The supercuspidal representations of <Emphasis Type="Italic">p</Emphasis>-adic classical groups

Let G be a unitary, symplectic or special orthogonal group over a locally compact non-archimedean local field of odd residual characteristic. We construct many new supercuspidal representations of G, and Bushnell–Kutzko types for these representations. Moreover, we prove that every irreducible supercuspidal representation of G arises from our constructions.     

Modeling the kinetics of large sets of reactions on metal surfaces

We are concerned with constructing and solving kinetic models for large-scale catalytic mechanisms involving hundreds of reactions. We need reliable estimates for hundreds of rate constants for each project we undertake. In order to obtain reliable estimates of activation barriers with co-adsorbate effects, we employ the UBI-QEP method whenever applicable. We also bring quantum mechanical electronic structure methods to bear when necessary. Herein we describe a new model for obtaining reasonable estimates for rate constants for reactions on metal surfaces that yields rate constants and rate constant parameters without large amounts of computer time. The model is based on a novel approach to surface-phase chemistry and a re-thinking regarding the phases from which surface adsorbates react. We will also discuss recent literature regarding trends in Arrhenius pre-exponential factors (prefactors).     

Polariton thermalization in GaN microcavities in the strong light–matter coupling regime

We discuss the thermalization of the polariton population from a bulk GaN λ/2 microcavity at room temperature. Simultaneous optical measurements of reflectivity and photoluminescence (PL), as well as time resolved measurements, reveal strong light–matter coupling. Transfer matrix theory is used to calculate reflectivity, absorption, and transmission coefficients for the structure. The PL emission is found to be thermalized, despite its very short lifetime, suggesting the existence of very fast energy relaxation channels.     

Ab initio equilibrium structures of unionized amino acids: alanine

The structures of two unionized conformations of alanine were optimized by relaxing all of their geometrical parameters using standard single determinant MO theory with Pulay's FORCE method a 4–21G basis. The results represent the best now available estimate for the unobserved geometry of this system.     

Sums of Five, Seven and Nine Squares

Let r _k(n) denote the number of representations of an integer n as a sum of k squares. We prove that

Synthesis and photophysical behavior of a novel zinc phthalocyanine containing a single carboxylic acid and three phenylthio substituents

Zinc 2, (3)-tri-(phenylthio)-2, (3)-carboxy phthalocyanine (ZnPc(COOH)(SPh)₃), zinc 2, (3)-tetra-(phenylthio) phthalocyanine (ZnPc(SPh)₄) and 2, (3)-tetra-(phenylthio) phthalocyanine (H₂Pc(SPh)₄) were synthesized and their photophysical behavior were compared with those of a number of zinc phthalocyanine (ZnPc) derivatives. ZnPc(COOH)(SPh)₃ and ZnPc(SPh)₄ had similar fluorescence (Φ_F=0.14) and triplet state (Φ_T=0.65) quantum yields in dimethylsulfoxide, hence showing no effects of the replacement of one of the phenylthio groups with a carboxylic acid group. ZnPc(COOH)(SPh)₃ displayed a slightly shorter triplet lifetime (τ_T=331 μs) than ZnPc (τ_T=350 μs) in DMSO, but within the range of ZnPc derivatives. The triplet lifetime for ZnPc(COOH)(SPh)₃ is much longer than for the symmetrical derivative (ZnPc(SPh)₄) with τ_T=149 μs in DMSO.     

Synthesis and Characterization of Anionic Poly(cyclopentadienylene vinylene) and Its Use in Conductive Hydrogels

The use of π‐conjugated polymers (CPs) in conductive hydrogels remains challenging due to the water‐insoluble nature of most CPs. Conjugated polyelectrolytes (CPEs) are promising alternatives because they have tunable electronic properties and high water‐solubility, but they are often difficult to synthesize and thus have not been widely adopted. Herein, we report the synthesis of an anionic poly(cyclopentadienylene vinylene) (aPCPV) from an insulating precursor under mild conditions and in high yield. Functionalized aPCPV is a highly water‐soluble CPE that exhibits low cytotoxicity, and we found that doping hydrogels with aPCPV imparts conductivity. We also anticipate that this synthetic strategy, due to its ease and high efficiency, will be widely used to create families of not‐yet‐explored π‐conjugated vinylene polymers.