A Stein deficit for the logarithmic Sobolev inequality

We provide some lower bounds on the deficit in the Gaussian logarithmic Sobolev inequality in terms of the so-called Stein characterization of the Gaussian distribution. The techniques are based on the representation of the relative Fisher information along the Ornstein-Uhlenbeck semigroup by the Minimum Mean-Square Error from information theory.     

Structural modulation of the dipolar-octupolar contributions to the NLO response in subphthalocyanines

Second order nonlinear optical properties of a series of trinitrosubphthalocyanine (SubPc) isomers were studied experimentally by electric field induced second harmonic (EFISH) generation and hyper Rayleigh scattering (HRS). These experimental values were compared to the ones obtained theoretically employing both sum over states (SOS) and finite field (FF) methods. From these studies, it was shown that the dipolar contributions to the beta tensor are very much dependent on the substitution pattern at the periphery of the subphthalocyanine macrocycle, whereas the octupolar contributions remain mostly unchanged. Consequently, it was deduced that SubPc is extremely well suited for the decoupling of octupolar and dipolar contribution to the NLO response.     

Crystal Structures and Packing of 2,4,6-tris(4-Fluorophenoxy)-1,3,5-triazine and 2,4,6-tris(3,4-Dimethylphenoxy)-1,3,5-triazine. New Materials for Octupolar Nonlinear Optics

The crystal structures and packing of 2,4,6-tris(4-fluorophenoxy)-1,3,5-triazine and 2,4,6-tris(3,4-dimethylphenoxy)-1,3,5-triazine are discussed. These structures have been determined as a continuation of a series of octupolar NLO materials we have been investigating. The crystal structures are characterized by C–H...F and C–H... hydrogen bonds, respectively. A characteristic of these triazine structures is the presence of dimeric Piedfort Units (PU) that are extended into more elaborate two-dimensional (2-D) networks. The structure of the fluoro derivative is compared with that of the corresponding unsubstituted and chloro/bromo-substituted derivatives. The structure of the dimethyl triazine is compared with that of the corresponding 4-methyl derivative. The noncentrosymmetric nature of the dimethyl derivative was confirmed by a powder SHG signal at 1.064 m of the order of 0.5 × KDP. Interestingly, the dimethyl derivative studied here is isostructural with the corresponding 4-methyl triazine. This H/Me isostructurality is shown to be an uncommon phenomenon by an analysis with the CSD.     

Loi du logarithme itéré dans C S) et fonction caractéristique empirique

Sommaire De nombreuses publications ont été consacrées ces dernières années à l'étude des propriétés limites des variables aléatoires lipschitziennes. Si le théorème de la limite centrale a trouvé dans les travaux de N.C. Jain et M.B. Marcus [9] et B. Heinkel [7] des conditions suffisantes en un sens meilleures possibles, la loi du logarithme itéré, bien qu'apparaisant comme corollaire immédiat de la propriété de limite centrale, était toujours à la recherche de conditions spécifiques. Nous présentons, dans notre première partie, une loi du logarithme itéré pour les variables aléatoires lipschitziennes sous des hypothèses qui lui sont propres. Dans la seconde, nous appliquons les techniques du cas lipschitzien à l'étude de la fonction caractéristique empirique en vue de préciser, dans leurs parties loi du logarithme itéré, les récents résultats de M.B. Marcus [15] et S. Csörg [3] concernant les propriétés limites de la fonction caractéristique empirique.     

Dipolar donor-acceptor-substituted schiff base complexes with large off-diagonal second-order nonlinear optical tensor components

The synthesis, characterization, and two-dimensional second-order nonlinear optical (NLO) response of a dipolar NiII donor- acceptor Schiff base complex and the related ligand are reported. Electric-field-induced second-harmonic generation and harmonic light (hyper-Rayleigh) scattering techniques, in combination with INDO/SCI-SOS theoretical calculations, were used to investigate the vector part of the hyperpolarizability tensor and the two-dimensional character of the molecular nonlinearity, respectively. Off-diagonal hyperpolarizability tensors can be related to charge-transfer transitions that are polarized perpendicular to the molecular dipolar axis, while parallel transitions account for the diagonal hyperpolarizability tensor. The role of the metal center in enhancing the two-dimensional NLO response of such molecules is twofold since it acts both as the donor and the bridging moiety of the planar donor-(pi-conjugate-bridge)-acceptor system. These dipolar two-dimensional molecules are interesting candidates from the perspective of polarization-independent NLO materials.     

Electrophoretic separation strategy for chiral pharmaceuticals using highly-sulfated and neutral cyclodextrins based dual selector systems

The enantiomeric separation of chiral pharmaceuticals was investigated using dual systems with mixtures of cyclodextrin derivatives. The dual cyclodextrin systems, consisting of one highly-sulfated (α-, β-, and γ-HSCD) and one neutral cyclodextrin, i.e. either heptakis (2,3,6-tri-O-methyl)-β-CD (TMCD), heptakis (2,6-di-O-methyl)-β-CD (DMCD) or hydroxypropyl-β-CD (HPCD), are tested on 25 pharmaceutical compounds with different acid-basic properties (16 basics, 8 acids and 1 neutral). The influence on the separation of the type and concentration of neutral CD in highly-sulfated cyclodextrins-based dual selector systems, is investigated. For 11 of 16 basic compounds, a better separation is obtained with the CD mixtures compared to the use of only a highly-sulfated CD. Mixtures with TMCD give better results than those with DMCD and HPCD. Results showed that dual CD systems are useful to achieve and to optimise chiral separations of compounds not (sufficiently) separated with HSCDs alone. For example, ibuprofen was not resolved with α-, β- or γ-HSCD, but could be separated with the mixture 25 mM TMCD and 5% HS-β-CD. Based on the obtained results, a dual CD systems based separation strategy is defined.     

Extreme values and a Gaussian central limit theorem

Summary We examine the central limit theorem with Gaussian limit law for a sequence of independent, identically distributed, vector valued random variables whose partial sums can be centered and normalized to be tight with non-degenerate limit laws. These results apply to the situation when the sequence is in the domain of attraction of a non-degenerate stable law of indexp(0,2], and are achieved by eliminating the extreme values from the partial sums.Supported in part by NSF Grant MCS-8219742Work done while visiting the University of Wisconsin, Madison, with partial support by NSF Grant MCS-8219742