11,778 research outputs found
The dominance hierarchy in root systems of Coxeter groups
If and are roots in the root system with respect to the standard
(Tits) geometric realization of a Coxeter group , we say that
\emph{dominates} if for all , is a negative root whenever
is a negative root. We call a positive root \emph{elementary} if it does not
dominate any positive root other than itself. The set of all elementary roots
is denoted by \E. It has been proved by B. Brink and R. B. Howlett (Math.
Ann. \textbf{296} (1993), 179--190) that \E is finite if (and only if) is
a finite-rank Coxeter group. Amongst other things, this finiteness property
enabled Brink and Howlett to establish the automaticity of all finite-rank
Coxeter groups. Later Brink has also given a complete description of the set
\E for arbitrary finite-rank Coxeter groups (J. Algebra \textbf{206} (1998)).
However the set of non-elementary positive roots has received little attention
in the literature. In this paper we answer a collection of questions concerning
the dominance behaviour between such non-elementary positive roots. In
particular, we show that for any finite-rank Coxeter group and for any
non-negative integer , the set of roots each dominating precisely other
positive roots is finite. We give upper and lower bounds for the sizes of all
such sets as well as an inductive algorithm for their computation
Relational Constraint Driven Test Case Synthesis for Web Applications
This paper proposes a relational constraint driven technique that synthesizes
test cases automatically for web applications. Using a static analysis,
servlets can be modeled as relational transducers, which manipulate backend
databases. We present a synthesis algorithm that generates a sequence of HTTP
requests for simulating a user session. The algorithm relies on backward
symbolic image computation for reaching a certain database state, given a code
coverage objective. With a slight adaptation, the technique can be used for
discovering workflow attacks on web applications.Comment: In Proceedings TAV-WEB 2010, arXiv:1009.330
Phytochemical studies on the medicinal plant Sutherlandia frutescens
Sutherlandia frutescens (L.) R. Br (Fabaceae) is a multipurpose medicinal plant with diverse biological activities, and has been widely used for the treatment of cancer, AIDS, diabetes, and infectious diseases in southern Africa. The primary goal of this study was to investigate the chemical constituents of S. frutescens and develop an analytical method to analyze this plant and the dietary supplements derived from this plant. The dissertation is composed of six chapters. Chapter 1 introduces the general background of S. frutescens, including traditional uses and chemical and biological studies on the plant. Chapter 2 describes the phytochemical studies that have led to the identification of eight new cycloartane-type triterpene glycosides, sutherlandiosides A-H, and four new flavonol glycosides, sutherlandins A-D. The structures of these compounds were established by a combination of chemical methods and extensive spectroscopic analyses and X-ray crystallography. Several cycloartane glycosides possess unique carbon skeletons. Chapter 3 describes an improved method for determination of the absolute configuration of monosaccharides, which is based on structure elucidation of sutherlandins. Chapter 4 summarizes the results of the biological activities of the isolated compounds from S. frutescens. The major compound sutherlandioside B in the plant shosome antiviral activities against EBV and Tacaribe virus. Chapter 5 presents a newly established HPLC-based analytical method for standardization of the herbal products using the isolated new compounds. Chapter 6 provides concluding remarks for the study of S. frutescens. A brief description of future studies is proposed
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