Counting and enumeration complexity with application to multicriteria scheduling

In this paper we tackle an important point of combinatorial optimisation: that of complexity theory when dealing with the counting or enumeration of optimal solutions. Complexity theory has been initially designed for decision problems and evolved over the years, for instance, to tackle particular features in optimisation problems. It has also evolved, more or less recently, towards the complexity of counting and enumeration problems and several complexity classes, which we review in this paper, have emerged in the literature. This kind of problems makes sense, notably, in the case of multicriteria optimisation where the aim is often to enumerate the set of the so-called Pareto optima. In the second part of this paper we review the complexity of multicriteria scheduling problems in the light of the previous complexity results.Received: November 2004 / Received version: March 2005MSC classification: 90B40, 90C29, 68Q15     

Beta-decay of 71Co and 73Co

A decay spectroscopy study of the neutron-rich cobalt isotopes has been performed using fragmentation of a ⁸⁶Kr³⁶⁺ beam and the new LISE2000 spectrometer at GANIL. For ⁷¹Co and ⁷³Co, the -delayed radiation has been observed for the first time, and the half-lives were found to be 79(5) ms and 41(4) ms, respectively. Features of the decay are discussed qualitatively in terms of nuclear models.     

Acid promoted enantioselective oxygen-atom transfer from N-alkyl binaphthyl-derived oxaziridines onto sulfides

Acid-promoted asymmetric sulfoxidations of prochiral sulfides using binaphthyl-derived oxaziridines have been studied. The reactions of dialkyl or aryl-alkyl sulfides gave good yields of the corresponding sulfoxides with enantiopurities ranging from 20% to 80%. The influence of temperature and strength of the acid catalyst on enantioselectivity was studied. The absolute configuration of the resulting major enantiomer varied with the structure of the sulfide.     

Enhanced core polarization in (70)Ni and (74)Zn

The reduced transition probabilities B(E2;0(+) --> 2(+)(1)) of the neutron-rich (74)Zn and (70)Ni nuclei have been measured by Coulomb excitation in a (208)Pb target at intermediate energy. These nuclei have been produced at Grand Accélérateur National d'Ions Lourds via interactions of a 60A MeV (76)Ge beam with a Be target. The B(E2) value for (70)Ni(42) is unexpectedly large, which indicates that neutrons added above N=40 strongly polarize the Z=28 proton core. In the Zn isotopic chain, the steep rise of B(E2) values beyond N=40 continues up to (74)Zn(44). The enhanced proton core polarization in (70)Ni is attributed to the monopole interaction between the neutron in the g(9/2) and protons in the f(7/2) and f(5/2) spin-orbit partner orbitals. This interaction could result in a weakening of magicity in (78)Ni(50).     

Multiple Unbounded Positive Solutions for Three-Point BVPs with Sign-Changing Nonlinearities on the Positive Half-Line

This work is concerned with the existence of unbounded positive solutions for a second-order nonlinear three-point boundary value problem on the positive half-line. The interesting points of the results are that the nonlinearity depends on the solution and its derivative and may change sign. Moreover, it satisfies general polynomial growth conditions. New existence results of nontrivial single and multiple positive solutions are proved using recent fixed point theorems on cones in a special Banach space.     

Price competition and store competition: Store brands vs. national brand

This paper studies pricing strategies in a market channel composed of one national brand manufacturer and two retailers who, each, carry their own store brand and a national brand products. The model accounts for product competition between store brands and the national brand products, as well as for store competition between retailers.     

A microwave-assisted and heteropolyacids-catalysed cyclocondensation reaction for the synthesis of 4(3H)-quinazolinones

We have investigated a microwave-assisted synthesis of 4(3H)-quinazolinones by condensation of anthranilic acid, orthoesters (or formic acid) and substituted anilines,using Keggin-type heteropolyacids (H(3)PW(12)O(40).13H(2)O, H(4)SiW(12)O(40).13H(2)O,H(4)SiMo(12)O(40).13H(2)O or H(3)PMo(12)O(40).13H(2)O) as catalysts. We found that the the use of H(3)PW(12)O(40).13H(2)O acid coupled to microwave irradiation allows a solvent-free, rapid (approximately 13min) and high-yielding reaction.     

On uniqueness and existence of entropy solutions for a nonlinear parabolic problem with absorption

The aim of this paper is to study, for L ¹-data, the absorption problem of parabolic type : with Dirichlet boundary conditions and initial conditions. Here a satisfies the classical Leray-Lions hypotheses and β(x, ·) is the subdifferential ∂j(x, ·), where j is a convex function such that j(·, 0) = 0. Existence and uniqueness of an entropy solution is established.      

Microwave‐Assisted Synthesis of Arylazoaminopyrazoles as Disperse Dyes for Textile Printing

The synthesis of heterocyclic azo‐dyes via conventional heating and microwave (MW) heating was investigated. From a sequence of reactions starting from cyanoacetic acid, 4‐arylazo‐2H‐pyrazol‐3‐ylamines and 4‐arylazo‐2‐phenyl‐2H‐pyrazol‐3‐ylamines were obtained. The structures these compounds were obtained by inspection of spectroscopic and analytical techniques including ¹H and ¹³C NMR spectroscopy, IR spectroscopy, mass spectrometry, and elemental analysis. The fastness properties and UV/Vis absorption spectroscopic data of these disperse dyes in printing polyester fabrics were investigated.