A transfer map for singular fibrations

Using a new group of singular chains on polyhedra, a transfer map is defined on the chain level for fibrations with singularities. These include usual transfer on homology as well as Oliver transfer and other cases.     

BRST cohomology and highest weight vectors. I

We initiate a program to study certain recent problems in non-compact coset CFT by the BRST approach. We derive a reduction formula for the BRST cohomology by making use of a twisting by highest weight modules. As illustrations, we apply the formula to the bosonic string model and a rank one non-compact coset model [DPL]. Our formula provides a completely new approach to non-compact coset construction.Partially supported by NSF Grant DMS-8703581     

BRST cohomology of the super-Virasoro Algebras

We study the superextension of the semi-infinite cohomology theory of the Virasoro Algebra. In particular, we examine the BRST complex with coefficients in the Fock Space of the RNS superstring. We prove a theorem of vanishing cohomology, and establish the unitary equivalence between a positive definite transversal space, a physical subspace and the zeroth cohomology group. The cohomology of a subcomplex is identified as the covariant equivalent of the well-known GSO subspace. An exceptional case to the vanishing theorem is discussed.Supported by NSF Grant DMS-8703581     

Semi-infinite homology and 2D gravity. I

In [33], we studied the constraint problem for two-dimensional quantum gravity in the conformal gauge. In this gauge, we proposed an ansatz for the gravitational sector. Using this ansatz, we established a striking connection between the matrix models and continuum 2D gravity. We also announced several results on semi-infinite homology of the Virasoro algebra with coefficients in a suitable class of positive energy modules. In this article, we will provide details of the proof of the announced results.Supported in part by the Alfred P. Sloan FoundationSupported by NSF Grant DMS-8703581     

Combinatorial criteria for uniqueness of Gibbs measures

We generalize previously known conditions for uniqueness of the Gibbs measure in statistical physics models by presenting conditions of any finite size for models on any underlying graph. We give two dual conditions, one requiring that the total influence on a site is small, and the other that the total influence of a site is small. Our proofs are combinatorial in nature and use tools from the analysis of discrete Markov chains, in particular the path coupling method. The implications of our conditions for the mixing time of natural Markov chains associated with the models are discussed as well. We also present some examples of models for which the conditions hold. © 2005 Wiley Periodicals, Inc. Random Struct. Alg., 2005     

Zirconium-mediated metathesis of imines: a study of the scope, longevity, and mechanism of a complicated catalytic system

By kinetically stabilizing imidozirconocene complexes through the use of a sterically demanding ligand, or by generating a more thermodynamically stable resting state with addition of diphenylacetylene, we have developed transition metal-catalyzed imine metathesis reactions that are mechanistically analogous to olefin metathesis reactions catalyzed by metal carbene complexes. When 5 mol % of Cp*Cp(THF)Zr=N(t)Bu is used as the catalyst precursor in the metathesis reaction between PhCH=NPh and p-TolCH=N-p-Tol, a 1:1:1:1 equilibrium mixture with the two mixed imines p-TolCH=NPh and PhCH=N-p-Tol is generated in C(6)D(6) at 105 degrees C. The catalyst was still active after 20 days with an estimated 847 turnovers (t(1/2) 170 m; TON = 1.77 h(-1)). When the azametallacyclobutene Cp(2)Zr(N(Tol)C(Ph)=C(Ph)) is used as the catalyst precursor under similar reaction conditions, a total of 410 turnovers are obtained after 4 days (t(1/2) 170 m; TON = 4.3 h(-1)). An extensive kinetic and equilibrium analysis of the metallacyclobutene-catalyzed metathesis of PhCH=N-p-Tol and p-F-C(6)H(4)CH=N-p-F-C(6)H(4) was carried out by monitoring the concentrations of imines and observable metal-containing intermediates over time. Numerical integration methods were used to fit these data to a detailed mechanism involving coordinatively unsaturated (16-electron) imido complexes as critical intermediates. Examination of the scope of reaction between different organic imines revealed characteristic selectivity that appears to be unique to the zirconium-mediated system. Several zirconocene complexes that could generate the catalytically active "CpCp'Zr=NAr" (Cp' = Cp or Cp*) species in situ were found to be effective agents in the metathetical exchange between different N-aryl imines. N-Alkyl aldimines were found to be completely unreactive toward metathesis with N-aryl aldimines, and metathesis reactions involving the two N-alkyl imines TolCH=NPr and PhCH=NMe gave slow or erratic results, depending on the catalyst used. Metathesis was observed between N-aryl ketimines and N-aryl aldimines, but for N-aryl ketimine substrates, the catalyst resting state consists of zirconocene enamido complexes, generated by the formal C-H activation of the alpha position of the ketimine substrates.     

STRUCTURE OF DYE AGGREGATES AND THE MECHANISM(S) OF PHOTOSENSITIZATION OF AgBr*,†

Abstract— This paper reports the present conclusions of an extended investigation on photo-sensitization of silver bromide. A general molecular packing structure for dye aggregates on the AgBr (111) surface is proposed. This structure, along with the observed spectral absorption displacements of small aggregates, is used to elucidate the phenomena of antisensitization and supersensitization. Supersensitization is seen as a partitioning of large dye aggregates into small aggregates by a deliberately added second component or by gaps between the aggregates. This partitioning isolates antisensitizing dye in a small fraction of the aggregates and minimizes its effect. The smallest aggregates are least likely to contain an antisensitizer, and show the highest quantum efficiency for photoconductivity and photographic action. Photoconductivity measurements establish that supersensitization occurs before the electron appears in the AgBr phase.
The question of direct electron injection vs. energy transfer as mechanisms for AgBr photosensitization is examined in terms of radiationless transfer to surface Ag₂S on AgBr. The absorption of surface Ag₂S is shown to be adequate for acceptance of Förster transfer from the dye, and surface Ag₂S is known to be photographically active. However, this mechanism is inefficient, and inadequate to account for observed high efficiency infrared sensitization. Direct electron injection is seen as the more probable mechanism for efficient dye sensitization of AgBr.     

119mSn-Mössbauer-spektren von funktionell substituierten stannylenen und ihren stannio-komplexen mit chrom,molybdän- und wolfram-carbonyl-acceptoren

^119mSn Mössbauer data for a series of base-stabilized, intermolecularly associated tin(II) compounds ith O, Cl, P and As atoms bonded to tin are compared with isomer shifts (IS) and quadrupole splittings (QS) of their stannio complex derivatives with Cr, Mo and W carbonyls. Coordination at the tin lone-pair atom decreases IS to ca. 2.1 ± 0.2 mm s^?1 and increases the QS. QS values reflect the highly associated nature of the complexes (CO)₅MSn(Cl)E(t-Bu)₂ (M Cr, W; E  P, As) which are bridged through μ-E(t-Bu)₂ groups.