Fairness in Scheduling

On-line machine scheduling has been studied extensively, but the fundamental issue of fairness in scheduling is still mostly open. In this paper we explore the issue in settings where there are long-lived processes which should be repeatedly scheduled for various tasks throughout the lifetime of a system. For any such instance we develop a notion ofdesiredload of a process, which is a function of the tasks it participates in. Theunfairnessof a system is the maximum, taken over all processes, of the difference between the desired load and the actual load.An example of such a setting is thecarpool problemsuggested by Fagin and Williams [IBM Journal of Research and Development27(2) (1983), 133–139]. In this problem, a set ofnpeople form a carpool. On each day a subset of the people arrive and one of them is designated as the driver. A scheduling rule is required so that the driver will be determined in a “fair” way.We investigate this problem under various assumptions on the input distribution. We also show that the carpool problems can capture several other problems of fairness in scheduling.     

Effects of alcohols on micellization and on the reaction methyl 4‐nitrobenzenesulfonate + Br− in cetyltrimethylammonium bromide aqueous micellar solutions

The effects of n‐hexanol, n‐pentanol, and n‐butanol on the critical micelle concentration (cmc), on the micellar ionization degree (α), and on the rate of the reaction methyl 4‐nitrobenzenesulfonate + Br^? have been investigated in cetyltrimethylammonium bromide (CTAB) aqueous solutions. An increase in the alcohol concentration present in the solution produces a decrease in the cmc and an increase in the micellar ionization degree. Kinetic data show that the observed rate constant decreases as alcohol concentration increases. This result was rationalized by considering variations in the equilibrium binding constant of the methyl 4‐nitrobenzenesulfonate molecules to the micelles, variations in the interfacial bromide ion concentration, and variations in the characteristics of the water–alcohol bulk phase provoked by the presence of alcohols. When these operative factors are considered, kinetic data in this and other works show that the second‐order rate constants in the micellar pseudophases of water–alcohol micellar solutions are quite similar to those estimated in the absence of alcohols. © 2004 Wiley Periodicals, Inc. Int J Chem Kinet 36: 634–641, 2004     

Micellar solutions of sulfobetaine surfactants in water-ethylene glycol mixtures: surface tension, fluorescence, spectroscopic, conductometric, and kinetic studies

Micellization in water-ethylene glycol (EG) N-dodecyl, N-tetradecyl, and N-hexadecyl-N,N-dimethyl-3-ammonio-1-propanesulfonate (SB3-12, SB3-14, and SB3-16, respectively) micellar solutions, with the weight percent of EG changing within the range 0-40, was studied by means of surface tension measurements. Information about the influence of the added EG on the aggregation number of the sulfobetaine micelles and on the polarity of the interfacial region of micelles was obtained through fluorescence and spectroscopic measurements. Surface tension measurements also provide information about the dependence of the surface excess concentration, the minimum area per surfactant molecule, the surface pressure at the cmc, and the standard Gibbs energy of adsorption on the added weight percent of the organic solvent. The Gordon parameter of the water-EG mixtures was also estimated by means of surface tension measurements. The thermodynamic and structural changes originated by the presence of EG control the micellar kinetic effects observed in the reaction methyl 4-nitrobenzenesulfonate + Br(-) occurring in the water-EG sulfobetaine micellar solutions. Information about the distribution of bromide ions between the bulk and micellar pseudophases was obtained through conductivity measurements. The kinetic micellar effects were quantitatively explained by using the pseudophase kinetic model.     

Energy migration in novel pH-triggered self-assembled beta-sheet ribbons

Energy migration between tryptophan residues has been experimentally demonstrated in self-assembled peptide tapes. Each peptide contains 11 amino acids with a Trp at position 6. The peptide self-assembly is pH-sensitive and forms amphiphilic tapes, which further stack in ribbons (double tapes) and fibrils in water depending on the concentration. Fluorescence spectra, quenching, and anisotropy experiments showed that when the pH is lowered from 9 to 2, the peptide self-assembly buries the tryptophan in a hydrophobic and restricted environment in the interior of stable ribbons as expected on the basis of the peptide design. These fluorescence data support directly and for the first time the presence of such ribbons which are characterized by a highly packed and stable hydrophobic interior. In common with Trp in many proteins, fluorescence lifetimes are nonexponential, but the average lifetime is shorter at low pH, possibly due to quenching with neighboring Phe residues. Unexpectedly, time-resolved fluorescence anisotropy does not change significantly with self-assembly when in water. In highly viscous sucrose-water mixtures, the anisotropy decay at low pH was largely unchanged compared to that in water, whereas at high pH, the anisotropy decay increased significantly. We concluded that depolarization at low pH was not due to rotational diffusion but mainly due to energy migration between adjacent tryptophan residues. This was supported by a master equation kinetic model of Trp-Trp energy migration, which showed that the simulated and experimental results are in good agreement, although on average only three Trp residues were visited before emission.     

