The purpose of this paper is to extend to monoids the work of Björner, Wachs and Proctor on the shellability of the Bruhat-Chevalley order on Weyl groups. Let M be a reductive monoid with unit group G, Borel subgroup B and Weyl group W . We study the partially ordered set of B×Borbits (with respect to Zariski closure inclusion) within a G × G-orbit of M . This is the same as studying a W ×W -or...

we consider the semigroup $s$ of highest weights appearing in tensor powers $v^{otimes k}$ of a finite dimensional representation $v$ of a connected reductive group. we describe the cone generated by $s$ as the cone over the weight polytope of $v$ intersected with the positive weyl chamber. from this we get a description for the asymptotic of the number of highest weights appearing in $v^{otime...

This paper examines the effect of five major pretreatments on the surface coverage Γ(m) of dodecanethiol self-assembled monolayer on polycrystalline gold electrode (C(12)SH-SAMs-Au). It is based on the electrochemical reductive desorption in the alkaline solution by cyclic voltammetry (CV). The five different pretreatment methods include: aqua regia pretreatment, reductive annealed pretreatment...

“In this remarkable book, David Easley and Jon Kleinberg bring all the tools of computer science, economics, and sociology to bear on one of the great scientific challenges of our time: understanding the structure, function, and dynamics of networks in society. Clearly written and covering an impressive range of topics, “Networks, Crowds, and Markets” is the ideal starting point for any student...

Supervenience physicalism attempts to combine non-reductionism about properties with a physical determination thesis in such a way as to ensure physicalism. I argue that this attempt is unsuccessful: the specific supervenience relation in question is either strong enough to ensure reductionism, as in the case of strong supervenience, or too weak to yield physical determination, as in the case o...

These are lecture notes that Tony Feng live-TEXed from a course given by Brian Conrad at Stanford in“winter” 2015, which Feng and Conrad edited afterwards. Two substitute lectures were delivered (by Akshay Venkatesh and Zhiwei Yun) when Conrad was out of town. This is a sequel to a previous course on the general structure of linear algebraic groups; some loose ends from that course (e.g., Cheva...

Æ-Keto acids can be reductively aminated to Æ-amino acids via amino acid dehydrogenase catalysis, with NAD(P)H as cofactor. The nitrogen source for the amine functionality is ammonia, the least expensive source. Regeneration of the co-factor NAD(P)+ back to NAD(P)H is required for synthesis and is commonly afforded via formate dehydrogenase catalyzed oxidation of formate to carbon dioxide or gl...

Let G be a reductive algebraic group and H be a connected semisimple subgroup of G. The dimension data consists of the collection { dimV H } with V H denoting the space of points in V fixed by H , and where (ρ, V ) runs through all representations of G. One may ask if the dimension data determine H up to conjugacy or at least isomorphism. In other words, If H and H ′ have the same dimension dat...

— We develop the relative theory of reductive group schemes, using dynamic techniques and algebraic spaces to streamline the original de-