The harmonic decomposition reconstruction for the exponential radon transform

The exponential Radon transform, a generalization of the Radon transform, is defined and studied as a mapping of function spaces. It is represented in terms of Fourier transform of its domain and range, and this leads to the harmonic decomposition reconstruction. The results are similar results of Tretiak and Metz. Foundation item: Supported by the National Natural Science Foundation of China (No. 19971064), Key Project of Science and Technology of Hubei Province Education Committee. Biography: Wang Jin-ping (1963-), male, Ph.D. candidate, research direction: numberical solution of singular integral equation and integral transformation etc.     

Resource Search in Unstructured Peer-to-Peer System Based on Multiple-Tree Overlay Structure

We propose a multiple-tree overlay structure for resource discovery in unstructured P2P systems. Peers that have similar interests or hold similar type of resources will be grouped into a tree-like cluster. We exploit the heterogeneity of peers in each cluster by connecting peers with more capacities closer to the root of the tree. The capacity of a peer can be defined in different ways （e.g. higher network bandwidth, larger disk space, more data items of a certain type etc.） according to different needs of users or applications.     

On the verge of <Emphasis Type="Italic">Umdeutung</Emphasis> in Minnesota: Van Vleck and the correspondence principle. Part one

In October 1924, The Physical Review, a relatively minor journal at the time, published a remarkable two-part paper by John H. Van Vleck, working in virtual isolation at the University of Minnesota. Using Bohr’s correspondence principle and Einstein’s quantum theory of radiation along with advanced techniques from classical mechanics, Van Vleck showed that quantum formulae for emission, absorption, and dispersion of radiation merge with their classical counterparts in the limit of high quantum numbers. For modern readers Van Vleck’s paper is much easier to follow than the famous paper by Kramers and Heisenberg on dispersion theory, which covers similar terrain and is widely credited to have led directly to Heisenberg’s Umdeutung paper. This makes Van Vleck’s paper extremely valuable for the reconstruction of the genesis of matrix mechanics. It also makes it tempting to ask why Van Vleck did not take the next step and develop matrix mechanics himself. This paper was written as part of a joint project in the history of quantum physics of the Max Planck Institut für Wissenschaftsgeschichte and the Fritz-Haber-Institut in Berlin.     

The Response of Debris-Flow Events to Solar Proton Flares （Ⅰ）

By analyzing the observation data from Dongchuan Debris Flow Observation and Research Station and historical data from year 1965 to 1990 gotten from National Astronomical Ob-servatories/Yunnan Observatory,the responding of debris flow in Jiangjia Ravine to Solar Proton Flare is studied. The following conclusion can be drawn. Solar Proton Flare,as one of most im-portant astronomical factors,affects the activity of debris flow in Yunnan. Generally,from 1965 to1990,the more active Solar Pro-ton Flare is,the greater the probability of high frequency and large runoff of debris flow is. On the contrary,the less active Solar Pro-ton Flare is,the greater the probability of low frequency,small runoff,and low sediment transport of debris flow is.     

Heterostructure in ZnO Nano-Tetrapods

1 Introduction 　　Nanoscale science and technology have attracted greatattention since the novel properties become dominant for well-known materials as their sizes reduced to some critical dimension. These properties frequently originate in lattice distortions, structure transformations etc[1]. The variations of size and structure ofnanocrystals lead to the change of their electronic structures. Very recently, nanoscale materials with different electronic structures were utilized in fabricating nanoscale junctions[2]. 　　……     

Which survey indicators are useful for monitoring consumption? Evidence from European countries

This paper assesses the information content of two survey indicators for consumption developments in the near future for eight European countries in the period 1985–1998. Empirical work on this topic typically focuses on consumer confidence, the perceptions of buyers of consumption goods. This paper examines whether perceptions of sellers of consumption goods, measured by retail trade surveys, may also improve short‐term monitoring of consumption. We find that both consumer confidence and retailer confidence embody valuable information, when analysed in isolation. For France, Italy and Spain we conclude that adding retail confidence does not improve the indicator model once consumer confidence has been included. For the UK the reverse case is obtained. For the remaining four countries we show that combining consumer sentiment and retail trade confidence into a composite indicator leads to optimal results. Our results suggest that incorporating information from retail trade surveys may offer significant benefits for the analysis of short‐term prospects of consumption. Copyright © 2004 John Wiley & Sons, Ltd.     

Exponential smoothing: Behavior of the ex-post sum of squares near 0 and 1

When using simple exponential smoothing on a given time series the nature of the relationship between the optimal smoothing constant and the autocorrelation structure of the series remains an unresolved question. Although numerical search routines can easily be used to find optimal values of the smoothing constant, they offer little insight into the nature of the relationship between the estimated smoothing constant and the structure of the underlying time series. We suggest that renewed investigations of the ex-post sum of squares function may prove helpful in this pursuit. Results are presented that illustrate how the optimal smoothing constant depends upon the value used to initialize the smoothing and upon the sample autocorrelation coefficients of the observed series. These results are based on a new formula for the derivative of the ex-post sum of squares function. In particular, the derivative is examined near 0 and 1, where great simplifications occur in its form, thereby facilitating investigations near these points. A necessary and sufficient condition is stated for when the ex-post sum of squares must have a positive derivative at 0 and the autocorrelation coefficients of the differenced series are shown to affect the sign of the derivative near 1. Based on these results, a general algorithm is presented as an alternative to grid search routines for minimizing the ex-post sum of squares.