Completely Simple Semigroups,Lie Algebras,and the Road Coloring Problem

Consider a semigroup generated by matrices associated with an edge-coloring of a strongly connected, aperiodic digraph. We call the semigroup Lie-solvable if the Lie algebra generated by its elements is solvable. We show that if the semigroup is Lie-solvable then its kernel is a right group. Next, we study the Lie algebra generated by the kernel. Lie algebras generated by two idempotents are analyzed in detail. We find that these have homomorphic images that are generalized quaternion algebras. We show that if the kernel is not a direct product, then the Lie algebra generated by the kernel is not solvable by describing the structure of these algebras. Finally, we discuss an infinite class of examples that are shown to always produce strongly connected aperiodic digraphs having kernels that are not right groups.     

Epimerization, diastereoselectivity and hemilability in dicationic chiral ruthenium complexes with bidentate (PS) bisphosphine monosulfide ligands

The binding of heterobidentate P^∧S ligands introduces metal-centered chirality to the planar chiral parent complex Ru(η⁶:η¹-NMe₂C₆H₄C₆H₄PCy₂)Cl₂. Observed diastereomeric ratios for the kinetic product vary dramatically depending upon ring size of the chelate formed with the P^∧S ligand. The complexes epimerize very slowly to thermodynamic product ratios that are substantially different from the kinetic product ratios.     

An algorithm for detecting abelian monopoles inSU 2-valued lattice gauge-Higgs systems

We present an algorithm which calculates the monopole number of anSU ₂-valued lattice gauge field, together with a lattice Higgs field, on a simplicial lattice of dimension ≧3. The calculation is gauge invariant. The expected value of the monopole density (for a fixed Higgs field) does not depend on the Higgs field. Partially supported by NSF grants DMS 8607168 and DMS 8907753 Partially supported by PSC-CUNY and by NSF grant DMS 8805485     

Resonant-cavity-enhanced photodetectors and LEDs in the mid-infrared

In this paper we outline the use of resonant-cavity enhancement for increasing the exterior coupling efficiency of photodetectors and light-emitting diodes (LEDs) in the mid-infrared (MIR) spectral region. This method is potentially very important in the MIR because encapsulation is not presently feasible due to the lack of suitable materials. Among other potential applications, resonant-cavity-enhanced (RCE) photodetectors and LEDs could be particularly suitable for greenhouse gas detection because of their ‘pre-tunable’ spectrally narrowed resonantly enhanced peaks. We also present the optical characterization of an InAs RCE photodetector aimed at the detection of methane gas (λ≈3.3 μm), and an InAs/InAs_0.91Sb_0.09 resonant-cavity LED (RCLED) aimed at carbon dioxide gas (λ≈4.2 μm). The high peak responsivity of the RCE photodetector was 34.7 A/W at λ=3.14 μm, and the RCLED peaked at λ=3.96 μm. These are among the longest operating wavelengths for III–V RCE photodetectors and RCLEDs reported in the literature.     

Brand Shifting in Hierarchical Markets: A New Model and Information Equivalency

The brand shifting problem is reviewed. A new allocation of brand shifting volume is shown to be compatible with a posited hierarchical (nested) market structure, unlike previous allocations. Like the Sanddabs model on which it is based, the new allocation, called Sanddabs/Nest, uses purchase tracking information but does not require brand similarity data. The paper shows Sanddabs/Nest is equivalent to a principle of Kullback information. Implications for brand management are detailed.     

A New Flow Instrument for Conductance Measurements at Elevated Temperatures and Pressures: Measurements on NaCl(aq) to 458 K and 1.4 MPa

A new flow electrical conductance instrument was constructed and tested on dilute NaCl solutions up to 458 K, and on more concentrated solutions (maximum 0.436 mol⋅kg⁻¹) at 373 K. The results of the new instrument agreed with those of previous authors within the estimated experimental errors. The model of Bernard et al. (J. Phys. Chem. 96, 3833–3840 (1992), MSA) was found to represent the high-temperature results without introducing an ion-pairing equilibrium constant. The Fuoss–Hsia conductance equation as given by Fernandez-Prini was found to represent the dilute concentrations with Λ° (NaCl) as the only adjustable parameter. It was found that Λ° (NaCl) could be expressed as a function of solvent viscosity and density by using three parameters found by regression of literature results between 278.15 and 523 K. This equation along with the FHFP theory permits the equivalent conductivity of dilute sodium chloride solutions to be calculated within the accuracy of the existing experimental measurements.     

Divinylsiloxane‐bisbenzocyclobutene‐based polymer modified with polystyrene–polybutadiene–polystyrene triblock copolymers

Divinylsiloxane‐bisbenzocyclobutene (DVS‐bisBCB) polymer has very low dielectric constant and dissipation factor, good thermal stability, and high chemical resistance. The fracture toughness of the thermoset polymer is moderate due to its high crosslink density. A thermoplastic elastomer, polystyrene–polybutadiene–polystyrene triblock copolymer, was incorporated into the matrix to enhance its toughness. The cured thermoset matrix showed different morphology when the elastomer was added to the B‐staged prepolymer or when the elastomer was B‐staged with the DVS‐bisBCB monomer. Small and uniformly distributed elastomer domains were detected by transmission electron micrographs (TEM) in the former case, but TEM did not detect a separate domain in the latter case. A high percentage of the polystyrene–polybutadiene–polystyrene triblock copolymer could be incorporated into the DVS‐bisBCB thermoset matrix by B‐staging the triblock copolymer with the BCB monomer. The elastomer increased the fracture toughness of DVS‐bisBCB polymer as indicated by enhanced elongation at break and increased K1c values obtained by the modified edge‐lift‐off test. Elastomer modified DVS‐bisBCB maintained excellent electrical properties, high T_g and good thermal stability, but showed higher coefficient of linear thermal expansion values. © 2006 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 44: 1591–1599, 2006