Asymptotic Lipschitz Regularity for Tug-of-War Games with Varying Probabilities

We prove an asymptotic Lipschitz estimate for value functions of tug-of-war games with varying probabilities defined in Ω ? ?ⁿ. The method of the proof is based on a game-theoretic idea to estimate the value of a related game defined in Ω ×Ω via couplings.

     

The Ricci flow in a class of solvmanifolds

In this paper, we study the Ricci flow of solvmanifolds whose Lie algebra has an abelian ideal of codimension one, by using the bracket flow. We prove that solutions to the Ricci flow are immortal, the ω-limit of bracket flow solutions is a single point, and that for any sequence of times there exists a subsequence in which the Ricci flow converges, in the pointed topology, to a manifold which is locally isometric to a flat manifold. We give a functional which is non-increasing along a normalized bracket flow that will allow us to prove that given a sequence of times, one can extract a subsequence converging to an algebraic soliton, and to determine which of these limits are flat. Finally, we use these results to prove that if a Lie group in this class admits a Riemannian metric of negative sectional curvature, then the curvature of any Ricci flow solution will become negative in finite time.     

Electrokinetics in extremely bimodal suspensions

Prompted by the results obtained by Mantegazza et al. [Nature Physics 1 (2005) 103], where the electric birefringence of suspensions of elongated particles was strikingly affected by the presence of a sea of very small (size ratio lower than 10:1) colloidal spheres, we have undertaken an investigation of other electrokinetic phenomena in suspensions containing various relative concentrations of large (Teflon or polystyrene latex) and small (nanometer-sized silica spheres) colloids. We have determined the quantities that might be greatly affected by the size distribution of the particles, mainly in the presence of ac electric fields, since the response of the suspensions will show very characteristic relaxations, dominated in principle by the size of the particles. In this work, we report on measurements of the dielectric dispersion of mixed particles as a function of the concentration, ionic strength, and field frequency. The results indicate that the response is not just a simple combination of those obtained with suspensions of the individual particles, and in fact the presence of even small amounts of the small particles affects considerably the frequency response of the suspensions.     

Asymmetric synthesis of beta-hydroxy sulfides controlled by remote sulfoxides

Reactions of (S)-alpha-(methylthio)-2-(p-tolylsulfinyl)benzyl carbanion with different carbonyl compounds proceeds with complete control of the configuration at the benzylic position. Aldehydes yield easily separable mixtures of beta-hydroxy sulfides, epimers at the hydroxylic carbon, where the stereoselectivity depends on steric factors (from 20% to >98% de).     

The development of full field interferometric methods for fluid velocimetry

The development of full field interferometry as a velocimetry technique in experimental fluid mechanics from its inception in 1977 to the present is discussed. In 1977, holographic interferometry (HI) was applied for the first time to measure the velocity field in a liquid flow. It was not until 1998 that the first application to a gaseous flow was reported. The only kind of speckle interferometry that has been applied to measure velocity fields so far is digital speckle pattern interferometry (DSPI). It was in 1999 that DSPI was demonstrated both in a liquid and a gaseous flow.     

Processing,properties and morphology of polypropylene-epdm blends

Blends of polypropylene and an elastomer (ethylene propylene diene terpolymer, EPDM) are systematically investigated to determine the effect of the rubber on the polymer properties. Five compositions on the complete range of blend compositions are analyzed. The study reported here is a first of a series which main objective is to analyze in a systematic way the influence of the different factors that determine the effectiveness of EPDM as an impact modifier for PP. In this first part of the study, the processing behavior of the PP-EPDM blends are analyzed and the mechanical properties of the processed blends (tensile, flexural and impact resistance) are examined. Halpin-Tsai and porosity models successfully represent the mechanical behavior of the blends. The model results allow a physical interpretation of the role of the dispersed phase in terms of the aspect ratio and of the stress concentration factors associated to the dispersed particles. Moreover, the mechanical properties are correlated with the morphology of the blends studied by scanning electron microscopy, where two phases are clearly observed in the complete range of compositions. The results show that PP-EPDM blends with at low rubber content present a good processability, without significant deterioration with respect to neat PP and with a considerable improvement of the room and low temperature performance.     

fac-Acetato-bis(pyrazole) complexes: A systematic study on intra- and intermolecular hydrogen bonds

