We extend graph rotation systems into a solid mathematical model for the development of an interactive-graphics cyclic-weaving system. It involves a systematic exploration and characterization of dynamic surgery operations on graph rotation systems, such as edge-insertion, edge-deletion, and edge-twisting. This talk explains the underlying mathematics and some high-level aspects of the programm...

A sophisticated adiabatic ground electronic state potential energy surface for a pure nitrogen ring !cyclic-N3) molecule is constructed based on extensive high-level ab initio calculations and accurate three-dimensional spline representation. Most of the important features of the potential energy surface are presented using various reduced dimensionality slices in internal hyperspherical coordi...

If p is prime, a compact Riemann surface X of genus g ≥ 2 is called cyclic p-gonal if it admits a cyclic group of automorphisms Cp of order p such that the quotient space X/Cp has genus 0. If in addition Cp is not normal in the full automorphism A, then we call X a non-normal p-gonal surface. In the following we classify all non-normal p-gonal surfaces. A. Wootton University of Portland 5000 No...

A closed Riemann surface X which can be realised as a p-sheeted covering of the Riemann sphere is called p-gonal, and such a covering is called a p-gonal morphism. A p-gonal Riemann surface is called real p-gonal if there is an anticonformal involution (symmetry) σ of X commuting with the p-gonal morphism. If the p-gonal morphism is a cyclic regular covering the Riemann surface is called real c...

The question of extendability of the action of a cyclic group of automorphisms of a compact Riemann surface is considered. Particular attention is paid to those cases corresponding to Singerman's list of Fuchsian groups which are not nitely-maximal, and more generally to cases involving a Fuchsian triangle group. The results provide partial answers to the question of which cyclic groups are the...

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...

Closed surfaces provide a useful model for 3-d shapes, with the data typically consisting of a cloud of points in R. The existing literature on closed surface modeling focuses on frequentist point estimation methods that join surface patches along the edges, with surface patches created via Bézier surfaces or tensor products of B-splines. However, the resulting surfaces are not smooth along the...

Solar thermal collectors represent a widely used type of system for the conversion of solar energy. In order to produce selective coatings on aluminium substrates to be used as absorber plates in high efficiency solar collectors, nickel pigmentation was applied to anodically oxidised surfaces. Electrochemical dc methods are used to study the oxidation of aluminium as functions of the following ...

finite affine groups are given by groups of translations and di-lations on finite cyclic groups. for cyclic groups of prime orderwe develop a time-scale (wavelet) analysis and show that for alarge class of non-zero window signals/vectors, the generatedfull cyclic wavelet system constitutes a frame whose canonicaldual is a cyclic wavelet frame.

There is a pressing need for new molecular tools to target protein surfaces with high affinity and specificity. Here, we describe cyclic messenger RNA display with a trillion-member covalent peptide macrocycle library. Using this library, we have designed a number of high-affinity, redox-insensitive, cyclic peptides that target the signaling protein G alpha i1. In addition to cyclization, our l...