Stereoisomeric flavor compounds LXXVII: 3-Butylhexahydrophthalides: Simultaneous enantioselective analysis,structure elucidation,and sensorial properties of the stereoisomers

Using heptakis-(2,3-di-O-acetyl-6-O-tert-butyldimethylsilyl)-β-cy-clodextrin as the chirul stationary phase in enantioselective gas chromatography, the simultaneous enantioselective analysis of all eight 3-butylhexahydrophthalide Stereoisomers was achieved. Fur-thermore, the odor characteristics and odor thresholds were investigated by enantioselective gas chromatography/olfactometry. Racemic standards were synthesized via hydrogenation and subsequent base catalyzed epimerization. Starting from racemic 3-butylphthalide. After separation by high performance liquid chromatography. Relative configurations of the pure diastereoisom-ers were determined by means of NOE-difference spectroscopy. The absolute configuration at C-3 was determined starting from (3S)-butylphthalide as an educt for hydrogenation and epimerization. Absolute configurations of all eight 3-butylhexahydrophtbalide stereoisomers are unambiguously concluded from the NOE-experi-ments in connection with the determination of the absolute configuration at C-3.     

Measure transport on Wiener space and the Girsanov theoremTransport de mesure sur l'espace de Wiener et théorème de Girsanov

Let (W,H,μ) be an abstract Wiener space, and assume that ν_i, i=1,2, are two probability measures on $\text{(W,}\text{B}\text{(W))}$ which are absolutely continuous with respect to μ. Assume that the Wasserstein distance between ν₁ and ν₂ is finite. Then there exists a map T=I_W+ξ of W into itself such that ξ:W→H is measurable and 1-cyclically monotone such that the image of ν₁ under T is ν₂. Moreover T is invertible on the support of ν₂. We give also some applications of this result such as the existence of the solutions of the Monge–Ampère equation in infinite dimensions. <strong>To cite this article: D. Feyel, A.S. Üstünel, C. R. Acad. Sci. Paris, Ser. I 334 (2002) 1025–1028.strong>     

Iterated maximal functions in variable exponent Lebesgue spaces

In this paper we study the iterated Hardy?CLittlewood maximal operator in variable exponent Lebesgue spaces with exponent allowed to reach the value 1. We use modulars where the L ^p(·)-modular is perturbed by a logarithmic-type function, and the results hold also in the more general context of such Musielak?COrlicz spaces.     

Uniformly Separated Sets and Gromov Hyperbolicity of Domains with the Quasihyperbolic Metric

In this article we prove comparative results on the Gromov hyperbolicity of plane domains equipped with the quasihyperbolic metric. By a comparative result we mean one which assumes hyperbolicity in one domain and obtains it in a different domain somehow related to the original one. We derive a characterization (simple to check in practical cases) of the Gromov hyperbolicity of a plane domain Ω* obtained by deleting from the original domain Ω any uniformly separated union of compact sets. We present as well a result about stability of hyperbolicity.     

Unraveling the Beautiful Complexity of Simple Lattice Model Polymers and Proteins Using Wang-Landau Sampling

We describe a class of “bare bones” models of homopolymers which undergo coil-globule collapse and proteins which fold into their native states in free space or into denatured states when captured by an attractive substrate as the temperature is lowered. We then show how, with the use of a properly chosen trial move set, Wang-Landau Monte Carlo sampling can be used to study the rough free energy landscape and ground (native) states of these intriguingly simple systems and thus elucidate their thermodynamic complexity.     

Doi–Hopf Modules Associated to Comodule Coalgebras

To any right comodule coalgebra C over a Hopf algebra H we associate a left H-comodule algebra A. Under certain conditions, in particular in the case where H has nonzero integrals, we show that the category of right C, H-comodules is isomorphic to a certain subcategory of the category of Doi–Hopf modules associated to A. As an application, we investigate the connection between C and the smash coproduct C ? H being right semiperfect.     

Inequality constrained ridge regression estimator

We carry out the idea of inequality constrained least squares (ICLS) estimation of Liew (1976) to the inequality constrained ridge regression (ICRR) estimation. We propose ICRR estimator by reducing the primal–dual relation to the fundamental problem of Dantzig and Cottle, 1967, Cottle and Dantzig, 1974 with Lemke (1962) algorithm. Furthermore, we conduct a Monte Carlo experiment.