Acetato-bis(pyrazole) complexes [Mo(η³-methallyl)(O₂CMe)(CO)₂(pz^∗H)₂], (methallyl = CH₂C(CH₃)CH₂) and fac-[M(O₂CMe)(CO)₃(pz^∗H)₂], (pz^∗H = pyrazole or 3,5-dimethylpyrazole, dmpzH; M = Mn, Re) are obtained from [Mo(η³-methallyl)Cl(CO)₂(NCMe)₂] or fac-[MBr(CO)₃(NCMe)₂] [M = Mn (synthesized in situ), Re], 2 equiv. of pyrazole, and 1 equiv. of sodium acetate for Mo complexes, or silver acetate for Mn or Re complexes. The chlorido-complexes [Mo(η³-methallyl)Cl(CO)₂L₂] (L = pzH, dmpzH), obtained from the same starting material by substitution of MeCN by pzH or dmpzH, are also described. The crystal structures of the fac-acetato-bis(dimethylpyrazole) complexes present the same pattern of intramolecular hydrogen bonds between the acetate and the dimetylpyrazole ligands, whereas the crystal structures of the fac-acetato-bis(pyrazole) complexes show different hydrogen bonds patterns, with intermolecular interactions. NMR data indicate that these interactions are not maintained in solution.     

Molybdenum- and tungsten(II) monometallic 3-(2-pyridyl)pyrazole and bimetallic 3-(2-pyridyl)pyrazolate complexes

Molybdenum and tungsten complexes containing the pypzH (3-(2-pyridyl)pyrazole) ligand as a chelating bidentate are prepared: [Mo(CO)(4)(pypzH)], cis-[MoBr(η(3)-allyl)(CO)(2)(pypzH)], cis-[MoCl(η(3)-methallyl)(CO)(2)(pypzH)], [MI(2)(CO)(3)(pypzH)] (M = Mo, W) from [Mo(CO)(4)(NBD)] or the adequate bis(acetonitrile) complexes. The deprotonation of the molybdenum allyl or methallyl complexes affords the bimetallic complexes [cis-{Mo(η(3)-allyl)(CO)(2)(μ(2)-pypz)}](2) or [cis-{Mo(η(3)-methallyl)(CO)(2)(μ(2)-pypz)}](2) (μ(2)-pypz = μ(2)-3-(2-pyridyl-κ(1)N)pyrazolate-2κ(1)N). The allyl complex was subjected to an electrochemical study, which shows a marked connection between both metallic centres through the bridging pyridylpyrazolates.     

Structure and evolution of strange attractors in non-elastic triangular billiards

We study non-elastic billiard dynamics in an equilateral triangular table. In such dynamics, collisions with the walls of the table are not elastic, as in standard billiards; rather, the outgoing angle of the trajectory with the normal vector to the boundary at the point of collision is a uniform factor λ < 1 smaller than the incoming angle. This leads to contraction in phase space for the discrete-time dynamics between consecutive collisions, and hence to attractors of zero Lebesgue measure, which are almost always fractal strange attractors with chaotic dynamics, due to the presence of an expansion mechanism. We study the structure of these strange attractors and their evolution as the contraction parameter λ is varied. For λ∈(0,1/3), we prove rigorously that the attractor has the structure of a Cantor set times an interval, whereas for larger values of λ gaps arise in the Cantor structure. For λ close to 1, the attractor splits into three transitive components, whose basins of attraction have fractal boundaries.     

Asymmetric Nucleophilic Monofluorobenzylation of Carbonyl Compounds: Synthesis of Enantiopure vic‐Fluorohydrins and α‐Fluorobenzylketones

Asymmetric nucleophilic monofluoroalkylation of a broad range of aldehydes with an α‐fluoro‐γ‐sulfinylbenzyl carbanion takes place with complete control of the facial selectivity at the carbanion and good to high anti‐diastereoselectivity to give easily separable mixtures of two optically pure 1,2‐fluorohydrin derivatives (up to 24:1 anti/syn). Separation and removal of the p‐tolylsulfinyl group with tBuLi provides enantiomerically pure anti‐1,2‐disubstituted‐1,2‐fluorohydrins, whereas α‐fluorobenzylketones can be obtained by desulfinylation of the mixture followed by pyridinium chlorochromate oxidation (one‐pot process).