On the spectral norm of algebraic numbers

In this paper we continue to study the spectral norms and their completions ([4]) in the case of the algebraic closure $ \overline {\mathbb Q} $ of ? in ?. Let $ \widetilde{\overline{\mathbb{Q}}} $ be the completion of $ \overline {\mathbb Q} $ relative to the spectral norm. We prove that $ \widetilde{\overline{\mathbb{Q}}} $ can be identified with the R‐subalgebra of all symmetric functions of C(G), where C(G) denotes the ?‐Banach algebra of all continuous functions defined on the absolute Galois group G = Gal$ {\overline {\mathbb Q}} / {\mathbb Q} $. We prove that any compact, closed to conjugation subset of ? is the pseudo‐orbit of a suitable element of $ \widetilde{\overline{\mathbb{Q}}} $. We also prove that the topological closure of any algebraic number field in $ \widetilde{\overline{\mathbb{Q}}} $ is of the form $\widetilde{\mathbb{Q}[x]}$ with x in $ \widetilde{\overline{\mathbb{Q}}} $.     

Morse inequalities, a function space integral approach

In this paper we prove the Morse inequalities in the non-degenerate and degenerate cases. Like the approach of J.-M. Bismut, ours is based on the idea suggested by Witten. In fact, if anything, our approach is closer to Witten's original idea than Bismut's.     

X‐ray excited optical luminescence from crystalline silicon

Synchrotron based X‐ray excited optical luminescence (XEOL) has been measured with many direct bandgap semiconductors. We present XEOL measurements on crystalline silicon (Si), obtained despite of its indirect bandgap and the consequently low luminescence efficiency. Spectra of monocrystalline and multicrystalline (mc) Si at room temperature are compared to theoretical spectra. A possible application in the synchrotron‐based research on mc‐Si is exemplified by combining XEOL, X‐ray fluorescence (XRF) spectroscopy, photoluminescence (PL) spectroscopy, and microscope images of grain boundaries. This approach can be utilized to investigate the recombination activity of metal precipitates, to analyze areas of different lifetimes on mc‐Si samples and to correlate additional material parameters to XRF measurements. (© 2009 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

On Discrete groups of automorphisms of \mathbb P ^2_\mathbb{C }

We study the geometry and dynamics of discrete subgroups $\Gamma $ of $\mathrm{PSL}(3,\mathbb C )$ with an open invariant set $\Omega \subset \mathbb P _\mathbb{C }^2$ where the action is properly discontinuous and the quotient $\Omega /\Gamma $ contains a connected component whicis compact. We call such groups quasi-cocompact. In this case $\Omega /\Gamma $ is a compact complex projective orbifold and $\Omega $ is a divisible set. Our first theorem refines classical work by Kobayashi–Ochiai and others about complex surfaces with a projective structure: We prove that every such group is either virtually affine or complex hyperbolic. We then classify the divisible sets that appear in this way, the corresponding quasi-cocompact groups and the orbifolds $\Omega /\Gamma $ . We also prove that excluding a few exceptional cases, the Kulkarni region of discontinuity coincides with the equicontinuity region and is the largest open invariant set where the action is properly discontinuous.     

Synthesis,X‐ray characterization and density functional theory studies of N6‐benzyl‐N6‐methyladenine–M(II) complexes (M = Zn,Cd): The prominent role of π–π, C–H···π and anion–π interactions

We report the synthesis and X‐ray characterization of the N⁶‐benzyl‐N⁶‐methyladenine ligand (L) and three metal complexes, namely [Zn(HL)Cl₃]·H₂O ( 1 ), [Cd(HL)₂Cl₄] ( 2 ) and [H₂L]₂[Cd₃(μ‐L)₂(μ‐Cl)₄Cl₆]·3H₂O ( 3 ). Complex 1 consists of the 7H‐adenine tautomer protonated at N3 and coordinated to a tetrahedral Zn(II) metal centre through N9. The octahedral Cd(II) in complex 2 is N⁹‐coordinated to two N⁶‐benzyl‐N⁶‐methyladeninium ligands (7H‐tautomer protonated at N3) that occupy apical positions and four chlorido ligands form the basal plane. Compound 3 corresponds to a trinuclear Cd(II) complex, where the central Cd atom is six‐coordinated to two bridging μ‐L and four bridging μ‐Cl ligands. The other two Cd atoms are six‐coordinated to three terminal chlorido ligands, to two bridging μ‐Cl ligands and to the bridging μ‐L through N3. Essentially, the coordination patterns, degree of protonation and tautomeric forms of the nucleobase dominate the solid‐state architectures of 1 – 3 . Additionally, the hydrogen‐bonding interactions produced by the endocyclic N atoms and NH groups stabilize high‐dimensional‐order supramolecular assemblies. Moreover, energetically strong anion–π and lone pair (lp)–π interactions are important in constructing the final solid‐state architectures in 1 – 3 . We have studied the non‐covalent interactions energetically using density functional theory calculations and rationalized the interactions using molecular electrostatic potential surfaces and Bader's theory of atoms in molecules. We have particularly analysed cooperative lp–π and anion–π interactions in 1 and π⁺–π⁺ interactions in 3 .     

