FI代数的滤子

研究FI代数的滤子理论，建立F滤子、P滤子、Q滤子、C滤子之间的联系．     

Inégalités de Gagliardo-Nirenberg pour les semi-groupes d'opérateurs et applications

One shows the equivalence between an abstract form of a Gagliardo-Nirenberg inequality and an estimate of the decay of the L ¹–L norm of a semigroup of operators. This equivalence, contrary to the one with the classical Sobolev inequalities, allows the treatment of situations where the decay is exponential. Related results and applications are given.

Cet article a pu être terminé pendant un séjour de l'auteur à l'université d'Edimbourg.     

Polyèdre de Newton et distributionf + s . II

Sans résumé

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On the Shintani zeta function for the space of binary quadratic forms

Partially supported by NSF Grant DMS-8803085, DMS-8610730     

On Gauss's proof of Seeber's Theorem

Summary Gauss proved Seeber's Theorem, that the determinant of a reduced positive definite ternary quadratic form is at least half the product of its diagonal coefficients, by means of two determinantal identities whose origin has remained unclear. We examine Gauss's method from a general standpoint, as a method whereby, in certain circumstances, a polynomial in several variables may be shown to be non-negative on a convex polytope by representing it as a positive multilinear combination of the linear forms which determine the polytope. We show that Gauss's identities may be obtained in this manner and that the two identities can in fact be replaced by a simpler single identity which also gives Oppenheim's precise minimum for the determinant.     

Efficient parallel algorithms for shortest paths in planar digraphs

Efficient parallel algorithms are presented, on the CREW PRAM model, for generating a succinct encoding of all pairs shortest path information in a directed planar graphG with real-valued edge costs but no negative cycles. We assume that a planar embedding ofG is given, together with a set ofq faces that cover all the vertices. Then our algorithm runs inO(log² n) time and employsO(nq+M(q)) processors (whereM(t) is the number of processors required to multiply twot×t matrices inO(logt) time). Let us note here that wheneverq<n then our processor bound is better than the best previous one (M(n)).O(log² n) time,n-processor algorithms are presented for various subproblems, including that of generating all pairs shortest path information in a directedouterplanar graph. Our work is based on the fundamental hammock-decomposition technique of G. Frederickson. We achieve this decomposition inO(logn log*n) parallel time by usingO(n) processors. The hammock-decomposition seems to be a fundamental operation that may help in improving efficiency of many parallel (and sequential) graph algorithms.This work was partially supported by the EEC ESPRIT Basic Research Action No. 3075 (ALCOM) and by the Ministry of Industry, Energy and Technology of Greece.     

Convergence rate estimate for a domain decomposition method

Summary We provide a convergence rate analysis for a variant of the domain decomposition method introduced by Gropp and Keyes for solving the algebraic equations that arise from finite element discretization of nonsymmetric and indefinite elliptic problems with Dirichlet boundary conditions in ². We show that the convergence rate of the preconditioned GMRES method is nearly optimal in the sense that the rate of convergence depends only logarithmically on the mesh size and the number of substructures, if the global coarse mesh is fine enough.This author was supported by the National Science Foundation under contract numbers DCR-8521451 and ECS-8957475, by the IBM Corporation, and by the 3M Company, while in residence at Yale UniversityThis author was supported by the Applied Mathematical Sciences subprogram of the Office of Energy Research, U.S. Department of Energy under Contract W-31-109-Eng-38This author was supported by the National Science Foundation under contract number ECS-8957475, by the IBM Corporation, and by the 3M Company     

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.