Preduals of von Neumann Algebras

Proofs of two assertions are sketched. 1) If the Banach space of a von Neumann algebra A is the third dual of some Banach space, then the space A is isometrically isomorphic to the second dual of some von Neumann algebra A and the von Neumann algebra A is uniquely determined by its enveloping von Neumann algebra (up to von Neumann algebra isomorphism) and is the unique second predual of A (up to isometric isomorphism of Banach spaces). 2) An infinite-dimensional von Neumann algebra cannot have preduals of all orders.     

CHARACTERIZATION OF BEST APPROXIMATIONS IN METRIC LINEAR SPACES

Let (X,d) be a real metric linear space, with translation-invariant metric d and G a linear subspace of X. In this paper we use functionals in the Lipschitz dual of X to characterize those elements of G which are best approximations to elements of X. We also give simultaneous characterization of elements of best approximation and also consider elements of ε-approximation.     

Parallelizing simulated annealing algorithms based on high-performance computer

We implemented five conversions of simulated annealing (SA) algorithm from sequential-to-parallel forms on high-performance computers and applied them to a set of standard function optimization problems in order to test their performances. According to the experimental results, we eventually found that the traditional approach to parallelizing simulated annealing, namely, parallelizing moves in sequential SA, difficultly handled very difficult problem instances. Divide-and-conquer decomposition strategy used in a search space sometimes might find the global optimum function value, but it frequently resulted in great time cost if the random search space was considerably expanded. The most effective way we found in identifying the global optimum solution is to introduce genetic algorithm (GA) and build a highly hybrid GA+SA algorithm. In this approach, GA has been applied to each cooling temperature stage. Additionally, the performance analyses of the best algorithm among the five implemented algorithms have been done on the IBM Beowulf PCs Cluster and some comparisons have been made with some recent global optimization algorithms in terms of the number of functional evaluations needed to obtain a global minimum, success rate and solution quality.     

Prim-based support-graph preconditioners for min-cost flow problems

Support-graph preconditioners have been shown to be a valuable tool for the iterative solution, via a Preconditioned Conjugate Gradient method, of the KKT systems that must be solved at each iteration of an Interior Point algorithm for the solution of Min Cost Flow problems. These preconditioners extract a proper triangulated subgraph, with “large” weight, of the original graph: in practice, trees and Brother-Connected Trees (BCTs) of depth two have been shown to be the most computationally efficient families of subgraphs. In the literature, approximate versions of the Kruskal algorithm for maximum-weight spanning trees have most often been used for choosing the subgraphs; Prim-based approaches have been used for trees, but no comparison have ever been reported. We propose Prim-based heuristics for BCTs, which require nontrivial modifications w.r.t. the previously proposed Kruskal-based approaches, and present a computational comparison of the different approaches, which shows that Prim-based heuristics are most often preferable to Kruskal-based ones. This paper has been partially supported by the UE Marie Curie Research Training Network no. 504438 ADONET.     

Block Algorithms for Orthogonal Symplectic Factorizations

On the basis of a new WY-like representation block algorithms for orthogonal symplectic matrix factorizations are presented. Special emphasis is placed on symplectic QR and URV factorizations. The block variants mainly use level 3 (matrix-matrix) operations that permit data reuse in the higher levels of a memory hierarchy. Timing results show that our new algorithms outperform standard algorithms by a factor 3–4 for sufficiently large problems.This revised version was published online in October 2005 with corrections to the Cover Date.     

A posteriori error estimation for the dual mixed finite element method of the elasticity problem in a polygonal domain

In this article, we propose a residual based reliable and efficient error estimator for the new dual mixed finite element method of the elasticity problem in a polygonal domain, introduced by M. Farhloul and M. Fortin. With the help of a specific generalized Helmholtz decomposition of the error on the strain tensor and the classical decomposition of the error on the gradient of the displacements, we show that our global error estimator is reliable. Efficiency of our estimator follows by using classical inverse estimates. The lower and upper error bounds obtained are uniform with respect to the Lamé coefficient λ, in particular avoiding locking phenomena. © 2005 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2005.     

光纤双光栅用于温度和应变测量

FBG传感器在现实应用中的一个主要问题是温度和应力的交叉敏感问题，本文介绍了光纤双光栅同步测量温度和应力的原理，设计了一个光纤双光栅温度、应变测量实验系统，对光纤双光栅的温度和应变传感特性进行了初步的实验研究。实验结果很好地反映了光纤双光栅的温度和应变灵敏特征，也表明光纤双光栅具有多参量同时测量的能力。     

Parallel Split-Step Fourier Methods for Nonlinear Schrödinger-Type Equations

The nonlinear Schrödinger equation is of tremendous interest in both theory and applications. Various regimes of pulse propagation in optical fibers are modeled by some form of the nonlinear Schrödinger equation. In this paper we introduce sequential and parallel split-step Fourier methods for numerical simulations of the nonlinear Schrödinger-type equations. The parallel methods are implemented on the Origin 2000 multiprocessor computer. Our numerical experiments have shown that these methods give accurate results and considerable speedup.     

Genetic algorithms for solving the discrete ordered median problem

In this paper we present two new heuristic approaches to solve the Discrete Ordered Median Problem (DOMP). Described heuristic methods, named HGA1 and HGA2 are based on a hybrid of genetic algorithms (GA) and a generalization of the well-known Fast Interchange heuristic (GFI). In order to investigate the effect of encoding on GA performance, two different encoding schemes are implemented: binary encoding in HGA1, and integer representation in HGA2. If binary encoding is used (HGA1), new genetic operators that keep the feasibility of individuals are proposed. Integer representation keeps the individuals feasible by default, so HGA2 uses slightly modified standard genetic operators. In both methods, caching GA technique was integrated with the GFI heuristic to improve computational performance. The algorithms are tested on standard ORLIB p-median instances with up to 900 nodes. The obtained results are also compared with the results of existing methods for solving DOMP in order to assess their merits.