Hyperbolic polygons of minimal perimeter with given angles

We prove that, among all convex hyperbolic polygons with given angles, the perimeter is minimized by the unique polygon with an inscribed circle. The proof relies on work of Schlenker (Trans Am Math Soc 359(5): 2155–2189, 2007).     

Coloring planar graphs in parallel

We present NC algorithms for vertex and edge coloring planar graphs. The vertex coloring algorithm 5 colors any planar graph, and the edge coloring algorithm Δ edge colors planar graphs with Δ ≥ 23 (and Δ + 1 edge colors planar graphs with Δ < 23), where Δ is the maximum degree in the graph.     

Studying links via closed braids IV: composite links and split links

Summary The main result concerns changing an arbitrary closed braid representative of a split or composite link to one which is obviously recognizable as being split or composite. Exchange moves are introduced; they change the conjugacy class of a closed braid without changing its link type or its braid index. A closed braid representative of a composite (respectively split) link is composite (split) if there is a 2-sphere which realizes the connected sum decomposition (splitting) and meets the braid axis in 2 points. It is proved that exchange moves are the only obstruction to representing composite or split links by composite or split closed braids. A special version of these theorems holds for 3 and 4 braids, answering a question of H. Morton. As an immediate Corollary, it follows that braid index is additive (resp. additive minus 1) under disjoint union (resp. connected sum).Oblatum 29-XI-1988 & 25-I-1990Partially supported by NSF Grant #DMS-88-05672     

On list‐coloring outerplanar graphs

We prove that a 2‐connected, outerplanar bipartite graph (respectively, outerplanar near‐triangulation) with a list of colors L (v ) for each vertex v such that (resp., ) can be L‐list‐colored (except when the graph is K₃ with identical 2‐lists). These results are best possible for each condition in the hypotheses and bounds. © 2008 Wiley Periodicals, Inc. J Graph Theory 59: 59–74, 2008     

Preparation and structure of three solvatomorphs of the polymer [Co(dbm)2(4ptz)]n: spin canting depending on the supramolecular organization

The syntheses and X-ray structures of three isomeric 1D coordination polymers are reported. The complex [Co(dbm)2(MeOH)2] (1) was used as a precursor in these reactions. The preparation and structure of 1 is also presented; this mononuclear complex is in the cis configuration because this allows the formation of a network of intermolecular hydrogen bonds in the solid state. Reaction of 1 with 2,4,6-tris-(4-pyridyl)-1,3,5-triazine (4ptz) yields the polymers [Co(dbm)2(4ptz)]n.nTHF (2a), [Co(dbm)2(4ptz)]n.0.75nTHF.0.5nEt2O (2b), and [Co(dbm)2(4ptz)]n.3nDMF (2c) in the form of zigzag chains, instead of the expected honeycomb architectures. This is because of the establishment of extended pi-pi stacking throughout these solids, which could not have occurred otherwise. Compounds 2a, 2b, and 2c are solvatomorphs, and formation of either one of them depends on the exact conditions of crystallization, which lead to significant differences in the supramolecular organization of the chains. Bulk magnetic measurements on 2a reveal weak antiferromagnetic exchange within the chains and small ordering throughout the solid that results in the manifestation of the phenomenon of spin canting, whereas for 2c the different supramolecular organization causes the antiferromagnetic exchange not to result in spin canting.     

Biosynthesis of 4-methylproline in cyanobacteria: cloning of nosE and nosF genes and biochemical characterization of the encoded dehydrogenase and reductase activities

The biosynthesis of the unusual amino acid 4-methylproline in the Nostoc genus of cyanobacteria was investigated on the genetic and enzymatic level. Two genes involved in the biosynthesis were cloned and the corresponding enzymes, a zinc-dependent long-chain dehydrogenase and a Delta(1)-pyrroline-5-carboxylic acid (P5C) reductase homologue, were overexpressed in Escherichia coli and biochemically characterized. Putative substrates were synthesized to test enzyme substrate specificities, and deuterium labeling studies were carried out to reveal the stereospecificities of the enzymatic reactions with respect to the substrates as well as to the coenzymes.     

