A Reflection Principle and an Orthogonal Decomposition in Clifford Algebras

In this article we investigate spaces of functions defined in a domain Ω ? R with values in the Clifford algebra R _n. According to an inner product an orthogonal decomposition is proved. By this decomposition, we obtain a subspace A ₂(Ω) of regular functions with respect to the Dirac operator. In the orthogonal complement the Dirac equation with homogeneous boundary values is solvable. The decomposition can be proved in two ways: by a reflection principle and by Sobolev's regularity theorem. It will turn out, that the existence of the orthogonal decomposition and Sobolev's theorem is equivalent. So also a reflection principle will be proved, which describes the jump behavior of a Cauchy type integral. By the reflection principle, a countable dense subset of A ₂(Ω) can be obtained. Further considerations lead to a minimal generating system, by which the Bergman kernel function can be obtained. As a conclusion we also obtain Runge's theorem.     

易贡滑坡堰塞湖溃坝洪水分析

滑坡堰塞坝体主要由块石、碎石土等松散材料组成,随着上游水位的不断上升,极易失稳,一旦决口将对给下游人民的生命财产安全造成极大的威胁。因此,研究堰塞坝溃坝问题具有重要的学术意义和应用价值。2000 年 4 月 9 日,西藏林芝地区波密县易贡藏布河扎木弄沟发生大规模山体滑坡堵塞易贡藏布江,形成坝高60m,长约2500m,库容可达288×108m3,体积约28×108～30×108m3的滑坡堰塞湖, 2000年6月10日堰塞坝溃决。本文以易贡堰塞湖溃坝为例,从连续性方程及Navier Stokes方程出发,结合标准型湍流模型,并采用VOF方法进行自由面处理,基于流体计算软件Fluent模拟分析了溃坝洪水在下游弯曲河道的演进过程及不同位置的流速变化。数值模拟结果与实测资料记录基本一致,表明该模型能够模拟溃坝洪水在地形复杂弯曲河道中的演进过程。     

鞍点问题迭代解法收敛因子估计

分析Ｂａｎｋ（１９９０年）的论文中的求解鞍点问题的迭代解法,得到一个改进的收敛因子估计。     

A cutting plane algorithm for the General Routing Problem

The General Routing Problem (GRP) is the problem of finding a minimum cost route for a single vehicle, subject to the condition that the vehicle visits certain vertices and edges of a network. It contains the Rural Postman Problem, Chinese Postman Problem and Graphical Travelling Salesman Problem as special cases. We describe a cutting plane algorithm for the GRP based on facet-inducing inequalities and show that it is capable of providing very strong lower bounds and, in most cases, optimal solutions. Received: November 1998 / Accepted: September 2000?Published online March 22, 2001     

Food Web Implications of δ13C and δ15N Variability over 370 km of the Regulated Colorado River USA

Abstract

Dual stable isotope analysis in the regulated Colorado River through Grand Canyon National Park, USA, revealed a food web that varied spatially through this arid biome. Down-river enrichment of δ¹³C data was detected across three trophic levels resulting in shifted food webs. Humpack chub δ¹³C and δ¹⁵N values from muscle plugs and fin clips did not differ significantly. Humpback chub and rainbow trout trophic position is positively correlated with standard length indicating an increase in piscivory by larger fishes. Recovery of the aquatic community from impoundment by Glen Canyon Dam and collecting refinements for stable isotope analysis within large rivers are discussed.     

TWO BOUNDED HALF ORTHOTROPIC PLANE MATERIALS WITH CRACKS

ＴＷＯＢＯＵＮＤＥＤＨＡＬＦＯＲＴＨＯＴＲＯＰＩＣＰＬＡＮＥＭＡＴＥＲＩＡＬＳＷＩＴＨＣＲＡＣＫＳＣａｉＨａｉｔａｏ（蔡海涛）（ＣｅｎｔｒａｌＳｏｕｔｈＵｎｉｖｅｒｓｉｔｙｏｆＴｅｃｈｎｏｌｏｇｙ，Ｃｈａｎｇｓｈａ４１００８３，Ｃｈｉｎａ）Ａｂｓｔｒ...     

Duality of dams via mountain processes

We consider a G/M/1-type dam having finite capacity and a general release rule, and construct a ‘dual’ M/G/1-type dam with state-dependent jump sizes and without dry periods whose content process has the same stationary density (up to some transformation). For the dual dam the stationary distribution can be computed in closed form.     

旅行推销员问题的凸包收缩法

本提出一种用凸包收缩来解决旅行推销员问题。首先形成一个凸包初始环路。然后，逐个考察凸包内的点，按照增加值从小到大的顺序依次插入，直至考察完所有的点。从而得到一个包含所有点的环路，即旅行推销员问题的一个满意解。     

Positivity of second order linear recurrent sequences

We give a decision method for the Positivity Problem for second order recurrent sequences: it is decidable whether or not a recurrent sequence defined by u_n=au_n-1+bu_n-2 has only nonnegative terms.