Heuristic Algorithms and Scatter Search for the Cardinality Constrained P||Cmax Problem

We consider the generalization of the classical P||C_max problem (assign n jobs to m identical parallel processors by minimizing the makespan) arising when the number of jobs that can be assigned to each processor cannot exceed a given integer k. The problem is strongly NP-hard for any fixed k > 2. We briefly survey lower and upper bounds from the literature. We introduce greedy heuristics, local search and a scatter search approach. The effectiveness of these approaches is evaluated through extensive computational comparison with a depth-first branch-and-bound algorithm that includes new lower bounds and dominance criteria.     

How to assess and report the performance of a stochastic algorithm on a benchmark problem: mean or best result on a number of runs?

Some authors claim that reporting the best result obtained by a stochastic algorithm in a number of runs is more meaningful than reporting some central statistic. In this short note, we analyze and refute the main argument brought in favor of this statement.     

A non-isothermal Ginzburg–Landau model in superconductivity: Existence,uniqueness and asymptotic behaviour

In this paper we study a Ginzburg–Landau model which describes the behaviour of a superconducting material including thermal effects. We extend the traditional formulation of the problem, by introducing the temperature as an additional state variable. Accordingly, together with the Gor’kov–Eliashberg system, we introduce an evolution equation for the absolute temperature. We examine in detail the case which allows only variations of the concentration of superconducting electrons and of the temperature, neglecting the electromagnetic field. For this problem existence and uniqueness of the solution are shown. Finally we analyze the asymptotic behaviour of the solutions, proving that the system possesses a global attractor.     

A purely algebraic characterization of the hyperreal numbers

The hyperreal numbers of nonstandard analysis are characterized in purely algebraic terms as homomorphic images of a suitable class of rings of functions.

     

Crystal and molecular structure of nitrosyl(1,10-phenanthroline)-bis(triphenylphosphine)iridium(I) Dihexafluorophosphate, [Ir(NO)(phen)(PPh3)2][PF6]2

Summary The structure of [Ir(NO)(phen)(PPh₃)₂][PF₆]₂ has been determined from x-ray diffractometer data. The compound crystallizes in space groupPnam with four molecules in a unit cell witha = 19.924(12),b = 14.793(9) andc = 16.348(9) A. Full-matrix least-squares refinement has led to a final R value of 0.061 for the 4796 observed reflections. The structure consists of well-separated ions, and the geometry around the metal is trigonal bipyramidal with nitrosyl and bidentate 1,10-phenanthroline (in spite of the very narrow bite angle of 75.8°) ligands occupying the equatorial positions and the triphenylphosphine ligands the axial positions. The cation has an imposed crystallographicm symmetry. Important bond lengths are as follows: Ir-P, 2.391(3): Ir-N (nitrosyl) 1.700(12): Ir-N (1,10-phenanthroline) 2.103(12) and 2.142(11): N-O, 1.201(18)A. The nitrosyl ligand is linear [Ir-N-O = 179.9(9)°] so that this complex can be formulated as an NO⁺ complex of iridium(I).     

Age related changes in the thermal transition of Turkey leg flexor tendon collagen

A differential scanning calorimetric, thermogravimetric and electron microscopic investigation has been carried out on the uncalcified areas of turkey leg flexor tendon as a function of age. Rehydrated samples exhibit an increase of thermal stability with age. The H_D values drop from about 11 cal·g^–1 in the first weeks of life down to 7 cal·g^–1 after the 11th week.At about 11 weeks, the collagen fibril diameter distribution passes from unimodal to multimodal. The DSC curves as well as the TG-DTG curves recorded from dried samples do not show any appreciable difference with ageing. The variations in thermal behaviour of rehydrated samples and fibril diameter distribution could be related to modifications in water binding with ageing.The Authors are grateful to Dr. G. Fabris for discussion and help in the selection of the samples. They also wish to thank Mr. G. Pizzuto for excellent technical assistance. The financial support by Consiglio Nazionale delle Ricerche is gratefully acknowledged.     

Spectrophotometric titration of mercury(II) with ethylenedithiodiacetic acid

Summary Mercuric ions may be determined by titration with ethylenedithiodiacetic acid at a wavelength of 260 nm at any pH less than 1. The method is simple, rapid, and selective, and is applicable in solutions of high electrolyte concentration. Mercury(II) can be determined down to 1.5×10^–5 M with a relative standard deviation less than 2%.

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Zusammenfassung Quecksilber (II) läßt sich mit Äthylendithiodiessigsäure bei 260 nm und pH1 titrieren. Das Verfahren ist einfach, rasch und selektiv. Es läßt sich auch für Lösungen mit hoher Elektrolytkonzentration anwenden. Hg(II)-Konzentrationen über 1,5×10^–5 M sind mit einer relativen Standardabweichung unter 2% bestimmbar.

     

On the 2 and the 3-connectedness of ample divisors on a surface

Let X be a nonsingular complex projective surface and let D be an ample divisor on X such that the associated invertible sheaf is spanned by its global sections. We prove that D is 2-connected apart from a few cases we explicitly describe. We also provide a corresponding result for the 3-connectedness when D²10 and for the 4-connectedness when D²17 and D is very ample.