一类Lagrangian对偶问题的零对偶间隙性质及其最优路径的收敛性

针对一般的非线性规划问题,利用某些Lagrange型函数给出了一类Lagrangian对偶问题的一般模型,并证明它与原问题之间存在零对偶间隙．针对具体的一类增广La- grangian对偶问题以及几类由非线性卷积函数构成的Lagrangian对偶问题,详细讨论了零对偶间隙的存在性．进一步,讨论了在最优路径存在的前提下,最优路径的收敛性质．     

AdS/CFT duality at strong coupling

We study the strong-coupling limit of the AdS/CFT correspondence in the framework of a recently proposed fermionic formulation of the Bethe ansatz equations governing the gauge theory anomalous dimensions. We give examples of states that do not follow the Gubser-Klebanov-Polyakov law at a large ’t Hooft coupling λ, in contrast to recent results on the quantum string Bethe equations that are valid in that regime. This result indicates that the fermionic construction cannot be trusted at large λ, although it remains an efficient tool for computing the weak-coupling expansion of anomalous dimensions. Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 152, No. 2, pp. 213–224, August, 2007.     

Stable marker-particle method for the Voronoi diagram in a flow field

The Voronoi diagram in a flow field is a tessellation of water surface into regions according to the nearest island in the sense of a “boat-sail distance”, which is a mathematical model of the shortest time for a boat to move from one point to another against the flow of water. The computation of the diagram is not easy, because the equi-distance curves have singularities. To overcome the difficulty, this paper derives a new system of equations that describes the motion of a particle along the shortest path starting at a given point on the boundary of an island, and thus gives a new variant of the marker-particle method. In the proposed method, each particle can be traced independently, and hence the computation can be done stably even though the equi-distance curves have singular points.     

Lattice Boltzmann方法模拟多孔介质Klinkenberg效应

格子Boltzmann数值模拟方法是研究复杂的多孔介质结构特别是Klinkenberg效应的有效方法之一，对处理复杂边值问题尤其有效，用格子Boltzmann方法研究了气流穿越多孔介质问题，并将数值计算结果与实验结果进行了比较，结果表明格子Boltzmann方法是数值模拟气流穿越多孔介质问题的有效方法之一。     

L-型模糊格蕴涵代数

This paper introduced the concept of L-fuzzy sub lattice implication algebra and discussed its properties. Proved that the intersection set of a family of L-fuzzy sub lattice implication algebras is a L-fuzzy sub lattice implication algebra, that a L-fuzzy sub set of a lattice implication algebra is a L-fuzzy sub lattice implication algebra if and only if its every cut set is a sub lattice implication algebra, and that the image and original image of a L-fuzzy sub lattice implication algebra under a lattice implication homomorphism are both L-fuzzy sub lattice implication algebras.     

上海光源储存环磁聚焦结构设计

上海光源是一台正在建设中的低发射度第三代同步辐射光源. 经过优化后, 储存环有两种直线节长度, 周长432m,在能量3.5GeV下束流发射度为3.9nm.rad, 直线节处的β函数和色散函数有足够的调节范围. 跟踪研究表明, 即使带上磁铁高阶场误差, 储存环仍有足够大的动力学孔径和能量接受度.     

Ultra <Emphasis Type="Italic">LI</Emphasis>-ideals in lattice implication algebras and <Emphasis Type="Italic">MTL</Emphasis>-algebras

A mistake concerning the ultra LI-ideal of a lattice implication algebra is pointed out, and some new sufficient and necessary conditions for an LI-ideal to be an ultra LI-ideal are given. Moreover, the notion of an LI-ideal is extended to MTL-algebras, the notions of a (prime, ultra, obstinate, Boolean) LI-ideal and an ILI-ideal of an MTL-algebra are introduced, some important examples are given, and the following notions are proved to be equivalent in MTL-algebra: (1) prime proper LI-ideal and Boolean LI-ideal, (2) prime proper LI-ideal and ILI-ideal, (3) proper obstinate LI-ideal, (4) ultra LI-ideal. This work was supported by the Zhejiang Provincial Natural Science Foundation of China (Grant No. Y605389) and K. C. Wong Magna Fund in Ningbo University.     

Critical percolation exploration path and SLE 6: a proof of convergence

It was argued by Schramm and Smirnov that the critical site percolation exploration path on the triangular lattice converges in distribution to the trace of chordal SLE ₆. We provide here a detailed proof, which relies on Smirnov’s theorem that crossing probabilities have a conformally invariant scaling limit (given by Cardy’s formula). The version of convergence to SLE ₆ that we prove suffices for the Smirnov–Werner derivation of certain critical percolation crossing exponents and for our analysis of the critical percolation full scaling limit as a process of continuum nonsimple loops. Research of Charles M.Newman was partially supported by the US NSF under grants DMS-01-04278 and DMS-06-06696.     

多目标半定规划的加权中心路径法

对于线性型多目标半定规划问题，引进加权中心路径的概念，并利用单目标半定规划的中心路径法，提出了求解多目标半定规划问题的加权中心路径法，先得型对一个叔向量的有效解，然后在此基础上，提出了通过一次迭代得到对应一定范围内其他任意权向量的有效解的一步修正方法．     

Farthest-point queries with geometric and combinatorial constraints

In this paper we discuss farthest-point problems in which a set or sequence S of n points in the plane is given in advance and can be preprocessed to answer various queries efficiently. First, we give a data structure that can be used to compute the point farthest from a query line segment in O(log²n) time. Our data structure needs O(nlogn) space and preprocessing time. To the best of our knowledge no solution to this problem has been suggested yet. Second, we show how to use this data structure to obtain an output-sensitive query-based algorithm for polygonal path simplification. Both results are based on a series of data structures for fundamental farthest-point queries that can be reduced to each other.