On cohomology of finitely generated function groups

Let Γ be a non-elementary finitely generated Kleinian group with region of discontinuity Ω. Letq be an integer,q ≥ 2. The group Λ acts on the right on the vector space Π_2q?2 of polynomials of degree less than or equal to 2q ? 2 via Eichler action. We note by A_qq(Ω, Λ) the space of cusp forms for Λ of weight (?2q) and the space of parabolic cohomology classes by PH¹ (Λ, Π2q?2). Bers introduced an anti-linear map $$\beta _q^* :A^q \left( {\Omega ,\Gamma } \right) - - - \to PH^1 \left( {\Gamma ,\Omega _{2q - 2} } \right)$$ . We try to determine the class of Kleinian groups for which the Bers map is surjective. We show that the Bers map is surjective for geometrically finite function groups. We also obtain a characterization of geometrically finite function groups. As an application, we reprove theorems of Maskit on inequalities involving the dimension of the space of cusp forms supported on an invariant component and the dimension of the space of cusp forms supported on the other components for finitely generated function groups. We also show all these inequalities are equalities for geometrically finiteB-groups.     

On an Archimedean analogue of Tate's conjecture

We consider an Archimedean analogue of Tate's conjecture, and verify the conjecture in the examples of isospectral Riemann surfaces constructed by Vignéras and Sunada. We prove a simple lemma in group theory which lies at the heart of T. Sunada's theorem about isospectral manifolds.     

Experimental Design and Statistical Analysis of AGET ATRP of MMA in Emulsion Polymer Reactor

This study investigates atom transfer radical polymerization (ATRP) of methyl methacrylate (MMA) using activators generated by electron transfer (AGET) as the initiation technique in an emulsion well‐mixed 2L stirred tank reactor. The performance of the AGET ATRP of MMA is analyzed for five key independent variables, namely temperature, catalyst complex (CuBr2/dNbpy), initiator (EBiB), reducing agent (ascorbic acid), and surfactant (Brij 98). The reaction is carried out based on a two‐step polymerization procedure. A resolution 5 fractional factorial design technique is employed to assess the influence of the five independent variables on the monomer conversion, polymer average molecular weights, and polydispersity index (PDI). An input–output model is constructed from the data of 21 designed experimental tests. A statistical analysis of the results shows that the temperature is the most influential variable for the three output process responses. The initiator strongly affects the poly(methyl methacrylate) (PMMA) molecular weights. It is the least important key variable affecting MMA conversion and PDI, and the surfactant is the least one affecting PMMA Mn. On assessing the independent interactions effect, the interactions of temperature‐surfactant on conversion, and temperature‐initiator for PMMA M_n are considered. Process simulation in 3D mapping has demonstrated that model predictions agree well with experimental data.     

Hydride generation activity of arsenosugars and thioarsenicals

The major arsenosugar compounds have been reported to be hydride-generation-active, however to a lesser extent in comparison with the inorganic arsenicals. We report here for the first time the identity and quantity of the volatile arsenicals generated by As-sugar-SO₃, As-sugar-SO₄, dimethylarsinoyl acetic acid and dimethylarsinoyl ethanol. Only one major volatile compound was identified for all four compounds studied: dimethylarsine. This means that the As–C bond to the longer carbon chain was cleaved during the hydride-generation process. Theoretical calculations at the RHF/6-31G(d,p) ab initio level confirm that this As–C bond is much weaker than the As–CH₃ bonds. Furthermore, it was revealed that the sulphur analogue of dimethylarsinic acid (DMAS ) is hydride-generation-active at pH 7 in contrast to dimethylarsinic acid, despite the fact that arsenic is also pentavalent. This has been substantiated by the calculation of the change in susceptibility of the arsenic towards nucleophilic attack when oxygen is replaced by sulphur. Hence, DMAS can easily be mistaken for a trivalent arsenic species.     

Lifting orthogonal representations to spin groups and local root numbers

Representations ofD _k ^* k ^* for a quaternion division algebraD _k over a local fieldk are orthogonal representations. In this note we investigate when these orthogonal representations can be lifted to the corresponding spin group. The results are expressed in terms of local root number of the representation.     

Thermal smearing and screening in a strong magnetic field for Dirac materials in comparison with the two dimensional electron liquid

We compute and compare the effects due to a uniform perpendicular magnetic field as well as temperature on the static polarization functions for monolayer graphene (MLG), associated with the Dirac point, with that for the two-dimensional electron liquid (2DEL) with the use of comprehensive numerical calculations. The relevance of our study to the Friedel oscillations for the screening of the potential for a dilute distribution of impurities is reported too. Our results show substantial differences due to screening for the 2DEL and MLG which have not been given adequate attention previously.     

Direct determination of organic acids in wine and wine-derived products by Fourier transform infrared (FT-IR) spectroscopy and chemometric techniques

FT-IR with partial least squares (PLS) was used to establish a full calibration model for tartaric acid, malic acid, lactic acid, succinic acid, citric acid and acetic acid in wines, vinegars and spirits. Sample pre-treatment was not required except for filtering.     

A character relationship on GLn(ℂ)

In this paper we consider the character of an irreducible finite-dimensional algebraic representation of GL_mn(?) restricted to a particular disconnected component of the normalizer of the Levi subgroup GL_m(?)ⁿ of GL_mn(?), generalizing a theorem of Kostant on the character values at the Coxeter element.     

Electron paramagnetic resonance measurement of trapped radical concentrations in frontally polymerized and bulk‐polymerized multifunctional (meth)acrylates

For the first time, electron paramagnetic resonance spectroscopy was used to compare numbers and distributions of radicals produced in frontal free‐radical polymerization of multifunctional acrylates and methacrylates to those produced by bulk free‐radical polymerization. A comparison of radical concentrations was performed for individual polymers and selected copolymers of trimethylolpropane trimethacrylate (TMPTMA), 1,6‐hexanediol diacrylate, trimethylolpropane triacrylate, and pentaerythritol tetraacrylate (PETA). Frontally polymerized samples showed a large spike in intensity at the point of initiation. Within a few centimeters, the radical signal diminished to a steady state. The radical concentration remained almost constant over 3 months under helium in flame‐sealed tubes. The types of radicals were similar to those in bulk polymerization. For both TMPTMA and PETA, frontally polymerized samples had significantly higher numbers of radicals than did the bulk‐prepared samples, achieving concentrations as high as 8.7 × 10^?3 mol/kg in the frontally prepared samples of TMPTMA. © 2011 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem, 2011