The electronic absorption spectral line shape of a diatomic molecule with harmonic potential curves is calculated using the time correlation function formalism. Both the equilibrium shift and the frequency shift of the two linking electronic states ate taken into account. The spectrum is also calculated using the cumulated expansion which is related to the correlation function of the time-d...

We present extinction curves derived from the broad emission lines and continua of samples of 72 radio-loud and 1018 radio-quiet active galactic nuclei (AGNs). The curves are significantly flatter in the UV than curves for the local interstellar medium. The reddening curves for the radio-quiet Large Bright Quasar Survey quasars are slightly steeper than those of the radio-loud quasars in the UV...

A piecewise quintic G spline surface interpolating the vertices of a triangular surface mesh of arbitrary topological type is presented. The surface has an explicit triangular B ezier representation, is a ne invariant and has local support. The twist compatibility problem which arises when joining an even number of polynomial patches G continuously around a common vertex is solved by constructi...

Shape analysis methods have in the past few years become very popular, both for theoretical exploration as well as from an application point of view. Originally developed for planar curves, these methods have been expanded to higher dimensional curves, surfaces, activities, character motions and many other objects. In this paper, we develop a framework for shape analysis of curves in Lie groups...

A piecewise quintic G1 spline surface interpolating the vertices of a triangular surface mesh of arbitrary topological type is presented. The surface has an explicit triangular Bézier representation, is affine invariant and has local support. The twist compatibility problem which arises when joining an even number of polynomial patches G1 continuously around a common vertex is solved by constru...

This paper presents a brief overview and focuses on two key aspects of a technology for representing and recognizing complicated 2D and 3D shapes subject to partial occlusion and missing data, based on implicit polynomials. The two key aspects are new concepts and results for fast, robust, repeatable tting of implicit poly-nomials to data, and new approaches to representing and recognizing comp...

Partial stage and complete life-cycle growth curves of Brahman cattle were obtained for small, medium, and large frame sizes for a herd under grazing conditions in a subtropical environment. Data were grouped into three stages: birth to weaning (stage 1), weaning to 20 mo (males) or 32 mo (females) of age (stage 2), and 32 mo of age to maturity (females only; stage 3). Within each stage, multip...

In this paper, we give a ‘direct’ construction of the endomorphism ring of supersingular elliptic curves over a prime field Fp from ‘ideal classes’ of Q( √−p). We use the result to prove that the result of Kaneko on ‘minimal’ CM liftings of such supersingular elliptic curves is a best possible result. We also prove that the result of Elkies on ‘minimal’ CM liftings of all supersingular elliptic...

in this research work, the parameters affecting the settling velocity within the thickeners were studied by introducing an equivalent shape factor. several thickener feed samples of different densities including copper, lead and zinc, and coal were prepared. the settling tests were performed on the samples, and the corresponding settling curves were plotted. using the linear regression analysis...

We present an algorithm to approximate the variable radius ooset curves by cubic B ezier curves. The ooset curve is approximated by a cubic B ezier curve which interpolates the positions and derivatives of the exact ooset curve at both end points. Thus, it approximates the exact ooset curve very closely near the curve end points, but not necessarily in the middle of the curve. Given a xed base ...