Gauge theory on noncommutative spaces

We introduce a formulation of gauge theory on noncommutative spaces based on the notion of covariant coordinates. Some important examples are discussed in detail. A Seiberg-Witten map is established in all cases. Received: 6 March 2000 / Published online: 8 May 2000     

Cost-effective interrogation of single nucleotide polymorphisms using the mismatch amplification mutation assay and capillary electrophoresis

The ability to characterize SNPs is an important aspect of many clinical diagnostic, genetic and evolutionary studies. Here, we designed a multiplexed SNP genotyping method to survey a large number of phylogenetically informative SNPs within the genome of the bacterium Bacillus anthracis. This novel method, CE universal tail mismatch amplification mutation assay (CUMA), allows for PCR multiplexing and automatic scoring of SNP genotypes, thus providing a rapid, economical and higher throughput alternative to more expensive SNP genotyping techniques. CUMA delivered accurate B. anthracis SNP genotyping results and, when multiplexed, saved reagent costs by more than 80% compared with TaqMan real-time PCR. When real-time PCR technology and instrumentation is unavailable or the reagents are cost-prohibitive, CUMA is a powerful alternative for SNP genotyping.     

Neutrino dipole moments and charge radii in non-commutative space-time

In this paper we obtain a bound TeV on the scale of space-time non-commutativity considering photon-neutrino interactions. We compute *-dipole moments and *-charge radii originating from space-time non-commutativity and compare them with the dipole moments calculated in the neutrino-mass extended standard model (SM). The computation depends on the nature of the neutrinos, Dirac versus Majorana, their mass and the energy scale. We focus on Majorana neutrinos. The *-charge radius is found to be at TeV.Received: 17 June 2004, Published online: 18 August 2004     

Electron-Rich Diruthenium Complexes with π-Extended Alkenyl Ligands and Their F4TCNQ Charge-Transfer Salts**

The synthesis of dinuclear ruthenium alkenyl complexes with {Ru(CO)(PⁱPr₃)₂(L)} entities (L=Cl⁻ in complexes Ru₂-3 and Ru₂-7 ; L=acetylacetonate (acac⁻) in complexes Ru₂-4 and Ru₂-8 ) and with π-conjugated 2,7-divinylphenanthrenediyl ( Ru₂-3 , Ru₂-4 ) or 5,8-divinylquinoxalinediyl ( Ru₂-7 , Ru₂-8 ) as bridging ligands are reported. The bridging ligands are laterally π-extended by anellating a pyrene ( Ru₂-7 , Ru₂-8 ) or a 6,7-benzoquinoxaline ( Ru₂-3 , Ru₂-4 ) π-perimeter. This was done with the hope that the open π-faces of the electron-rich complexes will foster association with planar electron acceptors via π-stacking. The dinuclear complexes were subjected to cyclic and square-wave voltammetry and were characterized in all accessible redox states by IR, UV/Vis/NIR and, where applicable, by EPR spectroscopy. These studies signified the one-electron oxidized forms of divinylphenylene-bridged complexes Ru₂-7 , Ru₂-8 as intrinsically delocalized mixed-valent species, and those of complexes Ru₂-3 and Ru₂-4 with the longer divinylphenanthrenediyl linker as partially localized on the IR, yet delocalized on the EPR timescale. The more electron-rich acac⁻ congeners formed non-conductive 1 : 1 charge-transfer (CT) salts on treatment with the F₄TCNQ electron acceptor. All spectroscopic techniques confirmed the presence of pairs of complex radical cations and F₄TCNQ^.− radical anions in these CT salts, but produced no firm evidence for the relevance of π-stacking to their formation and properties.     

Droplet epitaxy of zinc-blende GaN quantum dots

Zinc-blende GaN quantum dots were grown on 3C-AlN(0 0 1) by a vapor–liquid–solid process in a molecular beam epitaxy system. We were able to control the density of the quantum dots in a range of 5×10⁸–5×10¹² cm⁻². Photoluminescence spectroscopy confirmed the optical activity of the GaN quantum dots in a range of 10¹¹–5×10¹² cm⁻². The data obtained give an insight to the condensation mechanism of the vapor–liquid–solid process in general, because the GaN quantum dots condense in metastable zinc-blende crystal structure supplied by the substrate, and not in the wurtzite crystal structure expected from free condensation in the droplet.     

Electrochemical Synthesis of Carbazoles by Dehydrogenative Coupling Reaction

A constant current protocol, employing undivided cells, a remarkably low supporting electrolyte concentration, inexpensive electrode materials, and a straightforward precursor synthesis enabling a novel access to N-protected carbazoles by anodic N,C bond formation using directly generated amidyl radicals is reported. Scalability of the reaction is demonstrated and an easy deblocking of the benzoyl protecting group is presented.     

Coxeter Groups, 2-Completion, Perimeter Reduction and Subgroup Separability

We show that all groups in a very large class of Coxeter groups are locally quasiconvex and have a uniform membership problem solvable in quadratic time. If a group in the class satisfies a further hypothesis it is subgroup separable and relevant homomorphisms are also calculable in quadratic time. The algorithm also decides if a finitely generated subgroup has finite index.