An algebraic approach to the vector ε-algorithm

The vector -algorithm is obtained from the scalar -algorithm by taking the pseudo-inverse of a vector instead of the inverse of a scalar. Thus the vector -algorithm is known only through its rules contrarily to the scalar -algorithm and some other extrapolation algorithms.The aim of this paper is to provide an algebraic approach to the vector -algorithm.     

Explicit inertial range renormalization theory in a model for turbulent diffusion

The inertial range for a statistical turbulent velocity field consists of those scales that are larger than the dissipation scale but smaller than the integral scale. Here the complete scale-invariant explicit inertial range renormalization theory for all the higher-order statistics of a diffusing passive scalar is developed in a model which, despite its simplicity, involves turbulent diffusion by statistical velocity fields with arbitrarily many scales, infrared divergence, long-range spatial correlations, and rapid fluctuations in time-such velocity fields retain several characteristic features of those in fully developed turbulence. The main tool in the development of this explicit renormalization theory for the model is an exact quantum mechanical analogy which relates higher-order statistics of the diffusing scalar to the properties of solutions of a family ofN- body parabolic quantum problems. The canonical inertial range renormalized statistical fixed point is developed explicitly here as a function of the velocity spectral parameter, which measures the strength of the infrared divergence: for<2, mean-field behavior in the inertial range occurs with Gaussian statistical behavior for the scalar and standard diffusive scaling laws; for>2 a phase transition occurs to a fixed point with anomalous inertial range scaling laws and a non-Gaussian renormalized statistical fixed point. Several explicit connections between the renormalization theory in the model and intermediate asymptotics are developed explicitly as well as links between anomalous turbulent decay and explicit spectral properties of Schrödinger operators. The differences between this inertial range renormalization theory and the earlier theories for large-scale eddy diffusivity developed by Avellaneda and the author in such models are also discussed here.     

Spherical models with a Gates-Penrose-type phase transition

Gates and Penrose have given criteria under which classical gases with weak long-range interactions fail to be described by the van der Waals equation with Maxwell's rule. Unfortunately, examples of equations of state for such systems have not yet been produced. This paper examines the Gates-Penrose class of interactions-i.e.,U (r)=q(r)+(r), in the limit0, where the Fourier transform (p) has a minimum at a nonzero value ofp-for the spherical model on a one-dimensional lattice. Free energy and magnetization isotherms are computed; it is seen that there is a phase transition, but that the zero-field spontaneous magnetization is always zero (a parahelicoidal phase). However, the pair-correlation function may exhibit either long-range order or the appearance of oscillation.     

N(~4S)+NO(X~2II)→N_2(X~3Σ_g~-)+O(~3P)反应的立体动力学(英文)

采用准经典轨线方法研究了在不同碰撞能下,碰撞反应N(4S) NO(X2!)→N2(X3"g-) O(3P)在两个最低势能面3A″和3A′产物与反应物之间的矢量相关.结果表明,对于不同的碰撞能,在两个势能面上反应产物的转动取向展示了不同的特征和趋势.发生在3A″势能面上的反应主要由外平面机理支配,而发生在3A′势能面上的反应倾向于受内平面机理支配.这些差异来自于两个势能面的不同构型.     

Correlations between topological features and physicochemical properties of molecules

The article reviews in brief, thede novo group additivity approach and, at length, the different topological approaches to obtain predictive and internally consistent correlations between various properties and structural features of molecules. The stress has mainly been on the molecular connectivity method. A new rational scheme for nomenclature of connectivity indices of different orders and types is introduced. The concept of the perturbation connectivity parameter developed by us recently has been applied to obtain correlations for molar refraction, boiling point, molar volume, heat of atomisation, heat of combustion, heat of vaporisation, magnetic susceptibility and critical constants of alkanes, alcohols and alkylbenzenes. A comparative study of various approaches reveals that the present perturbation topological approach has an edge over other similar methods.     

基于支持向量机的羰基化合物红外光谱研究

设计了一个4层分等级分类系统，通过支持向量机技术对羰基化合物的红外光谱成功地进行了信息分类和提取，并与人工神经网络进行比较，结果表明：支持向量机对羰基类化合物红外光谱分类效果优于人工神经网络；另外详细探讨了表征酰胺类化合物的特征光谱峰片段对识圳伯仲叔酰胺的影响，证明了酰胺的N-H伸缩振动峰对识别伯仲叔酰胺贡献最大，为构建红外光谱智能解析系统提供了定量依据。     

QSAR Studies on the COX-2 Inhibition by 3,4-Diarylcycloxazolones Based on MEDV Descriptor

Selective inhibition of cyclooxygenase-2 (COX-2) might avoid the side effects of current available nonsteroidal antiinflammatory drugs while retaining their therapeutic efficacy. A novel variable selection and modeling method based on prediction is developed to construct the quantitative structure-activity relationships (QSAR) between the molecular electronegativity distance vector (MEDV) based on 13 atomic types and the biological activities of a set of selective cyclooxygenase-2 inhibitory molecules, 3,4-diarylcycloxazolones (DAA) plus indomethacin,naproxen, and celecoxib. Using multiple linear regression, a 5-variable linear model is developed with the calibrated correlation coefficient of 0.9271 and root mean square error of 0.17 in modeling stage and the validated correlation coefficient of 0.9030 and root mean square error of 0.20 in leave-one-out validation step, respectively. To further test the predictive ability of the model, 20 DAA compounds are picked up to construct a training set which is used to build a QSAR model and then the model is employed to predict the biological activities of the balance compounds. The predicted correlation coefficient and root mean square error are 0.9332 and 0.19, respectively.     

On fluctuations in μ-space

A master equation is derived microscopically to describe the fluctuating motion of the particle density in . space. This equation accounts for the drift motion of particles and is valid for any inhomogeneous gas. The Boltzmann equation is obtained from the first moment of this equation by neglecting the second cumulant (the pair correlation function). The successive moments form coarse-grained BBGKY-like hierarchy equations, in which small spatial regions with r_ij < the force range are smeared out. These hierarchy equations are convenient for investigating the nonequilibrium long-range pair correlation function, which arises mainly from sequences of isolated binary collisions and gives rise to the much-discussed long-time tail and the logarithmic term in the density expansion of transport coefficients. It is shown to have a spatial long tail, like the Coulombic potential, in a steady laminar flow. The stochastic nature of the nonlinear Boltzmann-Langevin equation is also investigated; the random source term is found to be expressed as a linear superposition of Poisson random variables and to become Gaussian in special cases.     

The spherical limit forn-vector correlations

We investigate then limit of then-vector model single-spin and pairspin correlation functions. In this limit we show that the correlation functions become those of the corresponding spherical model.     

Quasi-column chromatography of barbituric acid derivatives II. Separation on Non-polar adsorbents using binary water-organic solvent mixtures as the mobile phase

Summary Twenty barbituric acid derivatives having four different types of substitution were separated in TLC-S chambers. Using non-polar adsorbents (silanized silica gel or silica gel coated with paraffin oil) and binary water-organic solvent mixtures as the mobile phase. Linear relationships between R_M and the concentration of the organic solvent were observed for the majority of the investigated compounds. The non-polar absorbents ensure a better separation than untreated silica gel especially for the therapeutically useful C₅ disubstituted barbiturates. The results can be used for the optimization of the systems for the chromatography of barbiturates. The R_f values were correlated with the number of carbon atoms of the substitutions, molecular connectivity and a parameter associated with the molecular volume. The best correlations were obtained for this last parameter.