Morse theory on timelike and causal curves

It is shown that the set of timelike curves in a globally hyperbolic space-time manifold can be given the structure of a Hubert manifold under a suitable definition of timelike. The causal curves are the topological closure of this manifold. The Lorentzian energy (corresponding to Milnor's energy, except that the Lorentzian inner product is used) is shown to be a Morse function for the space of causal curves. A fixed end point index theorem is obtained in which a lower bound for the index of the Hessian of the Lorentzian energy is given in terms of the sum of the orders of the conjugate points between the end points.     

Simulation from Wishart Distributions with Eigenvalue Constraints

Abstract

This article provides an efficient algorithm for generating a random matrix according to a Wishart distribution, but with eigenvalues constrained to be less than a given vector of positive values. The procedure of Odell and Feiveson provides a guide, but the modifications here ensure that the diagonal elements of a candidate matrix are less than the corresponding elements of the constraint vector, thus greatly improving the chances that the matrix will be acceptable. The Normal hierarchical model with vector outcomes and the multivariate random effects model provide motivating applications.     

Phase equilibria for salt-induced lysozyme precipitation: Effect of salt type and temperature

The salt-induced precipitation of lysozyme from aqueous solutions was studied through precipitation assays in which the equilibrium compositions of the coexisting phases were determined. Lysozyme precipitation experiments were carried out at 5, 15 and 25 °C and pH 7.0 with ammonium sulfate, sodium sulfate and sodium chloride as precipitating agents. In these experiments a complete separation of the coexisting phases (liquid and solid) could not be achieved. Nevertheless it was possible to determine the composition of the precipitate. The enzymatic activity of lysozyme in the supernatant phase as well as in the precipitate phase was also determined. The activity balance suggests that there is a relationship between the composition of the true precipitate and the total activity recovery.     

Novel manganese(III) oxidation chemistry: X-ray crystal structures of (1α,2α,4β)-1,2-diacetoxy-4-(4-methoxyphenyl)-6-methoxy-1,2,3,4-tetrahydronaphthalene (compound A) and (1α,2α,4β)-1,2-diacetoxy-4-(2-methoxyphenyl)-8-methoxy-1,2,3,4-tetrahydronaphthalene (compound B)

CompoundA is (1,2,4)-1,2-diacetoxy-4-(4-methoxyphenyl)-6-methoxy-l,2,3,4-tetrahydronaphthalene, C₂₂H₂₄O₆,M _r=384.43, monoclinic, P2₁/n, witha=11.074(3),b=10.353(4),c=17.616(4)Å,=94.96(2)°,V=2012.1ų,D _calc=1.27 g cm^–3 and=0.55 cm^–1 forZ=4. Least-squares refinement of 1371 observed [F ₀5 (F ⁰)] reflections led to the final agreement index ofR=0.052. A twofold disorder was observed for the 1-acetoxy group whereas the 2-acetoxy group was ordered. CompoundB, (1,2,4)-1,2-diacetoxy-4-(2-methoxyphenyl)-8-methoxy-l,2,3,4-tetrahydronaphthalene, C₂₂H₂₄O₆,M _r=384.43, crystallizes in the monoclinic space group, P2₁/c, witha=16.209(2),b=10.076(1),c=13.357(4)Å,=111.41(2)°,V=2030.9ų,D _calc=1.26 g cm^–3 and=0.54 cm^–1 forZ=4. A final agreement index ofR=0.045 was realized by least-squares refinement of 1486 observed [F _o5 (F _o)] reflections. Intermolecular interactions in the cell lattices of compoundsA andB are noted. The title compoundsA andB were prepared by manganese(III) acetate oxidative dimerization of two molecules of 4-methoxystyrene and 2-methoxystyrene, respectively.     

Study of the thermal decomposition of flame-retarded unsaturated polyester resins by thermogravimetric analysis and Py-GC/MS

The thermal degradation behaviours of flame-retarded unsaturated polyester resin formulations containing ammonium polyphosphate (APP), Cloisite 25A nanoclay and zinc based smoke suppressants have been studied using thermogravimetric analysis (TGA) combined with infrared analysis of the evolved gases (EGA) and pyrolysis/gas chromatography-mass spectrometry (GC/MS). In TGA-EGA experiments, the mass loss as a function of temperature has been correlated with the evolution of carbon monoxide (CO) and carbon dioxide (CO₂) and oxygen (O₂) consumption as measured by an oxygen analyser. The effect of APP, Cloisite 25A and the smoke suppressants on the evolution of CO and CO₂ has been examined. The decomposition behaviour of flame-retarded polyester resins under isothermal pyrolytic conditions was investigated and the evolved gaseous products were collected and qualitatively and semi-quantitatively analysed via GC/MS. The addition of APP does not yield many new gaseous products relative to the unmodified polyester resin neither does the presence of zinc borate (ZB) and zinc stannate (ZS) together with APP. Possible chemical interactions are discussed in an attempt to explain the observed results.     

Kinetics of gas-phase hydrolysis of ethyl acetate catalyzed by immobilized lipase

Reactions catalyzed by supported enzymes present important advantages when compared with those in aqueous media or organic solvents: separation of enzymes from substrate is easily accomplished, enzyme stability may be improved, and control of the reaction products is more accurate. We present the experimental results of the kinetic study of ethyl acetate hydrolysis in gaseous phase catalyzed by a commercial immobilized lipase (Lipozyme IM; Novo Nordisk). The hydrolysis reaction was studied as a function of ethyl ester and water partial pressure at a constant temperature of 318 K. The amount of biocatalyst used was varied between 100 and 300 mg, and the reaction was studied in a flow-through glass microreactor. Under the conditions used, water was an important parameter in the gas-phase reaction. Activation energy was 24.8 kJ/mol and the overall order of reaction was one. Finally a Bi-Bi reaction mechanism is proposed.     

Neolipid enzymatic synthesis

Applied Biochemistry and Biotechnology - Enzymatic coupling of aminopolyols and medium-chain length fatty acids was carried out via the reverse action of a fungal lipase. Model reactants and...     

Probing synergism, antagonism, and additive effects in poly(vinyl ester) (PVE) composites with fire retardants

Potential fire retardants, including copper hydroxy dodecyl sulfate (CHDS), organically-modified montmorillonite (Cloisite 15A), and resorcinol di-phosphate (RDP), were added to pure poly(vinyl ester) (PVE) individually or in combinations at low concentration formulations. Thermogravimetric analysis and cone calorimetry were used to study the thermal stability and fire performance of the composites. Synergistic, antagonistic, and additive effects were observed depending on the specific formulation. Time to self-sustained combustion is greatly reduced, but the flame extinguishes faster, for the composites containing CHDS alone or in combination with either RDP or Cloisite 15A compared to the virgin polymer. The presence of copper in PVE composites containing additive, CHDS, may be responsible for the enhanced thermal stability and fire performance.