Cohomology of the moduli of parabolic vector bundles

The purpose of this paper is to compute the Betti numbers of the moduli space ofparabolic vector bundles on a curve (see Seshadri [7], [8] and Mehta & Seshadri [4]), in the case where every semi-stable parabolic bundle is necessarily stable. We do this by generalizing the method of Atiyah and Bott [1] in the case of moduli of ordinary vector bundles. Recall that (see Seshadri [7]) the underlying topological space of the moduli of parabolic vector bundles is the space of equivalence classes of certain unitary representations of a discrete subgroup Γ which is a lattice in PSL (2,R). (The lattice Γ need not necessarily be co-compact). While the structure of the proof is essentially the same as that of Atiyah and Bott, there are some difficulties of a technical nature in the parabolic case. For instance the Harder-Narasimhan stratification has to be further refined in order to get the connected strata. These connected strata turn out to have different codimensions even when they are part of the same Harder-Narasimhan strata. If in addition to ‘stable = semistable’ the rank and degree are coprime, then the moduli space turns out to be torsion-free in its cohomology. The arrangement of the paper is as follows. In § 1 we prove the necessary basic results about algebraic families of parabolic bundles. These are generalizations of the corresponding results proved by Shatz [9]. Following this, in § 2 we generalize the analytical part of the argument of Atiyah and Bott (§ 14 of [1]). Finally in § 3 we show how to obtain an inductive formula for the Betti numbers of the moduli space. We illustrate our method by computing explicitly the Betti numbers in the special case of rank = 2, and one parabolic point.     

A facile tandem double-dehydrative-double-Heck olefination strategy for pot-economic synthesis of (E)-distyrylbenzenes as multi-target-directed ligands against Alzheimer's disease employing C. elegans model

A concise, one pot and regioselective access to (E)-distyrylbenzenes (DSBs) from arylhalide and secondary phenylenediethanol, a stable precursor for in situ generation of divinylbenzene (DVB) to avoid its polymerization, is described for construction of double CC bond formation via tandem double-dehydrative-double-Heck (D-D-D-H) reaction using Palladium and ionic liquid [hmim]Br as a cooperative catalyst. It is noteworthy that this pot-economy approach also provides direct synthesis of hydroxylated distyrylbenzenes without requirement of protection-deprotection strategy. Importantly, the synthesized DSBs are tested for their protective activity against β amyloid reduction, acetylcholine esterase inhibition, lipid lowering and reactive oxygen species (ROS) reduction properties in transgenic Caenorhabditis elegans model wherein 1,3-bis((E)-4-(trifluoromethyl)styryl)benzene (5c) is found to be active across all above factors thus presenting lead molecule within multi-target-directed ligands (MTDLs) approach. Molecular docking studies were also performed to understand the interactions of potent DSBs with receptors.     

Intercalation Compounds of Cu2+ and Nl2+ — Exchanged Montmorillonite Clay with 8-Hydroxyquinoline

Montmorillonite clay mineral shows remarkable ion exchange, intercalation and swelling properties. It can act as a good host for large organic molecules. Intercalated coordination compounds can be prepared in the interlayer spaces of montmorillonite structure. Cu(II)- and Ni(II)- exchanged montmorillonite sorb 8-hydroxyquinoline (oxine) to form corresponding coordination compounds of the exchanged metal ions. Such compounds have been characterised by means of elemental analysts, infrared spectroscopy, magnetic susceptibility data and X-ray diffraction. These compound show good thermal stability.     

Experimental observations on the scaling of adsorption isotherms for nonionic surfactants at a hydrophobic solid-water interface

The self-assembly of nonionic surfactants in bulk solution and on hydrophobic surfaces is driven by the same intermolecular interactions, yet their relationship is not clear. While there are abundant experimental and theoretical studies for self-assembly in bulk solution and at the air-water interface, there are only few systematic studies for hydrophobic solid-water interfaces. In this work, we have used optical reflectometry to measure adsorption isotherms of seven different nonionic alkyl polyethoxylate surfactants (CH3(CH2)I-1(OCH2CH2)JOH, referred to as CIEJ surfactants, with I = 10-14 and J = 3-8), on hydrophobic, chemically homogeneous self-assembled monolayers of octadecyltrichlorosilane. Systematic changes in the adsorption isotherms are observed for variations in the surfactant molecular structure. The maximum surface excess concentration decreases (and minimum area/molecule increases) with the square root of the number of ethoxylate units in the surfactant (J). The adsorption isotherms of all surfactants collapse onto the same curve when the bulk and surface excess concentrations are rescaled by the bulk critical aggregation concentration (CAC) and the maximum surface excess concentration. In an accompanying paper we compare these experimental results with the predictions of a unified model developed for self-assembly of nonionic surfactants in bulk solution and on interfaces.     

