Electric-field-driven deracemization.

We demonstrate, both theoretically and experimentally, that it is possible to use an electric field to drive the formation of macroscopic chiral (conglomerate) domains from an initially homogeneous fluid racemate. Field-induced segregation is exhibited in a fluid smectic liquid-crystal phase of a racemic mesogen, wherein enantiomerically-enriched domains are readily identifiable by their chiral electro-optical response. The sharp field-generated boundaries that form between opposite-handed domains broaden by diffusion in the absence of field, but reform rapidly if the field is switched on again, providing unambiguous evidence for the field-driven physical separation of enantiomers. A mean-field model successfully describes the steady-state and the dynamic evolution of conglomerate formation.     

基于SVR和k-近邻群的组合预测在QSAR中的应用

为提高定量构效关系(QSAR)研究的预测精度,发展了一种新的基于支持向量机回归(SVR)非线性筛选分子结构描述符、基于k-近邻群的非线性组合预测方法.首先以均方误差(MSE)最小为原则,以留一法通过多轮末尾淘汰实施分子结构描述符的非线性SVR汰选并给出最优核函数和相应保留描述符;其次基于待测样本与训练样本保留描述符向量的欧氏距离,以不同k-近邻群子模型双重留一法预测值反映样本集的异质性;然后基于MSE最小,以留一法通过多轮末尾淘汰实施近邻群子模型的非线性SVR汰选并给出最优核函数和相应保留子模型;最后基于保留子模型以双重留一法实施组合预测.以取代苯胺和苯酚类化合物对大型溞的QSAR实例验证表明:新方法在所有参比模型中预测精度最高,且能更精细地反映描述符与化合物毒性间的非线性关系,具结构风险最小、非线性、适于小样本,能有效克服过拟合、维数灾和局极小,非线性筛选描述符和子模型,非线性组合预测,自动选择最优核函数及其相应参数,泛化推广能力优异、预测精度高等诸多优点,在QSAR研究中有广泛应用前景.     

带有随机初值的复值Ginzburg-Landau方程的弱平均动力学*

本文研究了无界域上的带有随机初值的复值Ginzburg-Landau方程.首先, 基于解过程的全局适定性, 建立了带有随机初值的Ginzburg-Landau方程的平均随机动力系统.然后, 证明了弱拉回平均随机吸引子的存在唯一性以及随机吸引子的周期性,并将其进一步推广到加权空间L²(?, L²_σ(R)).     

Estimation of a quantile in some nonstandard cases

A necessary condition for the asymptotic normality of the sample quantile estimator isf(Q(p))=F(Q(p))>0, whereQ(p) is thep-th quantile of the distribution functionF(x). In this paper, we estimate a quantile by a kernel quantile estimator when this condition is violated. We have shown that the kernel quantile estimator is asymptotically normal in some nonstandard cases. The optimal convergence rate of the mean squared error for the kernel estimator is obtained with respect to the asymptotically optimal bandwidth. A law of the iterated logarithm is also established.This research was partially supported by the new faculty award from the University of Oregon.     

Characterizations based on conditional expectations of the doubled truncated distribution

The expression of the continuous distribution function F(x) is obtained whenever % MathType!MTEF!2!1!+-% feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXafv3ySLgzGmvETj2BSbqefm0B1jxALjhiov2D% aebbfv3ySLgzGueE0jxyaibaiGc9yrFr0xXdbba91rFfpec8Eeeu0x% Xdbba9frFj0-OqFfea0dXdd9vqaq-JfrVkFHe9pgea0dXdar-Jb9hs% 0dXdbPYxe9vr0-vr0-vqpWqaaeaabiGaciaacaqabeaadaqaaqGaaO% qaaerbhv2BYDwAHbacfiGaa8xBaiaabIcacaWG4bGaaiilaiaadMha% caqGPaGaa8hiaiaab2dacaWFGaGaa8xraiaa-HcacaWFybGaa8hiai% aa-XhacaWFGaGaa8hEaiaa-bcacqGHKjYOcaWFGaGaa8hwaiaa-bca% cqGHKjYOcaWFGaGaa8xEaiaa-Lcaaaa!53EE!\[m{\rm{(}}x,y{\rm{)}} {\rm{ = }} E(X | x \le X \le y)\]is known. Moreover, we obtain the necessary and sufficient conditions so that any function m: ² is the conditional expectation % MathType!MTEF!2!1!+-% feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXafv3ySLgzGmvETj2BSbqefm0B1jxALjhiov2D% aebbfv3ySLgzGueE0jxyaibaiGc9yrFr0xXdbba91rFfpec8Eeeu0x% Xdbba9frFj0-OqFfea0dXdd9vqaq-JfrVkFHe9pgea0dXdar-Jb9hs% 0dXdbPYxe9vr0-vr0-vqpWqaaeaabiGaciaacaqabeaadaqaaqGaaO% qaaiaadweacaGGOaGaamiwaerbhv2BYDwAHbacfiGaa8hiaiaacYha% caWFGaGaa8hEaiaa-bcacqGHKjYOcaWFGaGaa8hwaiaa-bcacqGHKj% YOcaWFGaGaa8xEaiaacMcaaaa!4D0D!\[E(X | x \le X \le y)\]of a random variable X with continuous distribution function. Furthermore, we relate m(x,y) to order statistics.     

