Extension of the 2-p-opt and 1-shift algorithms to the heterogeneous probabilistic traveling salesman problem

The probabilistic traveling salesman problem is a well known problem that is quite challenging to solve. It involves finding the tour with the lowest expected cost for customers that will require a visit with a given probability. There are several proposed algorithms for the homogeneous version of the problem, where all customers have identical probability of being realized. From the literature, the most successful approaches involve local search procedures, with the most famous being the 2-p-opt and 1-shift procedures proposed by Bertsimas [D.J. Bertsimas, L. Howell, Further results on the probabilistic traveling salesman problem, European Journal of Operational Research 65 (1) (1993) 68–95]. Recently, however, evidence has emerged that indicates the equations offered for these procedures are not correct, and even when corrected, the translation to the heterogeneous version of the problem is not simple. In this paper we extend the analysis and correction to the heterogeneous case. We derive new expressions for computing the cost of 2-p-opt and 1-shift local search moves, and we show that the neighborhood of a solution may be explored in O(n²) time, the same as for the homogeneous case, instead of O(n³) as first reported in the literature.     

An Evershed type superconducting flywheel bearing

The objective of this work is to develop a bearing using high temperature superconductors (HTSs) for use in an energy storage flywheel. The experimental apparatus includes a cylindrical rotor levitated with the Evershed design in which the majority of the levitation force is provided by a permanent magnet arrangement and the stabilization of the system is achieved by HTS elements. The design characteristics and dynamics of the bearing associated with the rotor part are presented. The instrumentation measures the out of balance force and magnetomechanical stiffness associated with the rotor. A study of the rotational losses was performed using free spin down experiments associated with magnetic field variation measurements. The results are consistent with the loss being caused by hysteresis in the superconductor due to magnet inhomogeneity.     

Mixed symbolic–numerical computations with general DAEs II: An applications case study

A variety of theorems and properties of nonlinear DAEs were discussed in part I. This paper illustrates many of these ideas within the context of analyzing a specific nonlinear system that exhibits a variety of interesting features. This revised version was published online in June 2006 with corrections to the Cover Date.     

Bases for rings of coinvariants

We study the multiplicative structure of rings of coinvariants for finite groups. We develop methods that give rise to natural monomial bases for such rings over their ground fields and explicitly determine precisely which monomials are zero in the ring of coinvariants. We apply our methods to the Dickson, upper triangular and symmetric coinvariants. Along the way, we recover theorems of Steinberg [17] and E. Artin [1]. Using these monomial bases we prove that the image of the transfer for a general linear group over a finite field is a principal ideal in the ring of invariants. This research is supported in part by the Natural Sciences and Engineering Research Council of Canada     

Four contact electrical measurements on the anisotropic high-Tc superconductors: voltage reversals

We describe three mechanisms for the anomalous voltage reversals which are occasionally observed during four contact current-voltage measurements on the high temperature superconductors. Voltage reversals have been frequently observed for whiskers of the bismuth strontium calcium copper oxide (BSSCO) compounds, and we describe measurements made on high quality whiskers of the 2:2:1:2 and 2:2:2:3 phases. A simple model based on extreme anisotropy plus offset contacts can explain the gross features of four contact measurements in the ohmic flux-flow regime, but not the wealth of reversal phenomena found for the IVVI configuration in the lower temperature irreversibility region.     

Mass spectra of some sulphonyl azides

A series of sulphonyl azides decomposed upon electron-impact with loss of azide radical. This fragmentation was in marked contrast to the photochemical behaviour of the compounds. An interesting ortho-extrusion process occurred in the mass spectrum of 2,4,6-triisopropylbenzenesulphonyl azide.