Synthesis,Antiprotozoal Activity,and Cheminformatic Analysis of 2-Phenyl-2H-Indazole Derivatives

Indazole is an important scaffold in medicinal chemistry. At present, the progress on synthetic methodologies has allowed the preparation of several new indazole derivatives with interesting pharmacological properties. Particularly, the antiprotozoal activity of indazole derivatives have been recently reported. Herein, a series of 22 indazole derivatives was synthesized and studied as antiprotozoals. The 2-phenyl-2H-indazole scaffold was accessed by a one-pot procedure, which includes a combination of ultrasound synthesis under neat conditions as well as Cadogan’s cyclization. Moreover, some compounds were derivatized to have an appropriate set to provide structure-activity relationships (SAR) information. Whereas the antiprotozoal activity of six of these compounds against E. histolytica, G. intestinalis, and T. vaginalis had been previously reported, the activity of the additional 16 compounds was evaluated against these same protozoa. The biological assays revealed structural features that favor the antiprotozoal activity against the three protozoans tested, e.g., electron withdrawing groups at the 2-phenyl ring. It is important to mention that the indazole derivatives possess strong antiprotozoal activity and are also characterized by a continuous SAR.     

Generator‐collector Voltammetry at Dual‐plate Gold‐gold Microtrench Electrodes as Diagnostic Tool in Ionic Liquids

Ionic liquids provide high viscosity solvent environments with interesting voltammetric characteristics and new electrochemical mechanisms. Here, a gold‐gold dual‐plate microtrench electrode is employed in generator‐collector mode to enhance viscosity‐limited currents in ionic liquids due to fast feedback within small inter‐electrode gaps (5 μm inter‐electrode gap, 27 μm microtrench depth) and to provide a mechanistic diagnosis tool. Three redox systems in the ionic liquid BMIm⁺BF₄^? are investigated: (i) ferrocene oxidation, (ii) oxygen reduction, and (iii) 2‐phenyl‐naphthyl‐1,4‐dione reduction. Both transient and steady state voltammetric responses are compared. Asymmetric diffusion processes, reaction intermediates, and solubility changes in the ionic liquid are revealed.     

Dressings Loaded with Cyclodextrin–Hamamelitannin Complexes Increase Staphylococcus aureus Susceptibility Toward Antibiotics Both in Single as well as in Mixed Biofilm Communities

Bacteria reside within biofilms at the infection site, making them extremely difficult to eradicate with conventional wound care products. Bacteria use quorum sensing (QS) systems to regulate biofilm formation, and QS inhibitors (QSIs) have been proposed as promising antibiofilm agents. Despite this, few antimicrobial therapies that interfere with QS exist. Nontoxic hydroxypropyl‐β‐cyclodextrin‐functionalized cellulose gauzes releasing a burst of the antibiotic vancomycin and the QSI hamamelitannin are developed, followed by a sustained release of both. The gauzes affect QS and biofilm formation of Pseudomonas aeruginosa and Staphylococcus aureus in an in vitro model of chronic wound infection and can be considered as candidates to be used to prevent wound infection as well as treat infected wounds.

     

Genomic clustering of the Trypanosoma cruzi nonlong terminal L1Tc retrotransposon with defined interspersed repeated DNA elements

We have analyzed the genomic distribution and organization of the long interspersed nucleotide element (LINE) L1Tc, a nonlong terminal repeat (LTR) retrotransposon of Trypanosoma cruzi. The results indicate that the L1Tc element is dispersed along the parasite genome and that in some regions it is organized in tandem repeats. The data allowed us to define the existence of short direct-repeated sequences flanking the genomic L1Tc elements. Relevant is the finding that the LINE L1Tc is located in genomic regions rich in short interspersed nucleotide elements (SINE)-like sequences. In particular, the L1Tc element is found associated to E13-related sequences, redefined in this work and renamed RS13Tc, and to a newly described RS1Tc sequence. The RS1Tc sequence is present, per haploid genome, in about 3,200 copies. Northern blot analysis showed that the RS1Tc is being transcribed into RNAs of different sizes. The analysis of the chromosomal distribution of these elements in various strains of T. cruzi suggested that this type of clustering might be a common feature of the genome of these parasites.     

Novel syntheses of 3-anilino-pyrazin-2(1H)-ones and 3-anilino-quinoxalin-2-(1H)-ones via microwave-mediated Smiles rearrangement

In this Letter, we report a novel approach to the preparation of 3-anilino-pyrazin-2(1H)-ones and 3-anilino-quinoxalin-2(1H)-ones from the corresponding 3-halo pyrazin-2-amines and 3-haloquinoxalin-2-amines, using a microwave-mediated Smiles rearrangement.