Substructuring preconditioners for saddle-point problems arising from Maxwell's equations in three dimensions

This paper is concerned with the saddle-point problems arising from edge element discretizations of Maxwell's equations in a general three dimensional nonconvex polyhedral domain. A new augmented technique is first introduced to transform the problems into equivalent augmented saddle-point systems so that they can be solved by some existing preconditioned iterative methods. Then some substructuring preconditioners are proposed, with very simple coarse solvers, for the augmented saddle-point systems. With the preconditioners, the condition numbers of the preconditioned systems are nearly optimal; namely, they grow only as the logarithm of the ratio between the subdomain diameter and the finite element mesh size.

     

On Super Hamiltonian Semigroups

The concept of super hamiltonian semigroup is introduced. As a result, the structure theorems obtained by A. Cherubini and A. Varisco on quasi commutative semi-groups and quasi hamiltonian semigroups respectively are extended to super hamiltonian semigroups.     

Twin positive solutions for quasi-linear multi-point boundary value problems

In this paper, we investigate two classes of quasi-linear multi-point boundary value problems with sign-changing nonlinearity. By applications of fixed point index theory, sufficient conditions for the existence of twin positive solutions are established.     

Invariant ideals of twisted crossed products

We will prove a result concerning the inclusion of non-trivial invariant ideals inside non-trivial ideals of a twisted crossed product. We will also give results concerning the primeness and simplicity of crossed products of twisted actions of locally compact groups on -algebras. Received: 25 January 2002; in final form: 22 May 2002/Published online: 2 December 2002 This work is partially supported by Hong Kong RGC Direct Grant.     

The perturbation bounds for the solution of weighted kronecker product linear systems using thew-weighted drazin inverse

The classical perturbation theory is extended to the weighted Kronecker product linear systems W(A? B)Wx =h. Upper bounds are derived for the normwise condition number.     

A Construction of Optimal Constant Composition Codes

In this paper, a construction of optimal constant composition codes is developed, and used to derive some series of new optimal constant composition codes meeting the upper bound given by [13].     

Stability criterion for synchronization of linearly coupled unified chaotic systems

This paper investigates the synchronization of two linearly coupled unified chaotic systems. A new stability criterion for asymptotic synchronization is attained using the Lyapunov stability theory and linear matrix inequality (LMI) approach. A numerical example is given to illuminate the design procedure and advantage of the result derived.     

Partitioning series-parallel multigraphs into ν *-excluding edge covers

We prove that, for any given vertex ν* in a series-parallel graph G, its edge set can be partitioned into κ = min{κ′(G) + 1, δ(G)} subsets such that each subset covers all the vertices of G possibly except for ν*, where δ(G) is the minimum degree of G and κ′(G) is the edge-connectivity of G. In addition, we show that the results in this paper are best possible and a polynomial time algorithm can be obtained for actually finding such a partition by our proof.     

Detecting and Diagnostic Checking Multivariate Conditional Heteroscedastic Time Series Models

Two tests for multivariate conditional heteroscedastic models are proposed. One is based on the cross-correlations of standardized squared residuals and the other is a score (Lagrange multiplier) test. The cross-correlations test can be used to detect the presence of multivariate conditional heteroscedasticity whereas the other test can be used for diagnostic checking. Simulation studies on the size and power of the test statistics are reported. The application of the tests is illustrated by an example using the S & P 500 and Sydney All Ordinary Indexes.