MAJORATION DU NOMBRE DE RÉSONANCES PRÈS DE L'AXE RÉEL POUR UNE PERTURBATION ABSTRAITE À SUPPORT COMPACT DU LAPLACIEN

For compactly supported perturbations of Laplacian on R ⁿ , we show that the number of resonances of modulus ≤ r in a small angle θ near the real axis, can be bounded by the phase space volume of the union of certain trapped trajectories plus the counting function for a reference problem. This result can be useful to understand the relationship between resonances and the microlocal geometry of the problem.     

REMARQUES SUR LES QUADRIQUES ASSOCIEES AUX POINTS D'UNE SURFACE

<正> On sait que Lie a attachéàtout point d'une surface(x)unequadrique osculatrice appelée quadrique de, Lie.Nous avons montréque cette quadrique est la première d'une suite de quadriques Φ,Φ,... attachée intrinsèquement àtont point x de la surface (x),d(?)quadiques consécutives de cette suite se touchant en quatre points,caractéristiques pour les deux quadriques eu question.     

ON THE REGULARITY OF SOLUTIONS TO MONGE-AMPÈRE EQUATIONS ON HESSIAN MANIFOLDS

In this note, we show that the regularity results of [4] Luis, A. Caffarelli. 1990. Interior W^2,p estimates for solutions of the Monge-Ampère equation. Ann. of Math. 2, 131(1): 135–150.  [Google Scholar] generalize to Monge-Ampère equations on the class of compact Hessian manifolds. We prove C ^{2, α} regularity of locally convex viscosity solutions, which rules out the possibility of Pogorelov-type counterexamples on this class of manifolds. We also derive some a priori estimates, from which follow some existence theorems with minimal regularity assumptions, generalizing results in [7] Shiu'Yuen, Cheng. and Shing-Tung, Yau. 1982. “The real Monge-Ampère equation and affine flat structures”. In Proceedings of the 1980 Beijing Symposium on Differential Geometry and Differential Equations, Vol. 1, 2, 3 (Beijing, 1980) 339–370. Beijing: Science Press.  [Google Scholar] and [11] Philippe, Delanoë. 1989. Remarques sur les variètès localement hessiennes. Osaka J. Math., 26(1): 65–69.  [Google Scholar].

     

基于DE历表的岁差公式

本文论证了在编制DE200历表过程中,因转换坐标历元所产生的历表分点偏离,是由目前采用的岁差公式中的行星岁差部分不够准确引起的。利用Standish拟合DE102历表所得的黄道,推导了新的岁差公式。考虑到用天体测量方法只能直接测量日月岁差ψ,故认为在天文常数系统中采用ψ代替p作为基本常数更为合适。鉴于DE200历表已被天文年历所采用,为使天文年历中的天文常数相互自洽,建议对岁差基本常数作如下改交,取 J2000.0 每儒略世纪黄经总岁差 P=50291″.0966
J2000.0 黄赤交角 ε=23°26′21″.412
或用ψ取代pJ2000.0 每儒略世纪日月岁差 ψ=5038″.7803。     

DE SITTER宇宙中的红移问题

本文在把宇宙看作de Sitter宇宙、星系作为粒子沿测地线作径向运动、星系之间没有引力相互作用的近似下,将谐和条件用于相对论性宇宙论中的星系运动。给出了标准坐标系、de Sitter坐标系和共动坐标系之间的坐标变换,及地球上的观测者观测到的远方退行星系所发出光的光强的Poynting矢量。在不同坐标系中Poynting矢量有不同的形式。作为一级近似,三种不同坐标系中的速度-距离关系是相同的,但对高级近似,它们则有区别,这种差别只能由天文观测来核实。在把退行星系中每一恒星看作一电偶极子的假定下所得到的速度-距离关系依赖于退行星系中恒星的数目,或者说依赖于退行星系中物质的质量。因此,照此分析宇宙中星系运动是各向同性的,但物质分布不一定均匀。     

DÉVELOPPEMENTS ASYMPTOTIQUES DE L'OPÉRATEUR DE SCHRÖDINGER AVEC CHAMP MAGNÉTIQUE FORT

We consider the Schrödinger operator P _B (V) = P _B + V, in L ² (R ^2d ) where P _B = (i ? + BA(x))². Here V is a decreasing potential and B is a large constant. We assume that the magnetic field “dA(x)” is constant. For f ∈ C ₀ ^∞ (I), where I is an open interval noncontaining the origin, we obtain an asymptotic expansion in powers of B ^?1, of tr (f(P _B (V) ? BΛ)), when B → + ∞. Here B Λ is a fixed Landau level of σ (P _B ). We give plicitly the two leading terms. Hence, we get precise remainder estimates for the counting function of eigenvalues of P _B (V) near BΛ. We apply these results to the Pauli operator in the two-dimensional case.     

