The computation of characteristic classes of lattice gauge fields

AGL(p,C)-valued lattice gauge fieldu on a simplicial complex determines a principalGL(p,C)-bundle if the plaquette products are sufficiently small with respect to the maximum distortion coefficient of the transporters. A representative cocyclec _q for theq ^th Chern class of can be computed on each 2q-simplex by takingc _q() to be the intersection number of a certain singular 2q-cubeM with a Schubert-type variety _q in the space of allp×p matrices. This reduces to the solution of polynomial equations with coefficients coming fromu and thus avoids numerical integration or cooling-type procedures. An application of this method is suggested for the computation of the topological charge of anSU(3)-valued lattice gauge field on a 4-complex.Partially supported by NSF grant DMS 8607168Partially supported by PSC-CUNY and by NSF grant DMS 8805485     

Inner Derivations on σ-C*-Algebras

We prove the following two improvements of a result of Becker. (1) If A is a pro-C*-algebra, then every derivation on A is approximately inner. (2) If A is a separable σ-C*-algebra, and if every C* quotient of A has the property that every derivation on it is inner, then also every derivation on A is inner. We also give an example of a derivation on a separable σ-C*-algebra which is not inner but which induces an inner derivation on every C* quotient.     

High surface plasmon resonance sensitivity enabled by optical disks

We report a systematic, experimental, and theoretical investigation on the surface plasmon resonance (SPR) sensing using optical disks with different track pitches, including Blu-ray disk (BD), digital versatile disk (DVD), and compact disk (CD). Optical reflection measurements indicate that CD and DVD exhibit much higher SPR sensitivity than BD. Both experiments and finite-difference time-domain simulations reveal that the SPR sensitivity is significantly affected by the diffraction order of the SPR peaks and higher diffraction order results in lower sensitivity. Numerical simulations also show that very high sensitivity (～1600 nm per refractive index unit) is achievable by CDs.     

A concise total synthesis of largazole, solution structure, and some preliminary structure activity relationships

A total synthesis of largazole that proceeds in 8 steps from commercial materials is reported, along with some structure-activity relationships. A combination of NMR studies and molecular modeling have also provided a preliminary picture of the conformation of largazole.     

Comparison of the photophysics of an aggregating and non-aggregating aluminium phthalocyanine system incorporated into unilamellar vesicles

The hydrophobic sensitizer, aluminium phthalocyanine chloride (AIPcCI), and the amphiphilic sensitizer, cis-disulphonated aluminium phthalocyanine (cis-AIPcS₂), were incorporated into small unilamellar vesicles (SUVs) and large unilamellar vesicles (LUVs). AIPcCI exhibits aggregation, which increases with increasing sensitizer concentration, whereas cis-AlPcS₂ is monomeric at all concentrations studied. Complex fluorescence decays are observed, showing decay time distributions which broaden with increasing phthalocyanine concentration. The phthalocyanine aggregate, although non-fluorescent, influences the overall photophysical behaviour of the phthalocyanine-vesicle system. The effect of aggregation on the resulting photophysics of phthalocyanines was investigated by comparing aggregated and non-aggregated phthalocyanine systems. The implications for photodynamic therapy (PDT) are briefly discussed.     

Density functional theory studies of negishi alkyl-alkyl cross-coupling reactions catalyzed by a methylterpyridyl-Ni(I) complex

Density functional theory calculations were done to examine the potential energy surfaces of Ni(I)-catalyzed Negishi alkyl-alkyl cross-coupling reactions by using propyl iodide and isopropyl iodide as model alkyl electrophiles and CH 3ZnI as a model alkyl nucleophile. A four-step catalytic cycle involving iodine transfer, radical addition, reductive elimination, and transmetalation steps were characterized structurally and energetically. The reaction mechanism for this catalytic cycle appears feasible based on the calculated free energy profiles for the reactions. The iodine transfer step is the rate-determining step for the Ni(tpy)-CH 3 (tpy = 2,2'6',2'-terpyridine) reactions with alkyl iodides. For secondary alkyl electrophiles, the oxidative addition intermediate, Ni(III), prefers to undergo decomposition over reductive elimination, whereas for the primary alkyl electrophiles, Ni(III) prefers to undergo reductive elimination over decomposition based on comparison of the relative reaction rates for these two types of steps. In addition, thermodynamic data were employed to help explain why the yield of the coupled product is very low from the Ni(II)-alkyl halide reactions with organozinc reagents.     

Probing ruthenium-acetylide bonding interactions: synthesis, electrochemistry, and spectroscopic studies of acetylide-ruthenium complexes supported by tetradentate macrocyclic amine and diphosphine ligands

The synthesis and spectroscopic properties of trans-[RuL4(C[triple bond]CAr)2] (L4 = two 1,2-bis(dimethylphosphino)ethane, (dmpe)2; 1,5,9,13-tetramethyl-1,5,9,13-tetraazacyclohexadecane, 16-TMC; 1,12-dimethyl-3,4:9,10-dibenzo-1,12-diaza-5,8-dioxacyclopentadecane, N2O2) are described. Investigations into the effects of varying the [RuL4] core, acetylide ligands, and acetylide chain length for the [(-)C[triple bond]C(C6H4C[triple bond]C)(n-1)Ph] and [(-)C[triple bond]C(C6H4)(n-1)Ph] (n = 1-3) series upon the electronic and electrochemical characteristics of trans-[RuL4(C[triple bond]CAr)2](0/+) are presented. DFT and TD-DFT calculations have been performed on trans-[Ru(L')4(C[triple bond]CAr)2](0/+) (L' = PH3 and NH3) to examine the metal-acetylide pi-interaction and the nature of the associated electronic transition(s). It was observed that (1) the relationship between the transition energy and 1/n for trans-[Ru(dmpe)2{C[triple bond]C(C6H4C[triple bond]C)(n-1)Ph}2] (n = 1-3) is linear, and (2) the sum of the d(pi)(Ru(II)) --> pi*(C[triple bond]CAr) MLCT energy for trans-[Ru(16-TMC or N2O2)(C[triple bond]CAr)2] and the pi(C[triple bond]CAr) --> d(pi)(Ru(III)) LMCT energy for trans-[Ru(16-TMC or N2O2)(C[triple bond]CAr)2]+ corresponds to the intraligand pi pi* absorption energy for trans-[Ru(16-TMC or N2O2)(C[triple bond]CAr)2]. The crystal structure of trans-[Ru(dmpe)2{C[triple bond]C(C6H4C[triple bond]C)2Ph}2] shows that the two edges of the molecule are separated by 41.7 A. The electrochemical and spectroscopic properties of these complexes can be systematically tuned by modifying L4 and Ar to give E(1/2) values for oxidation of trans-[RuL4(C[triple bond]CAr)2] that span over 870 mV and lambda(max) values of trans-[RuL4(C[triple bond]CAr)2] that range from 19,230 to 31,750 cm(-1). The overall experimental findings suggest that the pi-back-bonding interaction in trans-[RuL4(C[triple bond]CAr)2] is weak and the [RuL4] moiety in these molecules may be considered to be playing a "dopant" role in a linear rigid pi-conjugated rod.