A one-to-one correspondence is proved between the N -rooted ribbon graphs, or maps, with e edges and the (e−N + 1)-loop Feynman diagrams of a certain quantum field theory. This result is used to obtain explicit expressions and relations for the generating functions of N -rooted maps and for the numbers of N -rooted maps with a given number of edges using the path integral approach applied to th...

OBJECTIVES We sought to gain more insight into the arrhythmogenic etiology of idiopathic ventricular fibrillation (VF) by assessing ventricular depolarization and repolarization properties by means of various electrocardiographic (ECG) techniques. BACKGROUND Idiopathic VF occurs in the absence of demonstrable structural heart disease. Abnormalities in ventricular depolarization or repolarizat...

We demonstrate the direct reconstruction of 3D atomic images from measured low-energy electron diffraction (LEED) intensity spectra. A multiple-incident angle and multiple-energy integral are first applied to the spectra to obtain a map of interatomic vectors. From this map, a nonbulk interatomic vector is chosen that points to a desired reference atom. A second integral transformation, using t...

This paper presents a boundary integral equation method for computing numerical conformal mapping of bounded multiply connected region onto an annulus with spiral slits region and its inverse. The method is an extension of the author’s method for computing the Annulus with circular slits map of bounded multiply connected regions (see [Sangawi, A. W. K., Murid, A. H. M., Nasser, M. M. S.: Annulu...

We analyze the spectrum of a certain singular integral operator on the space (L2(fi))3 where fi is contained in three dimensional Euclidean space and has a Lipschitz continuous boundary. This operator arises in the integral formulation of the magnetostatic field problem. We decompose (L2(fi))3 into invariant subspaces: in one where the operator is the zero map; in one, the identity map; and in ...

One of the most recent solved problem of the theory of hamiltonian dynamical systems with two degrees of freedom is finishing a proof of the exponentially small transversality of the separatrices for the standard map ([1], [2], [3], [4]). The central point if the proof is a construction of an analytic integral along the unstable separatrix. Only the article [4] contains the complete evidence of...

In this paper, using Waldhausen’s standard degree 1-maps between handlebodies, we show that the Casson invariant of oriented integral homology 3-spheres is a homotopy invariant. This provides a map from homotopy classes of oriented integral homology 3-spheres to the integers. It also gives an obstruction to finding orientationreversing self homotopy equivalences of such 3-manifolds.

Conventional integral equation methods for diffraction gratings require lattice sum techniques to evaluate quasi-periodic Green's functions. The boundary integral equation Neumann-to-Dirichlet map (BIE-NtD) method in Wu and Lu [J. Opt. Soc. Am. A 26, 2444 (2009)], [J. Opt. Soc. Am. A 28, 1191 (2011)] is a recently developed integral equation method that avoids the quasi-periodic Green's functio...