Formation of a quaternary carbon center through the Pd(0)/PhCOOH-catalyzed allylation of cyclic beta-keto esters and 1,3-diketones with alkynes

Formation of a quaternary carbon center through the allylation of beta-keto esters and 1,3-diketones with alkynes is accomplished by the use of Pd(0)/benzoic acid catalyst. Reactions of various cyclic beta-keto esters and 1,3-diketones with alkynes in the presence of Pd(2)dba(3).CHCl(3) (5 mol %), PPh(3) (40 mol %), and PhCOOH (10 mol %) proceeded at 100 degrees C in toluene (5 M) to give the corresponding allylation products in high yields in a regio- and stereoselective manner. The possibility of asymmetric allylation is also discussed.     

Structure,insertion electrochemistry,and magnetic properties of a new type of substitutional solid solutions of copper,nickel, and iron hexacyanoferrates/hexacyanocobaltates

Substitutional solid solutions of metal hexacyanometalates in which low-spin iron(III) and cobalt(III) ions populate the carbon-coordinated sites were synthesized and studied by powder diffraction including Rietveld refinement, cyclic voltammetry of immobilized microparticles, diffuse reflection vis-spectrometry, and magnetization techniques. The continuous solid solution series of potassium copper(II), potassium nickel(II), and iron(III) [(hexacyanoferrate(III))(1-x)(hexacyanocobaltate(III))(x)] show that the substitution of low-spin iron(III) by cobalt(III) in the hexacyanometalate units more strongly affects the formal potentials of the nitrogen-coordinated copper(II) and high-spin iron(III) ions than those of the remaining low-spin iron(III) ions. In the case of copper(II) and iron(III) [(hexacyanoferrate(III))(1-x)(hexacyanocobaltate(III))(x)] the peak currents decrease much more than can be explained by stoichiometry, indicating that the charge propagation is slowed by the substitution of low-spin iron(III) by cobalt(III). The Rietveld refinement of all compounds confirmed the structure initially proposed by Keggin for Prussian blue and contradicts the structure described later by Ludi. The dependencies of lattice parameters on composition exhibit in all series of solid solutions studied similar, although small, deviations from ideality, which correlate with the electrochemical behavior. Finally, a series of solid solutions of the composition KNi(0.5)(II)Cu(0.5)(II)[Fe(III)(CN)(6)](1-x)[Co(III)(CN)(6)](x), where both the nitrogen- and carbon-coordinated metal ions are mixed populated and were synthesized and characterized. These are the first examples of solid solutions of metal hexacyanometalates with four different metal ions, where both the nitrogen- and the carbon-coordinated sites possess a mixed population.     

Microwave-enhanced Pd(0)/acetic acid catalyzed allylation reactions of C, N, and O-pronucleophiles with alkynes

An efficient method for the allylation of C, N, and O-nucleophiles with alkynes under solvent-free conditions and by microwave activation is established. The process can be termed as a real eco-chemical process since no waste elements are produced in the reaction, moreover it is solvent free. This technique can also be used for the allylation of dimethyl methylmalonate, which proves inert under the previously reported reaction conditions (refluxing in 1,4-dioxane).     

3-Nitroso-4-hydroxy-5,6-benzocoumarin as a specific reagent for the detection of cobalt

Microchimica Acta - The complexation of 3-nitroso-4-hydroxy-5,6-benzocoumarin with cobalt is used to detect cobalt in presence of various common ions. The spot test has been successfully used for...     

Gold-Catalyzed 1,2-Diarylation of Alkenes

Herein, we disclose the gold-catalyzed 1,2-diarylation of alkenes through the interplay of ligand-enabled Au^I/Au^III catalysis with the idiosyncratic π-activation mode of gold complexes. Unlike the classical migratory-insertion-based approach to 1,2-diarylation, the present approach not only circumvents the formation of direct Ar−Ar′ coupling and Heck-type side products but more intriguingly demonstrates reactivity and selectivity complementary to those of previously known metal catalysis (Pd, Ni, or Cu). Detailed investigations to underpin the mechanistic scenario revealed oxidative addition of aryl iodides to an Au^I complex to be the rate-limiting step owing to the non-innocent nature of the aryl alkene.