A global pinching theorem for compact surfaces inS 3 with constant mean curvature

LetM be a compact minimal surface inS ³. Y. J. Hsu^[5] proved that if S₂22, thenM is either the equatorial sphere or the Clifford torus, whereS is the square of the length of the second fundamental form ofM, ·₂ denotes theL ²-norm onM. In this paper, we generalize Hsu's result to any compact surfaces inS ³ with constant mean curvature.Supported by NSFH.     

Cyclical games with prohibitions

We consider a certain combinatorial game on a digraph for two cases of the price function. For one case the game in question extends the cyclical game studied in Ehrenfeucht and Mycielski (1979) and Gurvitch, Karzanov and Khachiyan (1988) which, in its turn, is a generalization of the well-known problem of finding a minimum mean cycle in an edge-weighted digraph. We prove the existence of optimal uniform stationary strategies for both cases and give algorithms to find such strategies.This work was partially supported by Chaire municipale, Mairie de Grenoble.     

Characterization of distribution of pi-electrons amongst benzenoid rings for Randić’s “algebraic” Kekulé structures

For benzenoid hydrocarbons the distribution of pi-electrons amongst rings is characterized in the context of Randis mode of assignment attending to the different Kekulé structures. In particular the mean and mean deviation from the mean are considered, and the benzenoids which achieve maximum deviation are identified.     

Ionic Interactions of Calcium Sulfate Dihydrate in Aqueous Sodium Chloride Solutions: Solubilities,Densities, Viscosities,Electrical Conductivities,and Surface Tensions at 35 <Superscript>∘</Superscript>C

The thermodynamic, volumetric, transport, and surface properties, solubilities, densities, viscosities, electrical conductivities, and surface tensions of calcium sulfate dihydrate in aqueous sodium chloride solutions have been measured at 35 C, with a view to determine the ionic interactions that occur in these solutions. The experimental density values have been used to calculate the mean apparent molar volumes of the ternary mixtures. Viscosity values have been analyzed using different empirical equations and the experimental values of the viscosity were combined with conductivity to yield the Walden product. Molar surface energies have been computed using experimental surface tension data. The experimental data have been fitted to polynomial equations by a least-squares analysis to obtain the coefficients and their standard errors. Results have been examined in the light of structure making or structure breaking effects of the various ions present in the solutions.     

Methodology for the calculation of the potential of mean force for a cation-pi complex in water.

We report potential of mean force (PMF) calculations on the interaction between the p-sulfonatocalix[4]arene and a monovalent cation (Cs(+)). It has been recently shown from microcalorimetry and (133)Cs NMR experiments that the association with Cs(+) is governed by favourable cation-pi interactions and is characterized by the insertion of the cation into the cavity of the macrocycle. We show that the PMF calculation based upon a classical model is not able to reproduce both the thermodynamic properties of association and the insertion of the cation. In order to take into account the different contributions of the cation-pi interactions, we develop a new methodology consisting of changing the standard PMF by an additional contribution resulting from quantum calculations. The calculated thermodynamic properties of association are thus in line with the microcalorimetry and (133)Cs NMR experiments and the structure of the complex at the Gibbs free-energy minimum shows the insertion of the cation into the cavity of the calixarene.