UN THORME DE STABILITDES PERTURBATIONS OBLIQUES DANS LE PROBLME DE MINIMISATION CONVEXE

On généralise des resultats de Laurent [1] pour perturbations horizontales et pour perturbations verticales au cas des perturbations obliques qui contiennent simultanément des perturbations horizontales de variables et des perturbations verticales des fonctions contraintes, en dormant une condition de stabilité et un théoréme de caracterisation des solution pour le problme initial.     

Environmental site evaluation of waste management facilities embedded into EUGÈNE model: A multicriteria approach

EUGÈNE is a sophisticated mixed integer linear programming model developed to help regional decision makers on long-term planning for solid waste management activities. The model removes almost every limitations encountered in other waste management models and contains a large quantity of variables and constraints. The method used to embed waste management environmental parameters in the EUGÈNE model consists in building global impact index (GII) for all site/facility combinations. First, an environmental and spatial evaluation of waste management facilities over sites is based on qualitative and quantitative criteria measuring biophysical and social impacts. Spatial analysis is carried out by geographical information system routines. Then, a multicriteria analysis ranks all site/facility combinations, according to their global performance based on all criteria. The net flow, computed by the PROMETHEE multicriteria outranking method, is considered as a GII to be embedded into EUGÈNE. The model objective function is thus modified to minimize total system cost and GII. Some practical results obtained for the City of Montreal are discussed.     

FURTHER RESULTS ON CORRELATION FUNCTIONS OF DE BRUIJN SEQUENCES

In this paper we develop some bounds for the correlation functions of sequences with perfod 2~nand specific linear complexities.These bounds are also applicable to the correlation functions of deBruijn sequences with span n and specific linear complexities.It is interesting that a conjecture of Chan,Games and Key's for the case of n=2~m can be proved easily by using the results developed here.Theirconjecture asserts that there are no de Bruijn sequences with span n and linear complexity 2~(n-1)+n+1.The comjecture was proved by Games by a different method.     

SUPER EDGE-CONNECTIVITY OF DE BRUIJN AND KAUTZ UNDIRECTED GRAPHS

The super edge-connectivity of a graph is an important parameter to measure fault-tolerance of interconnection networks. This note shows that the Kautz undirected graph is super edge-connected,and provides a short proof of Lue and Zhang‘s result on super edge-connectivity of the de Bruijn undirected graph.     

UNE LIAISON ENTRE UNE INEGALITE LOGARITHMIQUE DE WEISSLER SUR LE CERCLE ET UNE QUESTION D''''EXTREMUM DANS LE PROBLEME DES MOMENTS DE STIELTJES

On donne ici une amélioration légère d'une inégalité de Weissler sur le cercle, obtenue en posant et résolvant un problème génèral d'extrmum portant sur des moments de Stieltjes.     

十进制整数编码的DE算法模式集定理研究

为揭示差分进化算法(Di?erential Eveolution,简称DE)的动力学机制,提出了DE算法的十进制整数编码的概念,给出选择、交叉、变异等操作算子在推动种群演化和寻优的模式集定理,即DE算法在选择、交叉、变异等操作算子作用下,具有较低模式集阶、较短模式集距、较高适应度函数值的模式集的生存数量,随种群迭代次数的增加呈现指数级增长.同时还研究了收缩因子F与变异概率的相当性特征,将收缩因子F的范围缩小至(0, 1)区间.     

LE PROBLME DE DIRICHLET POUR LES QUATIONS HYPERBOLIQUES

<正> Après avoir constatéque le problème de Cauchy qui se posenaturellement pour les équations Iinéaires aux dérivées partielles àcaractéristiques réelles(dn moins pour le type “normal”,le seul quiintervienne en Physique mathématique),est au contraire impossibleen général pour les équations àcaractéristiques imaginaires,il étaitnaturel de rechercher,inversement,si le problème de Dirichletest correctement posè pour les équ ions du type hyperbolique,parexemple,pour léquation àdeux variables independantes (àlaquel nousnous bornerons)     

HARNACK INEQUALITIES FOR FUNCTIONS IN THE GENERAL DE GIORGI PARABOLIC CLASS

In this paper the authors prove that functions in the general De Giorgi parabolic class satisfy Harnack inequalities and hence extend the results obtained in the 1960 by Moser, Trudinger and Ladyzenskaja et al. in a sense.     

