Properties of optimal schedules in preemptive shop scheduling

In this work we show that certain classical preemptive shop scheduling problems with integral data satisfy the following integer preemption property: there exists an optimal preemptive schedule where all interruptions and all starting and completion times occur at integral dates. We also give new upper bounds on the minimal number of interruptions for various shop scheduling problems.     

Remarks on existence and uniqueness of Cournot–Nash equilibria in the non-potential case

This article is devoted to various methods (optimal transport, fixed-point, ordinary differential equations) to obtain existence and/or uniqueness of Cournot–Nash equilibria for games with a continuum of players with both attractive and repulsive effects. We mainly address separable situations but for which the game does not have a potential, contrary to the variational framework of Blanchet and Carlier (Optimal transport and Cournot–Nash equilibria, 2012). We also present several numerical simulations which illustrate the applicability of our approach to compute Cournot–Nash equilibria.     

PAT – a Reliable Path-Following Algorithm

This paper presents a new technique for the reliable computation of the -pseudospectrum defined by (A)={zC : _min(A–zI)} where _min is the smallest singular value. The proposed algorithm builds an orbit of adjacent equilateral triangles to capture the level curve (A)={zC : _min(A–zI)=} and uses a bisection procedure on specific triangle vertices to compute a numerical approximation to . The method is guaranteed to terminate, even in the presence of round-off errors.     

Thermal evolution and light curves of young bare strange stars

We study numerically the cooling of a young bare strange star and show that its thermal luminosity, mostly due to e(+)e(-) pair production from the quark surface, may be much higher than the Eddington limit. The mean energy of photons far from the strange star is approximately 10(2) keV or even more. This differs both qualitatively and quantitatively from the thermal emission from neutron stars and provides a definite observational signature for bare strange stars. It is shown that the energy gap of superconducting quark matter may be estimated from the light curves if it is in the range from approximately 0.5 MeV to a few MeV.     

On the mechanism of the P2-Na0.70CoO2→O2-LiCoO2 exchange reaction—Part I: proposition of a model to describe the P2-O2 transition

A model was proposed to describe the exchange reaction of sodium by lithium in P2 crystals. The exchange consists on the formation of nucleation centers and then on the growth of O2 domains in P2 crystals from these nucleation centers. Octahedral environments for lithium ions are obtained when one slab over two glides by (2/3,1/3,0) or by (1/3,2/3,0) in P2 structure. The existence of two different gliding vectors should lead to stacking faulted structures that can be simulated using DIFFaX software. The comparison of simulated and experimental XRD patterns for O2-LiCoO₂ (ex-Na_0.7CoO₂) has shown that in that case the growth of the O2 domains in the P2 crystals is faster than the formation of nucleation centers.     

Crystal packing mediates enantioselective ligand recognition at the peripheral site of acetylcholinesterase

Recently, alkylene-linked heterodimers of tacrine (1) and 5-amino-5,6,7,8-tetrahydroquinolinone (2, hupyridone) were shown to exhibit higher acetylcholinesterase (AChE) inhibition than either monomeric 1 or 2. Such inhibitors are potential drug candidates for ameliorating the cognitive decrements in early Alzheimer patients. In an attempt to understand the inhibition mechanism of one such dimer, (RS)-(+/-)-N-9-(1,2,3,4-tetrahydroacridinyl)-N'-5-[5,6,7,8-tetrahydro-2'(1'H)-quinolinonyl]-1,10-diaminodecane [(RS)-(+/-)-3] bisoxalate, the racemate was soaked in trigonal Torpedo californica AChE (TcAChE) crystals, and the X-ray structure of the resulting complex was solved to 2.30 A resolution. Its structure revealed the 1 unit bound to the "anionic" subsite of the active site, near the bottom of the active-site gorge, as seen for the 1/TcAChE complex. Interestingly, only the (R)-enantiomer of the 2 unit was seen in the peripheral "anionic" site (PAS) at the top of the gorge, and was hydrogen-bonded to the side chains of residues belonging to an adjacent, symmetry-related AChE molecule covering the gorge entrance. When the same racemate was soaked in orthorhombic crystals of TcAChE, in which the entrance to the gorge is more exposed, the crystal structure of the corresponding complex revealed no substantial enantiomeric selectivity. This observation suggests that the apparent enantiomeric selectivity of trigonal crystals of TcAChE for (R)-3 is mainly due to crystal packing, resulting in preferential binding of one enantiomeric inhibitor both to its "host" enzyme and to its neighbor in the asymmetric unit, rather than to steric constraints imposed by the geometry of the active-site gorge.