A general formalism is derived for analytically representing the scattering properties of ultracold atoms subject to one or more resonant photoassociation lasers. The resulting formulas cleanly separate laser intensities and detunings from overlap integrals of molecular wave functions. As a consequence, laser-induced energy shifts and line broadenings are given in an explicit form. In the case ...

We report a new ab initio study of the acetylene T3 potential energy surface, which clarifies the nature of its energy minimum, and present computed equilibrium geometries and diabatic frequencies. This information enables the computation of harmonic vibrational overlap integrals of T3 vibrational levels with the S1 3nu3 state. The results of this calculation support the interpretation of two l...

We consider ways to quantify the overlap of the parts of phase space important to two systems, labeled A and B. Of interest is how much of the A-important phase space lies in that important to B, and how much of B lies in A. Two measures are proposed. The first considers four total-energy distributions, formed from all combinations made by tabulating either the A-system or the B-system energy w...

‎In this paper‎, ‎we find a relation between the proportionality factors which arise from the functional equations of two families of local Rankin-Selberg convolutions for‎ ‎irreducible admissible representations of orthogonal groups‎, ‎or unitary groups‎. ‎One family is that of local integrals of the doubling method‎, ‎and the other family is‎ ‎that of local integrals expressed in terms of sph...

The optical multimode interconnection technology has become important due to increasing data rates in modern multi-processor systems. In this context, the coupling of optical waves into multimode waveguides has to be analyzed. Ray optical methods are preferred, but are not applicable for all geometries. As full-wave analysis using the mode matching technique is very extensive, we present a simp...

The generalized fuzzy valued $theta$-Choquet integrals will beestablished for the given $mu$-integrable fuzzy valued functionson a general fuzzy measure space, and the convergence theorems ofthis kind of fuzzy valued integral are being discussed.Furthermore, the whole of integrals is regarded as a fuzzy valuedset function on measurable space, the double-null asymptoticadditivity and pseudo-doub...

Ordinary differential equations(ODEs) with stochastic processes in their vector field, have lots of applications in science and engineering. The main purpose of this article is to investigate the numerical methods for ODEs with Wiener and Compound Poisson processes in more than one dimension. Ordinary differential equations with Ito diffusion which is a solution of an Ito stochastic differentia...