Purely affine elementary su(N) fusions

We consider three-point couplings in simple Lie algebras -- singlets in triple tensor products of their integrable highest weight representations. A coupling can be expressed as a linear combination of products of finitely many elementary couplings. This carries over to affine fusion, the fusion of Wess-Zumino-Witten conformal field theories, where the expressions are in terms of elementary fusions. In the case of su(4) it has been observed that there is a purely affine elementary fusion, i.e., an elementary fusion that is not an elementary coupling. In this note we show by construction that there is at least one purely affine elementary fusion associated to every su(N>3).Comment: 9 pages, LaTe

Fusion multiplicities as polytope volumes: N-point and higher-genus su(2) fusion

We present the first polytope volume formulas for the multiplicities of affine fusion, the fusion in Wess-Zumino-Witten conformal field theories, for example. Thus, we characterise fusion multiplicities as discretised volumes of certain convex polytopes, and write them explicitly as multiple sums measuring those volumes. We focus on su(2), but discuss higher-point (N>3) and higher-genus fusion in a general way. The method follows that of our previous work on tensor product multiplicities, and so is based on the concepts of generalised Berenstein-Zelevinsky diagrams, and virtual couplings. As a by-product, we also determine necessary and sufficient conditions for non-vanishing higher-point fusion multiplicities. In the limit of large level, these inequalities reduce to very simple non-vanishing conditions for the corresponding tensor product multiplicities. Finally, we find the minimum level at which the higher-point fusion and tensor product multiplicities coincide.Comment: 14 pages, LaTeX, version to be publishe

Relationship between use of ankle-foot orthoses and quality of life and psychological well being : a research plan

An ankle-foot orthosis (AFO) is an externally applied device that encompasses the joints of the ankle and foot, used to modify the structural and functional characteristics of the neuromuscular and skeletal systems(ISO,1989,a&b). AFOs are prescribed for people who have a loss of function affecting their mobility, experienced in wide range of conditions such as stroke, poliomyelitis, cerebral palsy, spina bifida and osteoarthritis

Bringing the World to UD

This presentation focuses on Mark Rasmussen’s work with the organization Engineers in Technical Humanitarian Opportunities of Service-Learning (ETHOS). The slides show his trips to Ireland and Ghana

A multimedia website for the Battle of Gettysburg

This thesis explains the development of a website for eighth graders about the Battle of Gettysburg. One purpose of the project is to provide several primary source documents, pictures, video from a reenactment of the Battle of Gettysburg, clips from movies about the Civil War, and other material that suppport the students in their learning. The second purpose is to fulffill standard 8.10 of History-Social Science Content Standards for eight grade. This project will help students fulfill this requirement

The acute effects of transdermal testosterone precursor administration on serum steroid hormone levels in females

Most governing sports authorities have banned the use of anabolic steroids as ergogenic aids. Recently, a transdermal testosterone precursor dietary supplement (AndrosteDERMRTM) has become available; athletes can apply the cream to their skin with the belief that it will increase serum testosterone levels, muscle mass, and strength. The purpose of this study was to measure the effects of one milliliter of AndrosteDERMRTM) applied to the inner surface of the upper arm on the serum levels of androstenedione, and free and total testosterone in female subjects. Serum levels were measured before application and every 45 minutes thereafter for six hours. Serum androstenedione, and free and total testosterone levels were analyzed using radioimmunoassay. Although the trend seemed to indicate that serum levels did not rise after application, several subjects had physiologically impossible values, which appear to be due to methodological errors. That information, along with the initial small number of subjects made the use of statistical treatment unwise and inferences about the population impossible

On the level-dependence of Wess-Zumino-Witten three-point functions

Three-point functions of Wess-Zumino-Witten models are investigated. In particular, we study the level-dependence of three-point functions in the models based on algebras $su(3)$ and $su(4)$. We find a correspondence with Berenstein-Zelevinsky triangles. Using previous work connecting those triangles to the fusion multiplicities, and the Gepner-Witten depth rule, we explain how to construct the full three-point functions. We show how their level-dependence is similar to that of the related fusion multiplicity. For example, the concept of threshold level plays a prominent role, as it does for fusion.Comment: 24 pages, no figure