Primal-Dual Interior-Point Algorithms for Semidefinite Optimization Based on a Simple Kernel Function

Interior-point methods (IPMs) for semidefinite optimization (SDO) have been studied intensively, due to their polynomial complexity and practical efficiency. Recently, J. Peng et al. introduced so-called self-regular kernel (and barrier) functions and designed primal-dual interior-point algorithms based on self-regular proximities for linear optimization (LO) problems. They also extended the approach for LO to SDO. In this paper we present a primal-dual interior-point algorithm for SDO problems based on a simple kernel function which was first presented at the Proceedings of Industrial Symposium and Optimization Day, Australia, November 2002; the function is not self-regular. We derive the complexity analysis for algorithms based on this kernel function, both with large- and small-updates. The complexity bounds are and , respectively, which are as good as those in the linear case. Mathematics Subject Classifications (2000) 90C22, 90C31.     

Numerical Analysis of the Behaviour of Tooth Intrarradial Posts by the Finite Element Method

The aim of this work is to study the behaviour of a carbon/epoxi post housed in a canine tooth after endodontic treatment in order to support the typical loads present during mastication. The three-D basic design of the dental piece consisting of tooth + post was carried out with a three-dimensional parametric design program. We study the stresses and displacements of the different elements of the dental piece under normal load conditions, and present the results and conclusions.     

Homoclinic Bifurcations in Symmetric Unfoldings of a Singularity with Three-fold Zero Eigenvalue

In this paper we study the singularity at the origin with three-fold zero eigenvalue forsymmetric vector fields with nilpotent linear part and 3-jet C^∞-equivalent to y δ/δx zδ/δy ax^2yδ/δz with a≠0. We first obtain several subfamilies of the symmetric versal unfoldings of this singularityby using the normal form and blow-up methods under some conditions, and derive the local and global bifurcation behavior, then prove analytically the existence of the Sil‘nikov homoclinic bifurcation for some subfamilies of the symmetric versal unfoldings of this singularity, by using the generalized Mel‘nikov methods of a homoclinic orbit to a hyperbolic or non-hyperbolic equilibrium in a highdimensional space.     

Energy Conservation with Non-Symplectic Methods: Examples and Counter-Examples

Energy conservation of numerical integrators is well understood for symplectic one-step methods. This article provides new insight into energy conservation with non-symplectic methods. Sufficient conditions and counter-examples are presented. AMS subject classification (2000) 65L06, 65P10, 37J99.Submitted June 2004. Accepted October 2004. Communicated by Syvert Nørsett.     

Analysis of a Class of Parallel Multigrid Smoothers

This paper proposes and analyzes a class of multigrid smoothers called the parallel multiplicative (PM) smoother by subspace decomposition techniques. It shows that the well known additive and multiplicative smoothers and the JSOR smoother are special cases of the PM smoother, and their smoothing properties can be obtained directly from the PM analysis. Moreover, numerical results are presented in this paper to show that the JSOR smoother is more robust and effective than the damped Jacobi smoother on current MIMD parallel computers. AMS subject classification (2000) 65N55, 65Y05.Received May 2004. Revised September 2004. Communicated by Per Lötstedt.Dexuan Xie: This work was partially supported by the National Science Foundation through grant DMS-0241236.     

On the Convergence Behaviour of Variable Stepsize Multistep Methods for Singularly Perturbed Problems

In this note, we investigate the convergence behaviour of linear multistep discretizations for singularly perturbed systems, emphasising the features of variable stepsizes. We derive a convergence result for A()-stable linear multistep methods and specify a refined error estimate for backward differentiation formulas. Important ingredients in our convergence analysis are stability bounds for non-autonomous linear problems that are obtained by perturbation techniques.     

A magnetic resonance device designed via global optimization techniques

In this paper we are concerned with the design of a small low-cost, low-field multipolar magnet for Magnetic Resonance Imaging with a high field uniformity. By introducing appropriate variables, the considered design problem is converted into a global optimization one. This latter problem is solved by means of a new derivative free global optimization method which is a distributed multi-start type algorithm controlled by means of a simulated annealing criterion. In particular, the proposed method employs, as local search engine, a derivative free procedure. Under reasonable assumptions, we prove that this local algorithm is attracted by global minimum points. Additionally, we show that the simulated annealing strategy is able to produce a suitable starting point in a finite number of steps with probability one.This work was supported by CNR/MIUR Research Program Metodi e sistemi di supporto alle decisioni, Rome, Italy.Mathematics Subject Classification (1991):65K05, 62K05, 90C56     

Electrochemical characterization of cationic surfactants’ adsorption on a disturbed n-alkanethiolate self-assembled monolayer-modified polycrystalline gold electrode

The adsorption of cetyltrimethylammonium bromide (CTAB) on disturbed n-alkanethiolate self-assembled monolayers (SAMs) was investigated by electrochemical methods with potassium ferricyanide [K₃Fe(CN)₆] as a probe. Compared with the completely restrained signal at ordinary compact n-alkanethiolate SAMs, the electrochemical response of K₃Fe(CN)₆ at the disturbed n-alkanethiolate SAMs was partly restored and became progressively reversible in the presence of increasing concentrations of CTAB, which was employed to characterize the adsorption of cationic surfactants on hydrophobic SAMs. The effect of CTAB concentration on electrochemical impedance spectroscopy (EIS) plots indicated that CTAB experienced two different types of adsorptive behavior at the disturbed n-alkanethiolate SAMs: monomer adsorption at low concentrations below 1×10^–6 M and monolayer adsorption at CTAB concentrations above 1×10^–5 M. The adsorption of a series of cationic surfactants with similar structures to CTAB on disturbed n-alkanethiolate SAMs was also explored. These surfactants had similar adsorptive behavior and showed nearly linear adsorption characteristics with the length of their hydrophobic tails.