Introduction of quantum finite-size effects in the Mie's theory for a multilayered metal sphere in the dipolar approximation: Application to free and matrix-embedded noble metal clusters

A mixed classical/quantum model for calculating the optical response of free and matrix-embedded multilayered metal spheres in the dipolar approximation is presented. The conduction electrons are quantum-mechanically treated in the framework of the time-dependent local-density-approximation formalism (TDLDA), whereas the surrounding matrix, the ionic metal backgrounds and the non-metallic materials are classically described through homogeneous charge distributions or/and dielectric media. Except for the TDLDA calculations, the present formalism is completely analytical and can be applied to coated spheres with any number of metal or dielectric layers. Contrary to the previous TDLDA-based models involving an inner or/and an outer dielectric medium (one or two interfaces), all the dielectric effects (screening and absorption) are self-consistently calculated. In particular, the interband transitions and the mutual interplay between the conduction and core electrons are self-consistently treated. The deficiencies of the previous models are analyzed, and the results are compared with the classical Mie's theory, over the entire spectral range. The building-up of the classical absorption spectrum, consisting of the surface plasmon resonance and the interband transitions, is clearly observed as the cluster size increases. Received 15 March 1999 and Received in final form 11 October 1999     

Infinitely divisible probabilities on discrete linear groups

We investigate the structure of infinitely divisible probability measures on a discrete linear group. It is shown that for any such measure there is an infinitely divisible elementz in the centralizer of the support of the measure, such that the translate of the measure byz is embeddable over the subgroup generated by the support of the measure. Examples are given to show that this reult is best possible.     

On the Local Solubility of Diophantine Systems

Let p be a rational prime number. We refine Brauer's elementary diagonalisation argument to show that any system of r homogeneous polynomials of degree d, with rational coefficients, possesses a non-trivial p-adic solution provided only that the number of variables in this system exceeds (rd ²)^2d-1. This conclusion improves on earlier results of Leep and Schmidt, and of Schmidt. The methods extend to provide analogous conclusions in field extensions of Q, and in purely imaginary extensions of Q. We also discuss lower bounds for the number of variables required to guarantee local solubility.     

Semi-parametric multivariate modelling when the marginals are the same

A model is developed for multivariate distributions which have nearly the same marginals, up to shift and scale. This model, based on “interpolation” of characteristic functions, gives a new notion of “correlation”. It allows straightforward nonparametric estimation of the common marginal distribution, which avoids the “curse of dimensionality” present when nonparametically estimating the full multivariate distribution. The method is illustrated with environmental monitoring network data, where multivariate modelling with common marginals is often appropriate.     

多组判别分析法在恶性卵巢肿瘤B超评分诊断中的应用

为了妇科恶性肿瘤的早期诊断，对病人进行Ｂ型超声波的检查和Ｂ超评分，并把Ｂ超评分数作为初始条件，利用多组判别分析法，将它们划分为良性、过渡性或畸胎瘤和恶性等三类，是利用多元统计分析对妇科恶性肿瘤早期诊断的一种尝试．     

Elliptic equations with indefinite concave nonlinearities near the origin

In this note existence of infinitely many solutions is proved for an elliptic equation with indefinite concave nonlinearities.     

Forms over number fields and weak approximation

Let K be a number field, and let be asmooth complete intersection defined over K. In this paper, weakapproximation is shown to hold for X provided s exceeds some functionof the degree and codimension of X. This is a corollary of a moregeneral result about the number of integral points on certain affine varieties in homogeneously expanding regions. This general result isestablished via a suitable adaptation of the Hardy-Littlewood Circle Method.     

Two interacting particles in a disordered chain IV: Scaling of level curvatures

The curvatures of two-particle energy levels with respect to the enclosed magnetic flux in mesoscopic disordered rings are investigated numerically. We find that the typical value of the curvatures is increased by interactions in the localised regime and decreased in the metallic regime. This confirms a prediction by Akkermans and Pichard (Eur. Phys. J. B 1, 223 (1998)). The interaction-induced changes of the typical curvatures at different energies and disorder strengths exhibit one-parameter scaling with a conductance-like single parameter. This suggests that interactions could influence the conductance of mesoscopic systems similarly. Received 24 August 1998     

Space-Like Form of Bethe-Salpeter Equation: Many Particles

The Gell-Mann and Low's technology and Bethe-Salpeter equation for manyparticles are first discussed. Then the space-like form of Bethe-Salpeter equation involving both the bound state and scatter state are extended to many-particle case. Consequently we build the formalism of the space-like equation with explicit Lorentz covariant form and without the difficulty of ghost states automatically.     

核子配对壳模型计算中的多体效应

戴断到Ｓ,Ｄ子空间的核子配对壳模型用于原子核＾１２８－１３４Ｘｅ和＾１３０－１３６Ｂａ的计算。为考虑多体效应,Ｓ,Ｄ对分别用变分法和Ｔａｍｍ－Ｄａｎｃｏｆｆ近似给定。用一个含有三个参数的哈密顿量系统地描述了Ｘｅ和Ｂａ同位素的能谱,本征态和电磁跃迁的强度。所得结果和实验结果符合得较好,并且在一定程度上改善了用表面δ相互作用决定的Ｓ,Ｄ对所得结果中的不足之处。