Correlation integral as a tool for distinguishing between dynamics and statistics in time series data

We propose a new test for time series data for proper choice of processing technique: dynamical or statistical. It is based upon the normalized slope of the correlation integral (, m) = m⁻¹d(ln C()) /d ln , where m is the embedding dimension. It is shown that when does not tend to 0 on the resolved range of scales as m grows, then there will be serious limitations for dynamical methods even if the data are dynamical by nature. In the latter case it means that the length of time series does not allow to resolve small scales, and on large scales the delay reconstruction for any m mixes true and false neighbours of points and therefore restricts the application of dynamical techniques, such as estimating Lyapunov exponents or predicting time series.     

衍射光学元件的解析分析方法

从波动光学传播的菲涅尔衍射出发，探讨一次光学转换形成任意要求的图形的问题。导得两平行传播平面的函数关系，从而在确定像面分布的条件下可以逆求出原始面的振幅与倍相分布。文中给出了几个实例，充分表明这是有实用价值的一种衍射光学元件设计方法。     

Photoelectron diffraction study of a catalytically active overlayer: C2H2 on Pd{111}

A quantitative structure determination of a newly discovered (2×2) adsorption phase of acetylene chemisorbed on Pd{111} has been performed by scanned-energy mode photoelectron diffraction: this phase corresponds to the threshold coverage for the catalytic conversion of acetylene to benzene. The carbon atoms in the C₂H₂ molecule are located almost over bridge sites with a C–C bond length of 1.34+0.10 Å, the centre of the molecule being positioned almost over a hollow site. Of the two hollow sites the hcp site (directly above a second layer Pd atom) is favoured, particularly by a subset of the data most sensitive to this aspect of the structure, but the full analysis indicates that the fcc site (above a third layer Pd atom) cannot formally be excluded. The adsorption site adopted by acetylene in the higher coverage phase on Pd{111} is essentially identical. This is the dominant structure in the coverage regime which is catalytically active for the conversion of acetylene to benzene. The implications of these findings for acetylene coupling reactions over Pd{111} are discussed.     

一种位相板衍射图样的图像处理新方法

本文介绍了在半导体激光光纤和位相板相结合的准直情况下，利用ＣＣＤ探测器测量大尺寸形位误差的原理，并针对位相板衍射图像的特点，提出了一种处理此类衍射图样的图像处理新方法——投影法。同在时间上采用的多次平均的方法相比较，投影法相当于采用了空间上的平均，消除了ＣＣＤ表面保护玻璃形成的干涉条纹的影响，对空气扰动也起到了很好的抑制作用。并且使二维图像处理变为一维计算，大大提高了计算速度     

On the inversion of the classical second virial coefficient

For a large class of intermolecular potentials, the values of the second virial coefficient at a discrete set of temperature points in an arbitrarily small neighborhood of the origin determine the potential uniquely.     

Measuring the efficiency of trigonometric series estimates of a density

Some types of density estimators, particularly those based on trigonometric series, converge reasonably quickly to their limit except in the neighbourhood of one or two singularities. In this situation the mean integrated square error, the traditional measure of the efficiency of a density estimator, is an unsatisfactory measure. The notion of partial mean integrated square error is introduced and used to compare the performance of trigonometric series estimators. The results lead to consideration of some new estimators which have excellent properties from the points of view of both efficiency and ease of computation.     

Computing particle velocity and intensity in diffracting systems

In a previous paper the authors have shown how it is possible to compute the acoustic pressure due to an axi-symmetric radiator with different boundary conditions. The technique involves the conversion of a double integral to a single integral by means of a geometric transform, and may be applied with the Green's function appropriate to each boundary condition.The present work shows how the form of the single integrals makes it possible to derive and compute both the particle velocity and the wave intensity. It has become apparent that the particle velocity must be described as an elliptic vector. A new concept, the ‘diffraction front’, has been defined as a surface in which there is no net energy transfer, and this has been applied to the evaluation of the magnitude and direction of energy flow. Plots have been made of flow lines and diffraction fronts, and also three-dimensional representations of energy intensity have been made for those acoustic fields in which pressure has already been evaluated.     

Structure determination of Ls-threonine by neutron diffraction

The structure of the aminoacid, L_s-threonine [NH ₃ ⁺ CH(CHOHCH₃)COO^?], space groupP2₁2₁2₁,a=13.630(5),b=7.753(1),c=5.162(2) Å,z=4, has been determined from neutron diffraction data using direct methods. The intensities of 1148 neutron Bragg reflections were measured from a single crystal. The structural parameters were refined by the method of least squares using anisotropic temperature factors. The finalR(F ²) is 0.068. The structure was also refined from the x-ray data of Shoemakeret al (1950J. Am. Chem. Soc. 72 2328); there is good agreement between the two sets of heavy atom parameters. The parameters of hydrogen atoms are of course more precisely determined in our neutron study. The molecular conformation and the hydrogen bonding scheme are discussed. Weighted average values of bond distances and angles from 14 aminoacid structures with ionized carboxylic groups studied by neutron diffraction at Brookheven and Trombay are also presented.