D.C. Versus Copositive Bounds for Standard QP

The standard quadratic program (QPS) is min_xεΔx^TQx, where is the simplex Δ = {x ⩽ 0 ∣ ∑_i=1ⁿ x_i = 1}. QPS can be used to formulate combinatorial problems such as the maximum stable set problem, and also arises in global optimization algorithms for general quadratic programming when the search space is partitioned using simplices. One class of ‘d.c.’ (for ‘difference between convex’) bounds for QPS is based on writing Q=S−T, where S and T are both positive semidefinite, and bounding x^T Sx (convex on Δ) and −x^Tx (concave on Δ) separately. We show that the maximum possible such bound can be obtained by solving a semidefinite programming (SDP) problem. The dual of this SDP problem corresponds to adding a simple constraint to the well-known Shor relaxation of QPS. We show that the max d.c. bound is dominated by another known bound based on a copositive relaxation of QPS, also obtainable via SDP at comparable computational expense. We also discuss extensions of the d.c. bound to more general quadratic programming problems. For the application of QPS to bounding the stability number of a graph, we use a novel formulation of the Lovasz ϑ number to compare ϑ, Schrijver’s ϑ′, and the max d.c. bound.     

Septal repair implants: evaluation of magnetic resonance imaging safety at 3 T

Specialized implants are used for transcatheter closure of septal defects, including atrial and ventricular septal defects, and patent foramen ovale. These metallic devices may pose a risk to patients undergoing magnetic resonance imaging (MRI) procedures especially if performed at 3 T. Therefore, this investigation evaluated MRI safety at 3 T for septal repair implants (CardioSEAL Septal Repair Implant and STARFlex Septal Repair Implant, NMT Medical, Boston, MA, USA) by characterizing magnetic field interactions, heating and artifacts. These implants exhibited minor magnetic field interactions; heating was not excessive (+0.5°C); and artifacts will only create a problem if the area of interest is in the same area as or near these devices. Thus, the findings indicated that it would be safe for a patient with these implants to undergo MRI at 3 T or lower. Importantly, because of the minor magnetic field interactions, MRI may be performed immediately after implantation.     

Relaxation of an optimal control problem involving a perturbed sweeping process

We establish first, in the setting of infinite dimensional Hilbert space, a result concerning the existence of solutions for perturbed sweeping processes whose perturbations are Lipschitz single-valued maps. Then we use this result to extend to the infinite dimensional setting a relaxation result concerning optimal control problems involving such processes. Dedicated to R. Tyrrell Rockafellar on the occasion of his 70th birthday     

A determination of the toroidal k-metacyclic groups

Kronecker studied a class of groups 〈p, p - 1, r〉, whose commutator subgroups are prime cyclic of order p, and whose commutator quotient groups are cyclic of order p - 1. These are now commonly called the K-metacyclic groups. It follows from the classical work of Maschke that none of the K-metacyclic groups except 〈3, 2, 2〉 has a planar Cayley graph. It is proved here that only for p = 5 and p = 7 is a K-metacyclic group 〈p, p - 1, r〉 toroidal. To achieve this result, this paper develops a methodology for using Proulx's classification of toroidal groups by presentation to determine whether an explicitly given group is toroidal.     

Properties of blends containing two liquid crystalline polymers

Blends containing two, wholly aromatic, naphthalene-based liquid crystalline polymers (LCPs) are studied. Experimental results show that the viscosities of the resulting blends are lower than the parent LCPs over the entire shear-rate range investigated. The orientation development following capillary flow demonstrates, that over a defined blend composition range, some blends have higher orientability than the constituent polymers. This is further manifested in the tensile and flexural properties of injection-molded specimens. A detailed analysis indicates that in the composition range where synergistic effects are observed in orientation development as well as in mechanical properties, only one glass transition temperature is detected. This suggests that “miscibility” is desirable for obtaining maximum properties in these blend systems.     

Comment on “the question of an upper bound on entropy”

We show that the upper bound on the entropy of a finite system proposed by Qadir is not universal and consequently neither interesting nor relevant to the Bekenstein-Unruh-Wald debate.     

Laser Stark spectroscopy of DCN and DC15N

Using a CO laser, laser Stark resonance spectra were measured for the CN stretching fundamentals (the 00⁰1-00⁰0 bands) of D¹²C¹⁴N and D¹²C¹⁵N near 1925 cm^?1. Laser Stark resonances were also measured for the hot band 01¹1-01¹0 of D¹²C¹⁴N. In addition to accurately determining the band centers, dipole moments are given for the different vibrational states involved.     

Author index to volume 114B

A two-dimensional spin system [the U(∞) chiral model] is shown to exhibit a non-rough phase in contrast to the folklore that two-dimensional spin systems do not possess the roughening phenomenon.     

A mixed integer and multiple objective programming model to analyze coal handling in New England

Mandated electric generation coal conversions in New England could place a severe strain on the coal handling and transportation facilities in New England ports. This paper presents an analytical scheme leading to the development of optimal plans for the reuse and redevelopment of marine transport networks in New England. Utilizing the port inventory that provides information on existing coal handling facilities and the capability of the ports to increase capacity of existing facilities or locating new facilities, a mathematical programming model is used to determine the optimal capacity, placement and railrod and marine interface of coal handling facilities within and between the New England ports and converting power plants.Initially a mixed integer programming model with a least cost objective is formulated. It is then expanded to a multiobjective programming problem in order to provide information to the port planners and decision makers on the tradeoffs between the costs and temporal efficiency of coal transporation and handling for various locational configurations.     

Critical evaluation of voltammetric analysis of fat-soluble vitamins

High precision, sensitivity, reliability, and specificity, coupled with simplicity, are essential requirements for a good quantitative analytical technique. With these parameters in mind recent developments have been incorporated into voltammetric methods for the quantification of fat-soluble vitamins.