Elementary abelian p-subgroups of algebraic groups

Let be an algebraically closed field and let G be a finite-dimensional algebraic group over which is nearly simple, i.e. the connected component of the identity G ⁰ is perfect, C _G(G ⁰)=Z(G ⁰) and G ⁰/Z(G ⁰) is simple. We classify maximal elementary abelian p-subgroups of G which consist of semisimple elements, i.e. for all primes p char .Call a group quasisimple if it is perfect and is simple modulo the center. Call a subset of an algebraic group toral if it is in a torus; otherwise nontoral. For several quasisimple algebraic groups and p=2, we define complexity, and give local criteria for whether an elementary abelian 2-subgroup of G is toral.For all primes, we analyze the nontoral examples, include a classification of all the maximal elementary abelian p-groups, many of the nonmaximal ones, discuss their normalizers and fusion (i.e. how conjugacy classes of the ambient algebraic group meet the subgroup). For some cases, we give a very detailed discussion, e.g. p=3 and G of type E ₆, E ₇ and E ₈. We explain how the presence of spin up and spin down elements influences the structure of projectively elementary abelian 2-groups in Spin(2n, ). Examples of an elementary abelian group which is nontoral in one algebraic group but toral in a larger one are noted.Two subsets of a maximal torus are conjugate in G iff they are conjugate in the normalizer of the torus; this observation, with our discussion of the nontoral cases, gives a detailed guide to the possibilities for the embedding of an elementary abelian p-group in G. To give an application of our methods, we study extraspecial p-groups in E ₈( ).Dedicated to Jacques Tits for his sixtieth birthday     

Electroproduction of strangeness

Formalism for the electroproduction of strange particles based on the one photon exchange approximation and the Feynman diagrams representation of hadron current is reviewed. Different photoproduction models are compared with available photo and electroproduction data. New experiments are proposed that may resolve existing uncertainties and inconsistencies. The formation of hypernuclei via kaon electroproduction is investigated theoretically and compared with other reactions involving purely hadronic processes.     

Organo-tricyanoborates as tectons: illustrative coordination polymers based on copper(I) derivatives

The first systematic study on the use of tricyanoborates as ligands is presented. The tricyanoborates [RB(CN)3]- (R = oct and Ph) can be prepared by direct cyanation of RBCl2 precursors as well as by thermolysis of the corresponding isocyanides [RB(NC)3]-. The first organo-cyanogallates [RGa(CN)3]- (R = Bu, C6H2-2,4,6-Me3) were prepared from the corresponding dichloride, the structure of Et4N[mesGa(CN3] being confirmed crystallographically. The reaction of equimolar [RB(CN)3]- (R = oct, Ph) and [Cu(MeCN)4]+ afforded two-dimensional polymers [RB(CN)3Cu(NCMe)]. The sheets arise via conjoined hexagonal B3Cu3(CN)6 rings with chair conformations. The reaction of excess [PhB(CN)3]- and [Cu(MeCN)4]+ gives the polymer [K(18-crown-6)]{Cu[PhB(CN)3]2}. Treatment of [PhB(CN)3]- with [Cu(PCy3)2(NCMe)x]PF6 gave the one-dimensional polymer [PhB(CN)3Cu(PCy3)2], wherein two of the three BCN substituents are coordinated.     

Application of ionic liquids as low-volatility plasticizers for PMMA

Room temperature ionic liquids (ILs) based on imidazolium salts, were found to be excellent plasticizers for poly(methyl methacrylate), with improved thermal stability, and the ability to reduce glass transition temperatures to near 0 °C. Because ILs have environmentally benign properties, they can be used in place of traditional chemicals in numerous products and processes. In this work, PMMA was formulated using dioctyl phthalate, DOP, as a traditional plasticizer, and properties were compared to PMMA plasticized with two ILs: butyl methylimidazolium/hexafluorophosphate, [bmim⁺][PF₆⁻], and hexyl methylimidazolium/hexafluorophosphate, [hmim⁺][PF₆⁻]. Formulations incorporated up to 30 vol.% DOP and 50 vol.% ILs. Bulk and plasticized polymers were characterized for glass transition temperature, elastic modulus, and the thermal stability of the plasticizers.     

The transverse hadronic energy accompanying weak bosons

We study the hadronic transverse energy (E _T ) accompanyingZ ⁰ events in \(p\bar p\) interactions and compare our result with the observedE _T distribution in minimum bias events. We expect excess transverse energy to accompanyZ ⁰'s. This effect can also be probed experimentally using Drell-Yan lepton pairs and represents an interesting way to probe the multi-gluon structure of QCD.