Fully adaptive multiresolution finite volume schemes for conservation laws

The use of multiresolution decompositions in the context of finite volume schemes for conservation laws was first proposed by A. Harten for the purpose of accelerating the evaluation of numerical fluxes through an adaptive computation. In this approach the solution is still represented at each time step on the finest grid, resulting in an inherent limitation of the potential gain in memory space and computational time. The present paper is concerned with the development and the numerical analysis of fully adaptive multiresolution schemes, in which the solution is represented and computed in a dynamically evolved adaptive grid. A crucial problem is then the accurate computation of the flux without the full knowledge of fine grid cell averages. Several solutions to this problem are proposed, analyzed, and compared in terms of accuracy and complexity.

     

A Representation of a Family of Secret Sharing Matroids

Deciding whether a matroid is secret sharing or not is a well-known open problem. In Ng and Walker [6] it was shown that a matroid decomposes into uniform matroids under strong connectivity. The question then becomes as follows: when is a matroid m with N uniform components secret sharing? When N = 1, m corresponds to a uniform matroid and hence is secret sharing. In this paper we show, by constructing a representation using projective geometry, that all connected matroids with two uniform components are secret sharing     

A fourth‐order compact finite difference scheme for the steady stream function–vorticity formulation of the Navier–Stokes/Boussinesq equations

A fourth‐order compact finite difference scheme on the nine‐point 2D stencil is formulated for solving the steady‐state Navier–Stokes/Boussinesq equations for two‐dimensional, incompressible fluid flow and heat transfer using the stream function–vorticity formulation. The main feature of the new fourth‐order compact scheme is that it allows point‐successive overrelaxation (SOR) or point‐successive underrelaxation iteration for all Rayleigh numbers Ra of physical interest and all Prandtl numbers Pr attempted. Numerical solutions are obtained for the model problem of natural convection in a square cavity with benchmark solutions and compared with some of the accurate results available in the literature. Copyright © 2003 John Wiley & Sons, Ltd.     

Multicuts in unweighted graphs and digraphs with bounded degree and bounded tree-width

The Multicut problem can be defined as: given a graph G and a collection of pairs of distinct vertices {s_i,t_i} of G, find a minimum set of edges of G whose removal disconnects each s_i from the corresponding t_i. Multicut is known to be NP-hard and Max SNP-hard even when the input graph is restricted to being a tree. The main result of the paper is a polynomial-time approximation scheme (PTAS) for Multicut in unweighted graphs with bounded degree and bounded tree-width. That is, for any ε>0, we present a polynomial-time (1+ε)-approximation algorithm. In the particular case when the input is a bounded-degree tree, we have a linear-time implementation of the algorithm. We also provide some hardness results: we prove that Multicut is still NP-hard for binary trees and that it is Max SNP-hard if we drop any of the three conditions (unweighted, bounded-degree, bounded tree-width). Finally we show that some of these results extend to the vertex version of Multicut and to a directed version of Multicut.     

A Generalization of a Two-Parameter Quantization for the Group GL 2(k)

We generalize a well-known two-parameter quantization for the group GL ₂(k) (over an arbitrary field k). Specifically, a certain class of Hopf algebras is constructed containing that quantization. The algebras are constructed given an arbitrary coalgebra and an arbitrary pair of its commuting anti-isomorphisms, and are defined by quadratic relations. They are densely linked to the compact quantum groups introduced by Woronowicz. We give examples of Hopf algebras that can be rowed up to the two-parameter quantization for GL ₂(k).     

可调实时时间差电子错位散斑技术及应用

本文首次提出一种可调实时时间差电子错位散斑干涉技术,并成功地用于热变形测量,该方法还可用于长时间连续变形和瞬态大变形的位移测量。叙述了该技术的原理,给出了一些应用的实验结果。     

从B~0到E(p，q)和E_0(p，q)空间的复合算子(英文)

设φ是单位园盘D到自身的解析映射,X是D上解析函数的Banach空间,对f∈X,定义复合算子C_φ∶C_φ)(f)=fφ．我们利用从B~0到E(p,q)和E_0(p,q)空间的复合算子研究了空间E(p,q)和E_0(p,q),给出了一个新的特征．     

Canonical measures on the moduli spaces of compact Riemann surfaces

We study some explicit relations between the canonical line bundle and the Hodge bundle over moduli spaces for low genus. This leads to a natural measure on the moduli space of every genus which is related to the Siegel symplectic metric on Siegel upper half-space as well as to the Hodge metric on the Hodge bundle.     

Long-range predictive adaptive fuzzy relational control

A class of long-range predictive adaptive fuzzy relational controllers is presented. The plant behavior is described over an extended time horizon by a fuzzy relational model which is identified based on input-output closed-loop observations of the plant variables. In this class of adaptive controllers the control law attempts to minimize a quadratic cost over an extended control horizon. When used with linear models, this approach has revealed a significant potential for overcoming the limitations of one-step ahead schemes, such as the stabilization of non-minimum phase plants. Here, a uniform framework is adopted for implementing both the fuzzy model and the fuzzy controller, namely distributed fuzzy relational structures gaining from their massive parallel processing features and from the learning capabilities typical of the connectivist approaches. Issues such as maintenance during the adaptation process of the meaning of linguistic terms used at both fuzzy systems interfaces are addressed, namely by introducing a new design methodology for on-line fuzzy systems interface adaptation. The examples presented reinforce the claim of the usefulness of this new approach.     

微加工薄膜变形镜特性分析

 借助测量微加工薄膜变形镜驱动器的面形影响函数，分析了驱动器的电压-位移函数和驱动器之间的线性叠加性;通过对连续面形变形镜拟合像差的理论分析和实验研究，建立了微加工薄膜变形镜电压解耦模型。分析了对前36阶Zernike模式的拟合残差和拟合能力，指出微加工薄膜变形镜仅可用来拟合低级像差并且有较大的拟合能力和较小的拟合残差，而不能拟合高级像差。