On the supermodular knapsack problem

In this paper we introduce binary knapsack problems where the objective function is nonlinear, and investigate their Lagrangean and continuous relaxations. Some of our results generalize previously known theorems concerning linear and quadratic knapsack problems. We investigate in particular the case in which the objective function is supermodular. Under this hypothesis, although the problem remains NP-hard, we show that its Lagrangean dual and its continuous relaxation can be solved in polynomial time. We also comment on the complexity of recognizing supermodular functions. The particular case in which the knapsack constraint is of the cardinality type is also addressed and some properties of its optimal value as a function of the right hand side are derived.Work done while the authors were visiting Rutgers University.     

Where are embarrassingly parallel problems? The atom-diatom quasiclassical reactivity

Summary The apparently embarrassingly parallel problem of calculating a batch of quasiclassical trajectories to evaluate cross sections or rate constants has been analyzed. The study shows that only an accurate evaluation of the performance parameters and a consequent appropriate restructuring of the computer code allows the achievement of high speedup and efficiency especially when large calculations are implemented on massively parallel systems.     

THE MECHANISM OF THE 9,10-DIBROMOANTHRACENE MEDIATED TRIPLET-SINGLET ENERGY TRANSFER IN THE TETRAMETHYL-1,2-DIOXETANE ENERGIZED RUBRENE LUMINESCENCE*

Abstract— The ternary chemiluminescent system consisting of tetramethyl-dioxetane (TMD), 9 ,10-dibromoanthracene (DBA) and rubrene (Ru) has been investigated in benzene solution and in polystyrene matrices. DBA has been found to mediate the energy transfer between excited triplet acetone (³K), generated from TMD, and rubrene resulting in the enhancement of the Ru emission and reduction in the DBA emission. A detailed kinetic analysis confirms that ca. 50% of the enhanced chemilumines-cence involves triplet-singlet (TS) energy transfer from ³K to DBA, followed by singlet-singlet (SS) energy transfer from DBA to Ru, the remainder ca. 50% being due to reabsorption of DBA fluorescence by rubrene. It is concluded that the TS energy transfer is of the resonance type, occurring with a rate of k^TS_K.DBA= (1.4 ± 0.4) ± 10⁹M^-1s^-1 and an efficiency of ø^TS_K.DBA= 0.3 ± 0.1. As expected, the SS energy transfer is also of the resonance type, taking place at comparable rates in benzene solution and in polystyrene matrices, is. k^SS_DBARU= 1.5 ± 10¹⁰ M^-1 and (2.2 ± 0.2) ± 10¹⁰M^-1s^-1, respectively.     

Fluorine core esca linewidths in CH3F and CF4

Ab initio calculations within the Hartree-Fock formation have been carried out on potential energy surfaces of the ground and the F_1s hole states of CH₃F and CF₄ in order to investigate linewidths of their ESCA spectra. The calculations show that potential energy surfaces of both hole states have dissociative character and can be approximated by straight lines in the region of interest. A simple formula for the ESCA fwhm linewidth is derived which yields results in good agreement with experiment. Theoretically derived relaxation and Koopmans' energies have been investigated as a function of geometry.     

On the phase equilibrium Stockmayer fluids

The fluid phase equilibrium of the Stockmayer fluid is investigated using a thermodynamic perturbation theory approach. The reference and the perturbation potential are the Lennard–Jones potential and the dipolar–dipolar interactions, respectively. They are assumed to be represented by the modified Benedict–Webb–Rubin equation of state [J.K. Johnson, J.A. Zollweg, K.E. Gubbins, Mol. Phys. 78 (1993) 591–618] and the Padé approximant [G. Stell, J.C. Rasaiah, H. Narang, Mol. Phys. 27 (1974) 1393–1414], respectively. The asymmetry found in an analogous study [M.E. van Leeuwen, B. Smit, E.M. Hendriks, Mol. Phys. 78 (1993) 271–283] based on the BWR equation of state [J.J. Nicolas, K.E. Gubbins, W.B. Streett, D.J. Tildesley, Mol. Phys. 37 (1979) 1429–1454] is now not observed on the vapour–liquid equilibrium coexistence curves of Stockmayer fluids with dipolar strength of μ^*2 = 1, 2, 3, and 4. Results agree with computer simulations for dipolar strength of μ^*2 = 1; however as strength dipole increases, liquid densities are over-estimated.     

Spectroscopic studies of the intermolecular interactions of Congo red and tinopal CBS with modified cellulose fibers

The adsorption of Congo red and tinopal CBS dyes on cellulose fibers was investigated using electronic absorption and fluorescence spectroscopies. Hydrogen bonds appear to be relevant for the dye-fiber interactions as indicated by the solvatochromism of Congo red in water, methanol, and dimethyl sulfoxide solutions, and when adsorbed on cellulose fibers. We also demonstrate that electrostatic interactions play an important role in the dye-medium interaction, through the analysis of absorption spectra of Congo red and fluorescence spectra of tinopal in aqueous solutions containing salt and in layer-by-layer nanostructured films with poly(allylamine hydrochloride). For instance, dye adsorption was enhanced when salt was added to the dipping solution, which was explained by the synergistic effect between the conformational changes of the cellulose and changes in the solvation layer around the cellulose chains and around dye molecules. On the basis of the fluorescence results for tinopal CBS, we inferred that dye aggregation is not relevant for adsorption on the fibers. In addition, fluorescence spectroscopy is proven very sensitive for studying the organization of dye molecules in layer-by-layer films, particularly those undergoing irreversible structural changes.     

Weighted Inequalities for Multilinear Potential Operators and their Commutators

We prove weighted strong inequalities for the multilinear potential operator T_f{\cal T}_{\phi} and its commutator, where the kernel ϕ satisfies certain growth condition. For these operators we also obtain Fefferman-Stein type inequalities and Coifman type estimates. Moreover we prove weighted weak type inequalities for the multilinear maximal operator M_j,L^B\mathcal{M}_{\varphi,L^{B}} associated to an essentially nondecreasing function φ and to the Orlicz space L ^B for a given Young function B. This result allows us to obtain a weighted weak type inequality for the operator T_f{\cal T}_{\phi}.     

Novel Applications of Raney Nickel/Isopropanol: Efficient System for the Reduction of Organic Compounds

Catalytic hydrogenation of various organic substrates with Raney nickel in isopropanol proceeds under mild conditions of temperature and pressure. Comparison with other catalysts systems evidenced the superiority of Raney nickel/isopropanol.