The generalized assignment problem with flexible jobs

The Generalized Assignment Problem (GAP) seeks an allocation of jobs to capacitated resources at minimum total assignment cost, assuming a job cannot be split among multiple resources. We consider a generalization of this broadly applicable problem in which each job must not only be assigned to a resource, but its resource consumption must also be determined within job-specific limits. In this profit-maximizing version of the GAP, a higher degree of resource consumption increases the revenue associated with a job. Our model permits a job’s revenue per unit resource consumption to decrease as a function of total resource consumption, which allows modeling quantity discounts. The objective is then to determine job assignments and resource consumption levels that maximize total profit. We develop a class of heuristic solution methods, and demonstrate the asymptotic optimality of this class of heuristics in a probabilistic sense.     

Pion form factor from 480 MeV to 1100 MeV

The pion form factor is measured in the reaction e⁺e^? → π⁺π^? for center of mass energies in the range 480–1100 MeV. Our results are first analysed in terms of the conventional Vector Meson Dominance formalism, and then taking into account the ωπ inelastic channel. The result of this later formalism is a pion form factor (F_π) which fits quite well all the existing data on F_π both in the timelike and spacelike regions, and pion mean square radius of 〈r_π²〉 = 0.460 ± 0.011 fm² or $\text{〈r}{}_{\mathrm{\pi }}{}^2\text{〉}{}^{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}\text{= 0.678 ± 0.008}\text{fm}$.     

Polyolefin soluble polyisobutylene oligomer‐bound metallophthalocyanine and azo dye additives

Metallophthalocyanines prepared with polyisobutyl (PIB) substituents have very high solubility in organic solvents including saturated hydrocarbons, toluene, and other low polarity organic solvents. In heptane, PIB‐bound metallophthalocyanines have solubility of about 0.1 g/mL at 25 °C, solubility values that are significantly higher than other substituted metallophthalocyanines. PIB terminally functionalized with metallophthalocyanines as well as PIB containing terminal azo dye groups also dissolve in molten hydrocarbon polymers like polyethylene or polypropylene. Thus, these highly chromogenic PIB‐bound dyes can be incorporated uniformly into the polyolefins to form colored polymer solids on cooling. Because only a low concentration of a highly hydrocarbon compatible dye is used, the crystallinity and thermal properties of the colored polyolefin products are not significantly affected. © 2013 Wiley Periodicals, Inc. J. Polym. Sci., Part A: Polym. Chem. 2014 , 52, 545–551     

A correlation for yield stress fluid flow through packed beds

Relatively few correlations are available for non-Newtonian fluid flows through packed beds, even though such fluids are frequently used in industry. In this paper, a correlation is presented for yield stress fluid flow through packed beds. The correlation is developed by introducing the yield stress model in place of the Newtonian model used in deriving Erguns equation. The resulting model has three parameters that are functions of the geometry and roughness of the particle surfaces. Two of the parameters can be deduced in the limit as the yield stress becomes negligible and the model reduces to Erguns equation for Newtonian fluids. The third model parameter is determined from experimental data. The correlation relates a defined friction factor to the dimensionless Reynolds and Hedstrom numbers and can be used to predict pressure drop for flow of a yield stress fluid through a packed bed of spherical particles. Conditions for flow or no-flow are also determined in the correlation. Comparison of model calculations, between a Newtonian and a yield stress fluid for flow penetration into a packed bed of spheres, shows the yield stress fluid initially performs similar to the Newtonian fluid, at large Reynolds numbers. At lower Reynolds numbers the yield stress effect becomes important and the flow rate significantly decreases when compared to the Newtonian fluid.     

Fluctuations of multiplicities in rapidity windows in sulphur-sulphur collisions at 200A GeV

Multiplicity distributions and their second moments fornegatively charged particles produced in³²S-S central and minimum bias interactions at 200A GeV are studied in various rapidity intervals. Fritiof and Venus models mostly describe the dependence of second moments on rapidity intervals in minimum bias interactions, but not in central collisions. For central collisions the behaviour of second moments might indicate enhanced multiplicity fluctuations.     

Conformational analysis of gossypol and its derivatives by molecular mechanics

Conformations and inversion pathways leading to racemization of all the tautomers of gossypol, gossypolone, anhydrogossypol, and a diethylamine Schiff's base of gossypol were investigated with MM3(2000). All forms have hindered rotation because of clashes between the methyl carbon atom and oxygen-containing moieties ortho to the bond linking the two naphthalene rings. Inversion energies generally agree with available experimental data. Gossypol preferentially inverts in its dihemiacetal tautomeric form through the cis pathway (where similar groups clash). Gossypolone inverts more easily than gossypol, and preferentially through the trans pathway (where dissimilar groups clash) when one of its outer rings has an enol-keto group and the other has an aldehyde group. Anhydrogossypol racemizes through the cis pathway. The bridge bond and the ortho exo-cyclic bonds in all the structures bend from planarity, and the inner naphthalene rings pucker to accommodate the inversion. For gossypol, the transition is achieved through greater bending of the exo-cyclic bonds (up to 12°) and less distortion of the inner benzyl rings (q≤0.34 Å), (up to 12.7°) . For gossypolone the transition occurs with greater distortion of the inner benzyl rings (q≤0.63 Å) and less out-of-plane bending (up to 8.4°). By isolating individual clashes, their contribution to the overall barrier can be analyzed, as shown for the dialdehyde tautomer of gossypol.     

Intensity perception. XII. Effect of presentation probability on absolute identification

Identification experiments using 13 tone-pulse stimuli (1000 Hz, 500 ms) spaced by equal decibel increments from 42 to 90 dB SPL were conducted under three conditions: all intensities equally likely (denoted Q), the middle intensity presented on roughly 1/3 of the trials (M), and each of the extreme intensities presented on roughly 1/5 of the trials (E). Experiments were performed both with and without feedback, and results were analyzed in terms of sensitivity and bias. Similar results were obtained with and without feedback: listeners generally shifted biases in the M and E conditions relative to the Q condition to increase percent-correct scores, but there were only minor changes in sensitivity from condition to condition. However, sensitivities were generally higher and biases more optimal when feedback was available. The results on sensitivity are consistent with those associated with payoff variation [Lippmann et al., J. Acoust. Soc. Am. 59, 129-134 (1976)], but are inconsistent with those reported for presentation probability variation in tone frequency identification [Cuddy et al., J. Exp. Psychol. 100, 218-220 (1973)]. In an auxilliary experiment concerned with tone frequency identification, results consistent with those obtained for intensity, but inconsistent with those reported by Cuddy et al., were obtained.