex L and a collection of pairs of spaces indexed by the vertices of L , one can define the “polyhedral product” of the collection with respect to L . We record a simple formula for its Euler characteristic. In special cases the formula simplifies further to one involving the h-polynomial of L .