Structures of two N-{2-([(5-amino-1,3,4-thiadiazol-2-yl)difluoromethyl]-4-halophenyl}acetamides

Abstract  

The compounds, N-{2-[(5-amino-1,3,4-thiadiazol-2-yl)difluoromethyl]-4-chlorophenyl}acetamide (1: X = Cl) and N-{2([(5-amino-1,3,4-thiadiazol-2-yl)difluoromethyl]-4-bromo-phenyl}acetamide (1: X = Br), are isostructural. The molecules are near ‘‘V’’ shaped with the angles between the two aromatic planes ca. 84° in each case. The various intermolecular interactions, namely N–H···O, N–H···N, N–H···F, and C–H···N hydrogen bonds and C–H···π, C–Cl···π and C–O···π interactions, generate 3-D arrays. Compound (1: X = Cl) crystallizes in the monoclinic space group P21/c with a = 16.9032(7) ?, 10.2193(4) ?, c = 7.5227(4) ?, β = 100.179(3)° and Z = 4. Compound (1: X = Br) crystallizes in the monoclinic space group P21/c with a = 17.2119(4) ?, 10.2167(2) ?, c = 7.5677(2) ?, β = 100.326(2)° and Z = 4.     

Numerical quenching of a system of equations coupled at the boundary

We study numerical approximations of solutions of the following system of heat equations, coupled at the boundary through a nonlinear flux: where p and q are parameters. We prove that the solutions of a semidiscretization in space quench in finite time. Moreover, we describe in terms of p and q the simultaneous versus non‐simultaneous quenching phenomena. We also find the numerical extinction sets. Finally, in order to obtain the correct quenching rates in the non‐simultaneous case we present some adaptive methods. Copyright © 2009 John Wiley & Sons, Ltd.     

Ehrhart Polynomials of Matroid Polytopes and Polymatroids

We investigate properties of Ehrhart polynomials for matroid polytopes, independence matroid polytopes, and polymatroids. In the first half of the paper we prove that, for fixed rank, Ehrhart polynomials of matroid polytopes and polymatroids are computable in polynomial time. The proof relies on the geometry of these polytopes as well as a new refined analysis of the evaluation of Todd polynomials. In the second half we discuss two conjectures about the h ^*-vector and the coefficients of Ehrhart polynomials of matroid polytopes; we provide theoretical and computational evidence for their validity.     

A characteristic property of the Euclidean disc

In this paper the following is proved: Let K ⊂ $ \mathbb{E}^2 $ \mathbb{E}^2 be a smooth strictly convex body, and let L ⊂ $ \mathbb{E}^2 $ \mathbb{E}^2 be a line. Assume that for every point x ∈ L/K the two tangent segments from x to K have the same length, and the line joining the two contact points passes through a fixed point in the plane. Then K is an Euclidean disc.     

Bounds for point recolouring in geometric graphs

We examine a recolouring scheme ostensibly used to assist in classifying geographic data. Given a drawing of a graph with bi-chromatic points, where the points are the vertices of the graph, a point can be recoloured if it is surrounded by neighbours of the opposite colour. The notion of surrounded is defined as a contiguous subset of neighbours that span an angle greater than 180 degrees. The recolouring of surrounded points continues in sequence, in no particular order, until no point remains surrounded. We show that for some classes of graphs the process terminates in a polynomial number of steps. On the other hand, there are classes of graphs with infinite recolouring sequences.     

GRASP with hybrid heuristic-subproblem optimization for the multi-level capacitated minimum spanning tree problem

We propose a GRASP using an hybrid heuristic-subproblem optimization approach for the Multi-Level Capacitated Minimum Spanning Tree (MLCMST) problem. The motivation behind such approach is that to evaluate moves rearranging the configuration of a subset of nodes may require to solve a smaller-sized MLCMST instance. We thus use heuristic rules to define, in both the construction and the local search phases, subproblems which are in turn solved exactly by employing an integer programming model. We report numerical results obtained on benchmark instances from the literature, showing the approach to be competitive in terms of solution quality. The proposed GRASP have in fact improved the best known upper bounds for almost all of the considered instances.     

Fast 2D NMR ligand screening using Hadamard spectroscopy

Fast 2D NMR-based screening can be achieved using Hadamard encoded spectroscopy to focus on the signals of interest (e.g., enzyme active or ligand recognition sites). By recording a set of Hadamard spectra (a "Hadamard constellation") with relative offsets comparable to the excitation bandwidth, quantitative ligand-induced shifts can be obtained from peak intensities.     

Polystachyne F, a 5,10-seco-neoclerodane from Salvia polystachya

A new 5,10-seco-neoclerodane diterpene, polystachyne F (1), was isolated from the aerial parts of Salvia polystachya. Its structure was established on the basis of its spectroscopic properties and X-ray crystallographic analysis. Some correlations in the NOESY spectrum of 1 suggested the existence of a conformational equilibrium.     

Isotope dilution-thermal ionisation mass spectrometric analysis for tin in a fly ash material

Isotope dilution-thermal ionisation mass spectrometry (ID-TIMS) analysis has been applied to the determination of tin in a fly ash sample supplied by the EC Joint Research Centre (Ispra, Italy). The proposed procedure includes the silica gel/phosphoric acid technique for tin thermal ionisation activation and a strict heating protocol for isotope ratio measurements. Instrumental mass discrimination factor has been previously determined measuring a natural tin standard solution. Spike solution has been prepared from ¹¹²Sn-enriched metal and quantified by reverse isotope dilution analysis. Two sample aliquots were spiked and tin was extracted with 4.5 M HCl during 25 min ultrasound exposure time. Due to the complex matrix of this fly ash material, a two-step purification stage using ion-exchange chromatography was required prior TIMS analysis. Obtained results for the two sample-spike blends (10.11 ± 0.55 and 10.50 ± 0.64 μmol g⁻¹) are comparable, both value and uncertainty. Also a good reproducibility is observed between measurements. The proposed ID-TIMS procedure, as a primary method and due to the lack of fly ash reference materials certified for tin content, can be used to validate more routine methodologies applied to tin determination in this kind of samples.