Exact semi-separation of variables in waveguides with non-planar boundaries

Counting non planar diagrams: an exact formula

We present an explicit solution of a simply stated, yet unsolved, combinatorial problem, of interest both in quantum field theory (Feynman diagrams enumeration, beyond the planar approximation) and in statistical mechanics (high temperature loop expansion of some frustrated lattice spin model). PACS: 02.10.Eb, 02.10.Nj, 05.50.+q ∗e-mail: [email protected] The problem of counting the number of r...

Thin Film Lasers Integrated with Planar Waveguides

Analysis of thick, non-planar boundaries using the discontinuity analyser

The advent of missions comprised of phased arrays of spacecraft, with separation distances ranging down to at least mesoscales, provides the scienti®c community with an opportunity to accurately analyse the spatial and temporal dependencies of structures in space plasmas. Exploitation of the multi-point data sets, giving vastly more information than in previous missions, thereby allows unique s...

An application of geometrical isometries in non-planar molecules

In this paper we introduce a novel methodology to transmit the origin to the center of a polygon in a molecule structure such that the special axis be perpendicular to the plane containing the polygon. The mathematical calculation are described completely and the algorithm will be showed as a computer program.

Bijections for Planar Maps with Boundaries

We present bijections for planar maps with boundaries. In particular, we obtain bijections for triangulations and quadrangulations of the sphere with boundaries of prescribed lengths. For triangulations we recover the beautiful factorized formula obtained by Krikun using a (technically involved) generating function approach. The analogous formula for quadrangulations is new. We also obtain a fa...