EXACT－VOLUME DIFFERENTIAL FORM DE RHAM COHOMOLOGY AND HAMILTON VARIATIONAL PRINCIPLE

ＥＸＡＣＴ－ＶＯＬＵＭＥＤＩＦＦＥＲＥＮＴＩＡＬＦＯＲＭＤＥＲＨＡＭＣＯＨＯＭＯＬＯＧＹＡＮＤＨＡＭＩＬＴＯＮＶＡＲＩＡＴＩＯＮＡＬＰＲＩＮＣＩＰＬＥＷａｎｇＪｉｃｈｕｎ（王继春）（Ｄｅｐｔ．Ｍａｔｈ．Ｐｈｙｓ．ｏｆＷｕｈａｎＵｎｌｙ．ｏｆＴｅｃｈｎ...     

混料模型D—最优试验设计的改进DE算法研究

差分进化算法(Differential Evolution Algorithm)有较强的全局收敛能力和稳健性,应用该算法可解决工程学、计算机科学等领域的一些复杂优化问题。本文介绍一个改进DE算法,该算法适用于混料模型的近似最优设计问题,对于具有附加约束试验域的混料问题也可高效求解。最后,本文给出应用改进DE算法求解混料模型D-最优试验设计的例子。     

ALGORITHME DE PERTURBATION DIRECTRICE POUR LE PROBLME D''''AJUSTEMENT DES DONNEES

In this paper we propose an algorithm, called Directrive Perturbation (PD-Algorithm), which decrease the maximum value of the absolute errors of a fitting formula obtained by a Least-Squares Method. Applying the algorithm we can increase the accuracy of the uniform approximation of the fitting formula with the original data (x_i, f(x_i)) (i=1, 2, ..., m). Further, after applying a finite number of times of the perturbation, we can obtain the formuala of Tchebycheff approximation.     

Riemannian流形中DE算法算子最优特征量的量子渐进估计

该文主要分析和探讨了差分进化算法(Differential Eveolutionary Algorithm,DE)在Riemannian流形中的几何关系,对P_(-ε)条件下Riemannian流形中的种群个体进行了收敛性分析,得到了迭代个体收敛精度与收敛速度的量子不确定渐进估计,如下式■其中,△_v~2为种群个体的速度分辨率,△_x_β~ε~2为种群个体带有误差的位置分辨率,(λ_ε)_i,i=1,2,…,n.从本质上说明了Riemannian流形中迭代个体的局部特征量是不能从收敛精度和收敛速度同时达到算法高效.     

ASYMPTOTIC PROPERTY FOR THE SOLUTION TO THE GENERALIZED KORTEWEG－DE VRIES EQUATION

ＡＳＹＭＰＴＯＴＩＣＰＲＯＰＥＲＴＹＦＯＲＴＨＥＳＯＬＵＴＩＯＮＴＯＴＨＥＧＥＮＥＲＡＬＩＺＥＤＫＯＲＴＥＷＥＧ－ＤＥＶＲＩＥＳＥＱＵＡＴＩＯＮＺＨＡＮＧＬＩＮＧＨＡＩ（张领海）（ＤｅｐｏｒｔｍｅｎｔｏｆＭａｔｈｅｍａｔｉｃｓ，ｔｈｅＯｈｉｏＳｔａｔ...     

THERMODYNAMIQUE DES ENSEMBLES DE CANTOR AUTOSIMILAIRES（THERMODYNAMICS OF SELF-SIMILAR CANTOR SETS）

ＴＨＥＲＭＯＤＹＮＡＭＩＱＵＥＤＥＳＥＮＳＥＭＢＬＥＳＤＥＣＡＮＴＯＲＡＵＴＯＳＩＭＩＬＡＩＲＥＳ（ＴＨＥＲＭＯＤＹＮＡＭＩＣＳＯＦＳＥＬＦ－ＳＩＭＩＬＡＲＣＡＮＴＯＲＳＥＴＳ）￥Ｇ．ＭＩＣＨＯＮ;Ｊ．ＰＥＹＲＩＥＲＥ（ＵｎｉｖｅｒｓｉｔｙｄｅＢｏｕ...