Remarkable polyhedra related to set functions,games and capacities

Set functions are widely used in many domains of operations research (cooperative game theory, decision under risk and uncertainty, combinatorial optimization) under different names (TU-game, capacity, nonadditive measure, pseudo-Boolean function, etc.). Remarkable families of set functions form polyhedra, e.g., the polytope of capacities, the polytope of p-additive capacities, the cone of supermodular games, etc. Also, the core of a set function, defined as the set of additive set functions dominating that set function, is a polyhedron which is of fundamental importance in game theory, decision-making and combinatorial optimization. This survey paper gives an overview of these notions and studies all these polyhedra.     

Synthesis and Characterization of GaIII,YIII, and LuIII Complexes with Etifenin and Analogues

Complexes of etifenin ( 1a ), disofenin ( 1b ), and mebrofenin ( 1c ) with Ga^III, Y^III, and Lu^III were synthesized and characterized by NMR spectroscopy and UV/Vis spectroscopy. Stability and protonation constants of the complexes of 1a were determined by potentiometry and distribution diagrams were calculated. It was shown that the Y^III and Lu^III species are most stable as bis chelates at higher pH, whereas the Ga^III complex degrades at pH < 4.5.     

Directional Hölder Metric Regularity

This paper studies the first-order behavior of the value function of a parametric optimal control problem with nonconvex cost functions and control constraints. By establishing an abstract result on the Fréchet subdifferential of the value function of a parametric minimization problem, we derive a formula for computing the Fréchet subdifferential of the value function to a parametric optimal control problem. The obtained results improve and extend some previous results.     

Reductions of Gauss–Codazzi Equations

We prove that conformally parameterized surfaces in Euclidean space of curvature c admit a symmetry reduction of their Gauss–Codazzi equations whose general solution is expressed with the sixth Painlevé function. Moreover, it is shown that the two known solutions of this type (Bonnet 1867, Bobenko et al. 1997) can be recovered by such a reduction.     

Structural relaxation and aging scaling in the Coulomb and Bose glass models

We employ Monte Carlo simulations to study the relaxation properties of the two-dimensional Coulomb glass in disordered semiconductors and the three-dimensional Bose glass in type-II superconductors in the presence of extended linear defects. We investigate the effects of adding non-zero random on-site energies from different distributions on the properties of the correlation-induced Coulomb gap in the density of states (DOS) and on the non-equilibrium aging kinetics highlighted by the density autocorrelation functions. We also probe the sensitivity of the system’s equilibrium and non-equilibrium relaxation properties to instantaneous changes in the density of charge carriers in the Coulomb glass or flux lines in the Bose glass.     

Does the reagent gas influence collisional activation when performing in situ chemical ionization with an ion trap mass spectrometer?

Users of ion trap mass spectrometers frequently develop methods that associate chemical ionization with tandem mass spectrometry detection. With apparatus using internal ionization, the chemical reagent is present in the trap during the collision induced dissociation (CID) step and one may wonder if the reagent influences the fragmentation ratios in MS/MS. We report a comparison of the fragmentation ratios of protonated molecules when using the most common reagents (methane, ammonia, methanol, acetonitrile, isobutane) for performing in situ chemical ionization. Four molecules were chosen in the medical field to serve as models: alprazolam, diazepam, flunitrazepam and acetaminophen. In the non-resonant CID mode, the influence of the reagent mass is clearly seen in spite of its low partial pressure in the ion trap; the reagent acts as a "heavy target": the degree of fragmentation increases with the molecular weight of the reagent. In the resonant CID mode, there is no evident correlation between the fragmentation ratio of MH(+) ions and the nature of the CI reagent; a slight shift of the secular frequency of the precursor ion, which tends to reduce the CID efficiency, could compensate for the "heavy target" effect underscored in the non-resonant mode.     

EPR and optical studies of erbium-doped beta-PbF2 single-crystals and nanocrystals in transparent glass-ceramics

beta-PbF(2) single-crystals and nanocrystals in transparent glass-ceramics doped with ErF(3) have been synthesized and studied with two complementary techniques: electron paramagnetic resonance (EPR) and optical spectroscopy (absorption, selective excitation, fluorescence). A comparative study shows that, in both single-crystals and glass-ceramics, Er(3+) ions occupy the same types of sites, leading to similar optical properties. An EPR investigation demonstrates that, in these materials, part of the Er(3+) ions occupy cubic symmetry sites. For these ions, we determine the crystal field splitting of the ground state (4)I(15/2) and the symmetry of its sublevels. We also provide evidence for the presence of another type of Er(3+) ions, not detectable by EPR but evidenced by optical spectroscopy. We clearly show that this Er(3+), which gives rise to up-conversion luminescence, corresponds to clusters associating Er(3+) and F(-) ions. In the single-crystals, the proportion of these two types of erbium ions is estimated. It strongly depends on the doping rate of the beta-PbF(2) crystals.     

Surface modification of thermoplastics--towards the plastic biochip for high throughput screening devices

Microarrays have become one of the most convenient tools for high throughput screening, supporting major advances in genomics and proteomics. Other important applications can be found in medical diagnostics, detection of biothreats, drug discovery, etc. Integration of microarrays with microfluidic devices can be highly advantageous in terms of portability, shorter analysis time and lower consumption of expensive biological analytes. Since fabrication of microfluidic devices using traditional materials such as glass is rather expensive, there is great interest in employing polymeric materials as a low cost alternative that is suitable for mass production. A number of commercially available plastic materials were reviewed for this purpose and poly(methylmethacrylate) Zeonor 1060R and Zeonex E48R were identified as promising candidates, for which methods for surface modification and covalent immobilization of DNA oligonucleotides were developed. In addition, we present proof-of-concept plastic-based microarrays with and without integration with microfluidics.