Extrinsic Killing spinors

 Under intrinsic and extrinsic curvature assumptions on a Riemannian spin manifold and its boundary, we show that there is an isomorphism between the restriction to the boundary of parallel spinors and extrinsic Killing spinors of non-negative Killing constant. As a corollary, we prove that a complete Ricci-flat spin manifold with mean-convex boundary isometric to a round sphere, is necessarily a flat disc. Received: 2 February 2002; in final form: 1 August 2002 / Published online: 1 April 2003 Mathematics Subject Classification (1991): 53C27, 53C40, 53C80, 58G25 The authors would like to thank Lars Andersson for helpful discussions and for bringing to our knowledge the information regarding Remark 4. We are also grateful to the referee for pointing out that Corollary 5 and Corollary 6 are only valid when the boundary is at least 2-dimensional. Research of S. Montiel is partially supported by a Spanish MCyT grant No. BFM2001-2967     

Pressure-temperature phase diagrams of smectogenic 4'-alkyl-4-cyanobiphenyls (9CB, 10CB, 11CB and 12CB)

The pressure-temperature ( p - T ) phase diagrams for four smectogenic members of the 4'-alkyl-4-cyanobiphenyl homologous series ( n CB, n =9, 10, 11 and 12) over the temperature range 320-410 K and pressure range 0.1-300 MPa (3 kbar) were constructed using DTA. At 1 atm 9CB exhibits nematic and smectic A d phases, while the other members show only the smectic A d phase. However, at elevated pressures the clearing line splits in the case of 10CB and 11CB which indicates the induction of a nematic phase. It was found that the triple point, where the isotropic, nematic and smectic phases coexist, is strongly shifted to higher pressures with increasing chain length. This was interpreted as being caused by a loss of the rod-like shape of the molecules containing longer alkyl tails which explore a range of conformations. The slope of the clearing line, d T /d p , depends strongly on the length of the alkyl chain for the n CB series, but does not show a step-wise change between the nematogenic and smectogenic members.     

Behaviors of the positive temperature coefficient of resistance of poly(styrene‐co‐n‐butylacrylate) filled with Ni‐plated core‐shell polymeric particles

Conductive composite films of poly(styrene‐co‐n‐butylacrylate) copolymers filled with low‐density, Ni‐plated core‐shell polymeric particles were prepared and their behaviors of positive temperature coefficient of resistance (PTCR) were investigated. When the conductive fillers in the composite film were loaded beyond the critical volume, 10 up to 25 vol %, composite films exhibited a unique electrical resistant transition behavior, which the electrical resistance rapidly increased by several orders of magnitude at the critical temperature. The PTCR transition temperature, in general, occurred before the glass transition temperature of polymer matrix. Further increased the conductive filler loading to 30 vol %, the overpacked conduction paths were formed in the entire composite and the PTCR effects became blurred. While the composite film treated with thermal cycle several times from room temperature up to 120 °C, the electrical resistivity increased accompanied with the shift of the PTCR transition to lower temperature. The reason might have been caused by the formed interfacial cracks within the composite film. © 2006 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 45: 322–329, 2007     

Un théorème de Choquet-Deny pour les groupes moyennables

Résumé SoitG un groupe moyennable connexe, locallement compact, à base dénombrable. Soit une mesure positive sur les boréliens deG. Nous étudions les fonctions boréliennes positivesh vérifiant: g G, . Sous de bonnes hypothèses sur , nous obtenons, pour ces fonctions, une représentation intégrale à l'aide d'exponentielles.

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Summary LetG be a connected locally compact separable amenable group. Let be a positive measure on the Borel -field ofG. We study the positive Borel functionsh onG which satisfy: g G, . Under smooth assumptions on , we establish an integral representation of these functions in term of exponentials.

     

Gradient elution capillary electrochromatography and hyphenation with nuclear magnetic resonance

Coupling of gradient capillary electrochromatography (gradient CEC) and capillary zone electrophoresis (CZE) with nuclear magnetic resonance spectroscopy (NMR) was performed using a recently developed capillary NMR interface. This technique was applied for the analysis of pharmaceuticals and food. An analgesic was investigated using isocratic and gradient continuous-flow CEC-NMR. Comparison of the results demonstrated the superiority of gradient CEC over isocratic CEC. Aspartame and caffeine, both ingredients of soft beverages, were separated and analyzed by continuous flow CZE-NMR. The order of elution could be reversed by altering the pH. This reversal led to an increased sample concentration in the NMR detection cell, thus allowing the acquisition of a totally correlated spectroscopy (TOCSY) two-dimensional (2-D) spectrum of the synthetic peptide aspartame.     

