Merging and splitting in cooperative games: some (im)possibility results

Allocation rules for cooperative games can be manipulated by coalitions merging into single players, or, conversely, players splitting into a number of smaller units. This paper collects some (im)possibility results on merging- and splitting-proofness of (core) allocation rules for cooperative games with side-payments.     

Intermolecular exchange-induction energies without overlap expansion

An approach to evaluate the second-order exchange-induction energies of symmetry-adapted intermolecular perturbation theory (SAPT) for single-determinant ground-state monomer wavefunctions has been derived. This approach is correct to all orders of the intermonomer overlap, that is, it takes multiple electron exchange between the monomers into account. The resulting formulae can be written in a compact way and implemented efficiently. Here, the method is employed to investigate the performance of the S ²- or single-exchange approximation at the Hartree-Fock-SAPT level. The list of test systems comprises the prototypical van der Waals- and hydrogen-bridge complexes Ne₂, Ar–HF, and (H₂O)₂, but also the systems HeCl^?, NeNa⁺ and Li⁺F^? involving closed-shell ions. It was found that the errors introduced by the S ²-approximation are more pronounced for the second-order exchange-induction energy than for the first-order exchange energy. While these errors tend to be negligible throughout the well region of complexes such as the neon dimer, they start to be significant in the repulsive part of the well regions of systems such as the water dimer, and in particular for the ionic lithium fluoride molecule. The consequences of these findings for the Hartree-Fock level estimate of higher-order induction plus exchange-induction energies, which is frequently employed in SAPT are also discussed.     

Comparison between preparative methodologies of nanostructured carbon nitride and their use as selective photocatalysts in water suspension

Carbon nitride photocatalysts have been prepared by different methodologies, such as chemical ultrasonic irradiation (sonochemical treatment), hydrothermal and ball milling and thermoexfoliation, and have been used for the selective oxidation of 5-hydroxymethyl-2-furaldehyde (HMF) to form 2,5-furandicarboxyaldehyde (FDC) in water suspension both under UV and natural solar irradiation. The physico-chemical features of the photocatalysts have been studied by X-ray diffraction, infrared spectroscopy, UV–Vis diffuse reflectance spectroscopy, photoluminescence spectroscopy, scanning electron microscopy, and specific surface area measurements. The results indicate that exfoliation of carbon nitrides can increase the conversion of HMF and the selectivity to FDC. In particular, samples exfoliated by both thermal and acidic ultrasonic irradiation treatments showed the best photocatalytic performance.     

Thermal transformation of polyacrylonitrile deposited on SBA-15 type silica

Thermogravimetry, diffuse reflectance infrared Fourier transform spectroscopy, and X-ray photoelectron spectroscopy (XPS) were used for the studying of thermally induced structural changes of polyacrylonitrile (PAN) deposited on the surface of SBA-15 type mesoporous silica. Polymer was introduced onto the support by the precipitation polymerization of acrylonitrile in aqueous suspension of SBA-15. Low temperature transformation (to 723?K) of the deposited PAN was analyzed. It was found that at about 523?K, exothermic cyclization of polymer chains to the so-called ladder form of PAN occurred. However, the total cyclization of PAN required higher carbonization temperatures, at which gradual dehydrogenation followed by graphitization was initiated. XPS revealed that the cyclic form of PAN and a relatively large amount of carbonyl species, formed during the carbonization of the PAN/SBA-15 composite at 623?K, were responsible for the high sorption capacity in the methyl?Cethyl ketone (MEK) vapor elimination. The efficiency in the MEK adsorption was also influenced by the content of PAN-derived carbon deposited on the SBA-15 surface.     

Thermal properties of fats extracted from powdered baby formulas

The aim of this research was to analyse composition, fatty acids distribution and oxidative stability of fats extracted from four samples of baby formulas. The fats were oxidized in a differential scanning calorimeter (DSC) under polythermal (dynamic) conditions and at normal pressure. The DSC experiments were carried out in an oxygen flow atmosphere using different, linearly programmed, heating rates in the range of 4?C12.5?°C/min. The extrapolated onset temperatures were determined using DSC exotherms and used for the assessment of the thermal oxidative stabilities of the samples. Activation energies (E _a), pre-exponential factors (Z) and reaction rate constants (k) for oil oxidation under DSC conditions were calculated using the Ozawa?CFlynn?CWall method and the Arrhenius equation. The melting characteristics of the studied fats were obtained. The fats extracted from the agglomerated samples with higher onset temperatures were more stable than the fats extracted from the initial samples of baby formulas.     

On certain arithmetic functions involving the greatest common divisor

The paper deals with asymptotics for a class of arithmetic functions which describe the value distribution of the greatest-common-divisor function. Typically, they are generated by a Dirichlet series whose analytic behavior is determined by the factor ζ²(s)ζ(2s − 1). Furthermore, multivariate generalizations are considered.     

Smart dampers control in a Remoissenet–Peyrard substrate potential

A model of spring-block on a moving plate with a nonlinear periodic substrate potential whose shape can be varied continuously as a function of a shape parameter is investigated. The dynamical study of the system for different values of the shape parameter involves the analysis of phase space, the construction of bifurcation diagrams, and the computation of the largest Lyapunov exponent. A smart damper associated with drag coefficient is proposed to reduce stick-slip and chaotic motions. The domain of validity of the control method is derived.