The vacuum energy of a scalar field in a spherically symmetric background field is considered. It is expressed through the Jost function of the corresponding scattering problem. The renormalization is discussed in detail and performed using the uniform asymptotic expansion of the Jost function. The method is demonstrated in an simple explicit example. Pacs number(s): 11.10-z; 02.30.-f; 11.10Gh ...

The quantization of the bosonic string in a general curved space-time has been the subject of intensive research for some time [1, 2, 3, 4]. Whereas the treatment by de Vega [1] relies on the canonical quantization, only few attempts of a path integral quantization have been made. Those attempts [3, 4] involved the semi-classical approximation, but despite their conceptual simplicity no attempt...

{ We consider the bilinear nite element method on a Shishkin mesh for the singularly perturbed elliptic boundary value problem ?" 2 (@ 2 u @x 2 + @ 2 u @y 2) + a(x; y)u = f(x; y) in two space dimensions. By using a very sophisticated asymptotic expansion of Han et al. 11] and the technique we used in 17], we prove that our method achieves almost second-order uniform convergence rate in L 2-norm...

In this paper, dependent and independent variable transformations are introduced to solve a generalized sinh–Gordon equation by using the binary F-expansion method and the knowledge of elliptic equation and Jacobian elliptic functions. Many different new exact solutions such as double periodic wave and complex wave solutions are obtained. Some previous results are extended. 2013 Elsevier Inc. A...

In this paper, employed exp-function method and F-expansion method, we study the BBM(m,n) equation with generalized evolution, four families of exact solutions of exp-function type are obtained. Under different parametric conditions, every family of solution can be reduced to some solitary wave solutions and periodic wave solutions. The results presented in this paper improve the previous resul...

In this paper, a generalized variable coefficient Gardner equation is investigated. Exp-function method combined with F-expansion method are used to determine six families of exact solutions of exp-function type for this equation. Under different parametric conditions, every family of solution can be reduced to some solitary wave solutions and periodic wave solutions. The results presented in t...

A. The von Mises Expansion Before diving into the auxiliary results of Section 5, let us first derive some properties of the von Mises expansion. It is a simple calculation to verify that the Gateaux derivative is simply the functional derivative of in the event that T (F ) = R (f). Lemma 8. Let T (F ) = R (f)dμ where f = dF/dμ is the Radon-Nikodym derivative, is differentiable and let G be som...

A technique is presented for determining the roots of a polynomial p(x) that is expressed in terms of an expansion in orthogonal polynomials. The roots are expressed as the eigenvalues of a nonstandard companion matrix Bn whose coefficients depend on the recurrence formula for the orthogonal polynomials, and on the coefficients of the orthogonal expansion. Some questions on the numerical stabil...

We present new criteria for a multary (or polyadic) quasigroup to be isotopic to an iterated group operation. The criteria are consequences of a structural analysis of biased expansion graphs. We mention applications to transversal designs and generalized Dowling geometries. 1. Associativity in multary quasigroups A multary quasigroup is a set with an n-ary operation for some finite n ≥ 2, say ...