Aspects of the Reduction of Double Bonds Using Cob (I)alamin as Catalys

The olefinic system in 3β-methoxy-4-cholesten-6 a-ol ( 2 ) is reduced using cob (I)alamin ( 1 ( I ); see Scheme 1) as catalyst, aqueous acetic acid as solvent and metallic zinc as electron source (cf. Schemes 2 and 3). Experimental evidence for an attack of 1 ( I ) on both faces of the double bond is presented. By the same catalyst (1 R)-10, 10-dimethyl-2-pinene- 10-carbonitrile ( 9 ) is first transformed to the menthene derivative 11 (see Schemes 4 and 5). The ring opening is then followed by a fast saturation of the disubstituted olefinic system in 11 , and ultimately the remaining double bond is reduced in a slow reaction. The cis-configurated saturated menthane derivative 16 is the main final product ( 16 / 17 ≈ 10:1).     

Equilibrium of the reaction between dissolved sodium sulfide and biologically produced sulfur

The equilibrium of the heterogeneous reaction between dissolved sodium sulfide and biologically produced sulfur particles has been studied. Biologically produced sulfur was obtained from a bioreactor of a hydrogen sulfide removal process in which the dominating organism is Thiobacillus sp. W5. Detailed knowledge of this reaction is essential to understand its effect on the process. The results were compared with the equilibrium of the reaction of sulfide with ‘inorganic’ elemental sulfur. The equilibrium between dissolved sodium sulfide and biologically produced sulfur particles can be described by an equilibrium constant, K_x, which consists of a weighted sum of constants for polysulfide ions of different chain length, rather than a true single equilibrium constant. For biologically produced sulfur pK_x = 9.10 ± 0.08 (21 °C) and 9.17 ± 0.09 (35 °C) with an average polysulfide chain length x = 4.91 ± 0.32 (21 °C) and 4.59 ± 0.31 (35 °C). The pK_x value for biologically produced sulfur is significantly higher than for reaction of dissolved sodium sulfide with inorganic sulfur (pK_x = 8.82; 21 °C). This difference is probably caused by the negatively charged polymeric organic layer, which is present on biologically produced sulfur but absent with “inorganic” sulfur. Specific binding of polysulfide ions to the organic layer results in a higher polysulfide concentration at the reaction site compared to the bulk concentration. This results in an apparent decrease of the measured equilibrium constant, K_x.     

Anionic oligomerization of methacrylonitrile

The anionic oligomerization of methacrylonitrile by alcoholic solutions of sodium alkoxide in dimethyl sulfoxide, methanol and ethanol was studied. The DP of the oligomers was directly proportional to the monomer concentration and inversely proportional to the alcohol concentration, in accordance with the equation DP = K[MAN]/[ROH], K being equal to K_p/K_tr. The value of K in DMSO (with sodium methoxidemethanol) was 2.9 ± 0.2, in methanol was 1.5 ± 0.1, and in ethanol (with sodium ethoxide as initiator) was 1.9 ± 0.1. The physical properties of the oligomers are given.     

Détermination des modèles d'imperfections de différentes variétés allotropiques du sulfure cuivreux (digénite cubique,chalcocite hexagonale “haute et basse température”, chalcocite orthorhombique)

From the study of the CuCuBrCu_2?εSC solid cell in the range of cubic digenite and “high temperature” hexagonal chalcocite we have deduced the laws of variation of the deviation from stoichiometry and the holes concentration with the equilibrium partial pressure of sulfur (δ and p are found to be proportional to ). The electronic model corresponding to the formation of associations (V^×_CuV′_Cu) in the presence of neutral vacancies V^×_Cu allows one to explain these laws. In the low temperature range (range of “low temperature” hexagonal chalcocite and orthorhombic chalcocite) the study of thermal variations of Hall coefficient permits us to propose the following models: (a) the deviation from stoichiometry of the “low temperature” hexagonal chalcocite is due to the simple ionized vacancies V′_Cu; (b) the deviation from stoichiometry of the orthorhombic chalcocite is due to the vacancies V′_Cu and to the associations (V^×_CuV^×_Cu).