Structural analyses and magnetic properties of 3D coordination polymeric networks of nickel(II) maleate and manganese(II) adipate with the flexible 1,2-bis(4-pyridyl)ethane ligand

Two novel inorganic-organic hybrid 3D extended networks of Ni(II) and Mn(II) having molecular formulas [(maleate)(2)Ni(3)(bpe)(4)(H(2)O)(4)](NO(3))(2).H(2)O (1) and [(adipate)Mn(bpe)] (2) (bpe = 1, 2-bis(4-pyridyl)ethane), respectively, have been synthesized and characterized by single-crystal X-ray diffraction studies and low-temperature (300-2 K) magnetic measurements. Compound 1 crystallizes in the monoclinic system, space group C2/c (No. 15), with chemical formula C(56)H(62)N(10)Ni(3)O(19), a = 30.955(4) A, b = 12.705(3) A, c = 17.058(5) A, beta = 117.26(2) degrees, and Z = 4. Compound 2 crystallizes in the triclinic system, space group Ponemacr; (No. 2), with chemical formula C(18)H(20)MnN(2)O(4), a = 8.492(2) A, b = 9.444(2) A, c = 11.533(3) A, alpha = 97.19(1) degrees, beta = 94.64(1) degrees, gamma = 105.02(1) degrees, and Z = 2. The structure determination reveals for both a 3D network. Compound 1 contains two crystallographically independent Ni(II) ions in different octahedral environments. Ni(1) lies on an inversion center, and its coordination environment comprises two chelating maleate anions and two bpe nitrogen donors, while the Ni(2) ion is surrounded by meridionally disposed three bpe N atoms, two water molecules, and one oxygen donor from the dicarboxylate anion. Of the three crystallographic independent bpe ligand, one presents an anti and the others a gauche conformation. The corresponding N-to-N distances are 9.344, 6.543, and 6.187 A. Variable-temperature magnetic susceptibility measurement of the complex reveals the existence of a dominant ferromagnetic interaction within the molecule. Compound 2 is composed of Mn(2) dimer units linked by adipate anions to form corrugated 2D sheets which, on interconnection through bpe (anti conformation, N-to-N distance of 9.391 A), produces an interpenetrated 3D alpha-polonium-related type net. Complex 2 reveals to be antiferromagnetic fitting data using a dimeric Mn(II) model that considers negligible magnetic transmission through the carbon skeleton of adipate and the bpe pathway.     

Electrical conductivity in vinyl chloride during polymerization

Vinyl chloride of good polymerization quality showed a measurable electrical conductivity. The ionic strength of redistilled VCM appeared to be independent of temperature in the range from 20 to 50°C, and to decrease at higher temperatures. Conductivity measurements during bulk polymerization of VCM showed that the conductivity decreased with conversion. Other results indicated that electrolytically active species, formed during the polymerization, were trapped in the polymer matrix.     

Residual‐based stabilization of the finite element approximation to the acoustic perturbation equations for low Mach number aeroacoustics

The acoustic perturbation equations (APE) are suitable to predict aerodynamic noise in the presence of a non‐uniform mean flow. As for any hybrid computational aeroacoustics approach, a first computational fluid dynamics simulation is carried out from which the mean flow characteristics and acoustic sources are obtained. In a second step, the APE are solved to get the acoustic pressure and particle velocity fields. However, resorting to the finite element method (FEM) for that purpose is not straightforward. Whereas mixed finite elements satisfying an appropriate inf–sup compatibility condition can be built in the case of no mean flow, that is, for the standard wave equation in mixed form, these are difficult to implement and their good performance is yet to be checked for more complex wave operators. As a consequence, strong simplifying assumptions are usually considered when solving the APE with FEM. It is possible to avoid them by resorting to stabilized formulations. In this work, a residual‐based stabilized FEM is presented for the APE at low Mach numbers, which allows one to deal with the APE convective and reaction terms in its full extent. The key of the approach resides in the design of the matrix of stabilization parameters. The performance of the formulation and the contributions of the different terms in the equations are tested for an acoustic pulse propagating in sheared‐solenoidal mean flow, and for the aeolian tone generated by flow past a two‐dimensional cylinder. Copyright © 2016 John Wiley & Sons, Ltd.