Dications of fluorenylidenes. The effect of substituent electronegativity and position on the antiaromaticity of substituted tetrabenzo[5.5]fulvalene dications

Oxidation of 3,6-disubstituted tetrabenzo[5.5]fulvalenes by SbF(5) results in the formation of dications that behave like two antiaromatic fluorenyl cations connected by a single bond. Both fluorenyl systems exhibit the paratropic shifts and nucleus independent chemical shifts (NICS) characteristic of antiaromatic species. Comparison with analogous 2,7-disubstituted tetrabenzo[5.5]fulvalenes reveals that the antiaromaticity of the substituted ring system can be altered substantially by changes in the placement of the substituents, possibly due to changes in the delocalization of charge in the system. Substituents in the 3,6-position decrease the antiaromaticity because of the increase in the benzylic resonance compared to 2,7-substituents.     

Reaction of methyl 4-nitrobenzenesulfonate with Br- in water-formamide tetradecyltrimethylammonium bromide micellar solutions

Summary The reaction methyl 4-nitrobenzenesulfonate + Br^- was studied in water-formamide tetradecyltrimethylammonium bromide micellar solutions. A pseudophase kinetic model was used to quantitatively rationalize the kinetic micellar effects observed     

Kinetic study in water-ethylene glycol cationic, zwitterionic, nonionic, and anionic micellar solutions

The spontaneous hydrolysis of phenyl chloroformate was studied in water-ethylene glycol, EG, cationic, zwitterionic, nonionic, and anionic micellar solutions, the surfactants being tetradecyltrimethylammonium bromide, tetradecyl-N,N-dimethyl-3-ammonio-1-propanesulfonate, tricosaoxyethylene glycol ether, and sodium dodecyl sulfate. The dependence of the observed rate constant on surfactant concentration as well as on the percentage by weight of EG, varying from 0 to 50 wt %, was investigated. Information about changes in the critical micelle concentrations, in the micellar ionization degrees (for ionic surfactants), in the aggregation numbers, and in the polarity of the interfacial region of the micelles upon changing the weight percent of EG was obtained through conductivity, surface tension, spectroscopic, and fluorescence measurements. A simple pseudophase model was adequate to rationalize the kinetic data. Micellar medium effects were explained by considering charge-charge interactions and polarity, ionic strength, and water content in the micellar interfacial region. The acceleration of the reaction produced by an increase in the amount of EG present in the mixture was explained on the basis of the substantial decrease in the equilibrium binding constant of phenyl chloroformate molecules to the micelles, resulting in the contribution of the reaction taking place in the bulk water-EG phase being more important. The weight percent of EG did not substantially influence the rate constant in the micellar pseudophase.     

Volumes of activation for dissociation of pentacyanoferrates(II) through pressure and salt effects on reactivity

Summary Dependences of rate constants on pressure (up to 1 kbar) and on added salt concentration (up to 6.0 mol dm^–3 LiNO₃, NaNO₃, NaCl, Na₂SO₄ or KNO₃) have been established for dissociative substitution of pentacyanoferrates(II), [Fe(CN)₅L]^3– with L = 4-cyanopyridine, 4,4-bipyridyl, 4-phenylpyridine and 4-t-butylpyridine. Activation volumes derived directly from pressure effects, and indirectly from salt effects via surface tension dependences and derived surfaces of activation, are reported, compared and discussed.     

Synthesis,Spectral and Magnetic Properties,and Crystal Structures of Copper(II) Pyridinecarboxylate Adducts with N‐Heterocyclic Ligands

Synthesis and characterization of seven new complexes [Cu(2‐MeSnic)₂(CH₃OH)]₂ (where 2‐MeSnic is 2‐methylthionicotinate), [Cu(2‐MeSnic)₂L₂]₂ (where L is pyridine — py, ethylnicotinate — Etnic and butylnicotinate — Bunic), [Cu(2‐MeSnic)₂L₂(H₂O)₂] (where L is py and nicotinamide — nia) and [Cu(2‐MeSnic)₂(N‐Menia)₂(H₂O)₂]·2H₂O (where N‐Menia is N‐methylnicotinamide) are reported. The characterization were based on elemental analysis, infrared, electronic and EPR spectra, and magnetic susceptibility measurements over a temperature range of 1.8 — 300 K or 70 — 300 K. Three complexes of different type were studied by X‐ray analysis. The molecule of [Cu(2‐MeSnic)₂(CH₃OH)]₂ has dimeric paddle‐wheel cage structure with a tetragonal pyramidal arrangement around Cu^II. The dimer results from the fact that carboxyl groups of four 2‐MeSnic anions function as bridging in a syn‐syn arrangement. On the other hand [Cu(2‐MeSnic)₂(py)₂]₂ forms dimers with hexacoordinated Cu^II atoms in highly distorted coordination octahedra, each with two oxygen atoms of bridging carboxyl groups in an anti‐anti arrangement of two 2‐MeSnic anions, with two oxygen atoms of one asymmetrically chelating 2‐MeSnic anion and with two nitrogen atoms of two pyridine ligands. The temperature independent EPR spectrum for this complex exhibits an axial signal which corresponds to almost isolated S = ¹/₂ magnetic ions. Magnetic data for the dimer show a weak antiferromagnetic interaction between the two metal ions with J = —0.65 cm^—1. The Cu^II atom in complex [Cu(2‐MeSnic)₂(py)₂(H₂O)₂] is hexacoordinated in an elongated centrosymmetrical tetragonal‐bipyramidal arrangement (4 + 2). Based on the molecular structure the electronic, infrared, electron paramagnetic resonance spectra and magnetic properties are discussed and stereochemistry as well as the mode of ligand coordination in new solid complexes under study have been determined.