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.     

Effect of the sixth axial ligand in CS-ligated iron(II)octaethylporphyrinates: structural and Mössbauer studies

The effect of a sixth ligand in a series of low-spin thiocarbonyl-ligated iron(II)octaethylporphyrinates has been investigated. Six-coordinate complexes have been synthesized and characterized by M?ssbauer and infrared spectroscopy and single-crystal X-ray structure determinations. The results are compared with the five-coordinate parent complex. The crystal structures of [Fe(OEP)(CS)(1-MeIm)] and [Fe(OEP)(CS)(Py)] are reported and discussed. The 1-methylimidazole and pyridine derivatives exhibit Fe-C(CS) bond distances of 1.703(4) and 1.706(2) A that are significantly longer than the 1.662(3) A reported for five-coordinate [Fe(OEP)(CS)] (Scheidt, W. R.; Geiger, D. K. Inorg. Chem. 1982, 21, 1208). The trans Fe-N(ligand) distances of 2.112(3) and 2.1550(15) A observed for the 1-methylimidazole and pyridine complex are approximately 0.13 A longer than those observed for analogous bis-ligated complexes and are consistent with a significant structural trans effect for the CS ligand. M?ssbauer investigations carried out for five- and six-coordinate thiocarbonyl derivatives with several different sixth axial ligands reveal interesting features. All derivatives exhibit very small isomer shift values, consistent with a very strong interaction between iron and CS. The five-coordinate derivative has delta(Fe) = 0.08 mm/s, and the six-coordinate complexes exhibit delta(Fe) = 0.14 to 0.19 mm/s at 4.2 K. The five-coordinate complex shows a large quadrupole splitting (DeltaE(q) = 1.93 mm/s at 4.2 K) which is reduced on coordination of the sixth ligand (DeltaE(q) = 0.42-0.80 mm/s at 4.2 K). Addition of a sixth ligand also leads to a small decrease in the value of nu(CS). Correlations in structural, IR, and M?ssbauer results suggest that the sixth ligand effect is primarily induced by changes in sigma-bonding. The structure of [Fe(OEP)(CS)(CH(3)OH)] is briefly reported. Crystal data: [Fe(OEP)(CS)(1-MeIm)] crystallizes in the monoclinic system, space group P2(1)/n, Z = 4, a = 9.5906(5) A, b = 16.704(4) A, c = 23.1417(6) A, beta = 100.453(7) degrees. [Fe(OEP)(CS)(Py)] crystallizes in the triclinic system, space group P1, Z = 5, a = 13.9073(6) A, b = 16.2624(7) A, c = 22.0709(9) A, alpha = 70.586(1) degrees, beta = 77.242(1) degrees, gamma = 77.959(1) degrees. [Fe(OEP)(CS)(CH(3)OH)] crystallizes in the triclinic system, space group P1, Z = 1, a = 9.0599(5) A, b = 9.4389(5) A, c = 11.0676(6) A, alpha = 90.261(1) degrees, beta = 100.362(1) degrees, gamma = 114.664(1) degrees.     

Sodium halides as the source of electrophilic halogens in green synthesis of 3-halo- and 3,n-dihalobenzo[b]thiophenes

A convenient methodology for the synthesis of mono- and di-halogenated benzo[b]thiophenes is described herein, which utilizes copper(II) sulfate pentahydrate and various sodium halides in the presence of substituted 2-alkynylthioanisoles. The proposed method is facile, uses ethanol as a green solvent, and results in uniquely substituted benzo[b]thiophene structures with isolated yields up to 96%. The most useful component of this methodology is the selective introduction of bromine atoms at every available position (2–7) around the benzo[b]thiophene ring, while keeping position 3 occupied by a specific halogen atom such as Cl, Br or I. Aromatic halogens are useful reactive handles; therefore, the selective introduction of halogens at specific positions would be valuable in the targeted synthesis of bioactive molecules and complex organic materials via metal-catalyzed cross coupling reactions. This work is a novel approach towards the synthesis of dihalo substituted benzo[b]thiophene core structures, which provides a superior alternative to the current methods discussed herein.     

Evolutionary hybrid approaches for generation scheduling in power systems

Generation scheduling (GS) in power systems is a tough optimisation problem which continues to present a challenge for efficient solution techniques. The solution is to define on/off decisions and generation levels for each electricity generator of a power system for each scheduling interval. The solution procedure requires simultaneous consideration of binary decision and continuous variables. In recent years researchers have focused much attention on developing new hybrid approaches using evolutionary and traditional exact methods for this type of mixed-integer problems. This paper investigates how the optimum or near optimum solution for the GS problem may be quickly identified. A design is proposed which uses a variety of metaheuristic, heuristics and mathematical programming techniques within a hybrid framework. The results obtained for two case studies are promising and show that the hybrid approach offers an effective alternative for solving the GS problems within a realistic timeframe.     

A coordination polymer of (Ph3P)AuCl prepared by post-synthetic modification and its application in 1-hexene/n-hexane separation

PCM-10 is a porous phosphine coordination material based on Ca(II) and tris(p-carboxylated) triphenylphosphine. The material provides a unique 3-dimensional surface of P(III) Lewis base sites, which is ideal for post-synthetic functionalization. The addition of Au(I) yields an advanced material that can selectively adsorb 1-hexene over n-hexane at room temperature.     

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.     

Robust tracking control of nonlinear unmatched uncertain systems via event-based adaptive dynamic programming

Nonlinear Dynamics - In this paper, a novel robust tracking control strategy for nonlinear unmatched uncertain systems is formulated using the event-based adaptive dynamic programming (ADP)...     

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.