Convergence to equilibrium of critical branching particle systems and superprocesses,and related nonlinear partial differential equations

We consider a class of multitype particle systems in ^d undergoing spatial diffusion and critical stable multitype branching, and their limits known as critical stable multitype Dawson-Watanabe processes, or superprocesses. We show that for large classes of initial states, the particle process and the superprocess converge in distribution towards known equilibrium states as time tends to infinity. As an application we obtain the asymptotic behavior of a system of nonlinear partial differential equations whose solution is related to the distribution of both the particle process and the superprocess.Research partially supported by CONACyT (Mexico), CNRS (France) and BMfWuF (Austria).     

The bestL 2-approximation by finite sums of functions with separable variables

Summary We consider the problem of the best approximation of a given functionh L ² (X × Y) by sums _k=1 ⁿ f _k f _k, with a prescribed numbern of products of arbitrary functionsf _k L ² (X) andg _k L ² (Y). As a co-product we develop a new proof of the Hilbert—Schmidt decomposition theorem for functions lying inL ² (X × Y).     

The dating of Ptolemy's Almagest based on the coverings of the stars and on lunar eclipses

This paper is a natural extension and continuation of the authors' studies of the astronomical dating problem of Ptolemy's famous Almagest. In previous papers, the authors suggested and developed a new geometrical-statistical method for dating ancient star catalogues. This method was then applied to Ptolemy's Almagest. The results obtained do not confirm the traditional dating of the Almagest (2nd century AD or 2nd century BC) but shift it to the epoch AD 600–1300. In this paper, we extend our analysis to other parts of the Almagest and study the dating problem for series of lunar eclipses described in the Almagest and for the covering of stars by planets. The results obtained completely agree with our previous results and give the same time interval, AD 600–1300.     

Well posed cauchy problems for complex nonlinear equations must be semilinear

The first author was supported in part by CNPq     

Dirichlet norms,capacities and generalized isoperimetric inequalities for Markov operators

We define the notion of p-capacity for a reversible Markov operator on a general measure space and prove that uniform estimates for the ratio of capacity and measure are equivalent to certain imbedding theorems for the Orlicz and Dirichlet norms. As a corollary we get results on connections between embedding theorems and isoperimetric properties for general Markov operators and, particularly, a generalization of the Kesten theorem on the spectral radius of random walks on amenable groups for the case of arbitrary graphs with non-finitely supported transition probabilities.     

全气相化学激光体系的直流放电研究

 为了提高化学激光体系(AGIL)中F原子的产率，采用直流放电引发方式，对棒式电极的放电特性进行了研究。在对NF3/He混合气体进行解离时，通过选择不同平衡电阻，得到了3 kW左右的放电注入功率。用光谱分析仪对F原子产率进行了测量。通过拟合计算可得：一个NF3分子能够解离出1.3～1.5个F原子。     

Optical characterization of thin thermal oxide films on copper by ellipsometry

A complete optical characterization in the visible region of thin copper oxide films has been performed by ellipsometry. Copper oxide films of various thicknesses were grown on thick copper films by low temperature thermal oxidation at 125 °C in air for different time intervals. The thickness and optical constants of the copper oxide films were determined in the visible region by ellipsometric measurements. It was found that a linear time law is valid for the oxide growth in air at 125 °C. The spectral behaviour of the optical constants and the value of the band gap in the oxide films determined by ellipsometry in this study are in agreement with the behaviour of those of Cu₂O, which have been obtained elsewhere through reflectance and transmittance methods. The band gap of copper oxide, determined from the spectral behaviour of the absorption coefficient was about 2 eV, which is the generally accepted value for Cu₂O. It was therefore concluded that the oxide composition of the surface film grown on copper is in the form of Cu₂O (cuprous oxide). It was also shown that the reflectance spectra of the copper oxide–copper structures exhibit behaviour expected from a single layer antireflection coating of Cu₂O on Cu. Received: 19 July 2001 / Accepted: 27 July 2001 / Published online: 17 October 2001     

分子超激发态结构的理论研究:F2离子对解离效率谱研究

在量子数亏损理论框架下,利用多重散射自洽场方法和Feynman传播子算法研究了高分辨的F2分子超激发态结构;该超激发态能够解离为正负离子对F^＋（^3P2,1,0）＋F^-（^1S0）.理论分析能够清楚地标识其振动分辨谱,并很好地与实验测量符合.文章还阐述了发展分子超激发态结构研究的前景.     

Spectral line competition in a coaxial electron-beam-pumped high pressure Ar/Xe laser

In order to study the kinetic mechanism of the e-beam pumped Ar/Xe laser, the temporal profiles of individual laser lines during multiline oscillation have been measured as a function of power deposition (1–12MW/cm³) and gas laser pressure (2–14 bar) using a short pulse (30 ns) coaxial electron beam as excitation source. It was found that the optimum output energy at each pressure was obtained at the same specific power deposition.Strong line competition has been observed between the 2.65 and 1.73 m transitions. In order to explain our results we suggest that besides electron collision mixing (ECM) between the 5d and 6p levels of Xe, there is also a redistribution between all 6p levels which strongly favours the lower levels at higher pumping densities.