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.     

Structure and dynamics of hydrated NH(4) (+): an ab initio QM/MM molecular dynamics simulation

A combined ab initio quantum mechanical/molecular mechanical (QM/MM) molecular dynamics simulation has been performed to investigate solvation structure and dynamics of NH(4) (+) in water. The most interesting region, the sphere includes an ammonium ion and its first hydration shell, was treated at the Hartree-Fock level using DZV basis set, while the rest of the system was described by classical pair potentials. On the basis of detailed QM/MM simulation results, the solvation structure of NH(4) (+) is rather flexible, in which many water molecules are cooperatively involved in the solvation shell of the ion. Of particular interest, the QM/MM results show fast translation and rotation of NH(4) (+) in water. This phenomenon has resulted from multiple coordination, which drives the NH(4) (+) to translate and rotate quite freely within its surrounding water molecules. In addition, a "structure-breaking" behavior of the NH(4) (+) is well reflected by the detailed analysis on the water exchange process and the mean residence times of water molecules surrounding the ion.     

The self-consistent mean spherical approximation for the one-component plasma

The consequences of choosing the adjustable hard-core diameter in the mean spherical approximation for the one-component plasma so as to achieve thermodynamic consistency between the energy and compressibility equations are investigated. Such a choice is found to be possible only for >8.5 and, although the resulting correlation functions are discontinuous, the height of the main peak in the static structure factor is remarkably accurate. Two especially noteworthy aspects of the thermodynamic results are that the compressibility equation is much more accurate than in any previous approximation free of input from computer simulations and that the nonstatic part of the internal energy has a ^1/4 dependence in the strong coupling limit in agreement with Monte Carlo data.