In this paper we sum over the spherical modes appearing in the expression for the Casimir energy of a conducting sphere and of a dielectric ball (assuming the same speed of light inside and outside), before doing the frequency integration. We derive closed integral expressions that allow the calculations to be done to all orders, without the use of regularization procedures. The technique of mo...

In this paper we discuss some topics that came up in Chapters 2 and 3 of Part III of [8]. These involve relations between derivatives of Cauchy integrals on curves and surfaces and curvatures of the curves and surfaces. In R for n > 2, “Cauchy integrals” can be based on generalizations of complex analysis using quarternions or Clifford algebras (as in [3]). Part of the point here is to bring ou...

We demonstrate how the complex integral formula for the Airy functions arises from Penrose’s twistor contour integral formula. We then use the Lax formulation of the isomonodromy problem with one irregular singularity of order four to show that the Airy equation arises from the anti-self-duality equations for conformal structures of neutral signature invariant under the isometric action of the ...

This paper is the second of a two-part series assessing the feasibility of using the J-integral with full-field deformation data from Digital Image Correlation (DIC) to characterize toughness in continuous fiber, SiCf/SiCc ceramic matrix composites (CMCs). In Part I, line and area integral adaptations of the J-integral were validated with analytical and experimental deformation fields. It was f...

We study the holomorphic properties of the MQCD by comparing the superpotentials in MQCD and the gauge theory. First we show that the superpotential defined as an integral of three form is NOT appropriate for generic situation with quarks. We report a resolution of the problem which works for the brane configurations of 90 degree rotation, including the true SQCD. The new definition does not ne...

This paper is concerned with solving large-scale eigenvalue problems by algebraic sub-structuring and contour integral. We combine Algebraic Sub-structuring (AS) method and the Contour Integral Rayleigh-Ritz (CIRR) method. The AS method calculates approximate eigenpairs fast and has been shown to be efficient for vibration and acoustic analysis. However, the application areas of this method hav...

A fully numerical method to calculate loop integrals, a numerical contour-integration method, is proposed. Loop integrals can be interpreted as a contour integral in a complex plane for an integrand with multi-poles in the plane. Stable and efficient numerical integrations an along appropriate contour can be performed for tensor integrals as well as for scalar ones appearing in loop calculation...

C cosh(zs) (sin z − sin x)n+1 dz, y = sinn+1 x ∮ C cosh(zs) (cos z − cos x)n+1 dz, s2 = −λ, and their associated second-order ordinary differential equationswhich are not studied are given. Complete solution is given by calculating residues for n = 1. The eigenvalues and eigenfunctions along with certain boundary conditions are explored for the first contour integral. The contour integral y(x) ...

The next-next-to-leading order QCD corrections to the e+e− annihilation into hadrons are considered. The stability of the predictions with respect to change of the renormalization scheme is discussed in detail for the case of five, four and three active quark flavors. The analysis is based on the recently proposed condition for selecting renormalization schemes according to the degree of cancel...

We present a fast contour-integral eigensolver for finding selected or all the eigenpairs of a non-Hermitian matrix based on a series of analytical and computational techniques, such as the analysis of filter functions, quick and reliable eigenvalue count via low-accuracy matrix approximations, and fast shifted factorization update. The quality of some quadrature rules for approximating a relev...