On the Convenience to Form Coalitions or Partnerships in Simple Games

A partnership in a cooperative game is a coalition that possesses an internal structure and, simultaneously, behaves as an individual member. Forming partnerships leads to a modification of the original game which differs from the quotient game that arises when one or more coalitions are actually formed. In this paper, the Shapley value is used to discuss the convenience to form either coalitions or partnerships. To this end, the difference between the additive Shapley value of the partnership in the partnership game and the Shapley alliance value of the coalition, and also between the corresponding value of the internal and external players, are analysed. Simple games are especially considered. Research partially supported by Grant BFM 2003-01314 of the Science and Technology Spanish Ministry and the European Regional Development Fund.     

Experimental (NMR) and Computational (MD) Studies on the Inclusion Complexes of 1-Bromoadamantane with alpha-, beta-, and gamma-Cyclodextrin

The inclusion complexes between the most commonly used cyclodextrins (alpha-, beta-, and gamma-CD) and 1-bromoadamantane were prepared and studied experimentally by NMR methods and by molecular dynamics simulations (AMBER force field) with solvation. The NMR results suggest host/guest ratios of 2:1, 1:1, and 1:1 for the complexes with alpha-, beta-, and gamma-cyclodextrin, respectively, as well as defined geometries for the complexes. Averaged geometrical data from the molecular dynamics simulations agree with the complexation geometries deduced experimentally.     

Alliances, partnerships and the Banzhaf semivalue

The coordination of strategies in a cooperative game, when some players decide to act together, is the basis of the partnership notion. Nevertheless, in some situations, it may be more convenient to form an effective coalition or alliance. In this work, we consider the Banzhaf semivalue and use it to discuss the convenience to form either partnerships or alliances, especially in simple games. Throughout the paper, some mathematical properties of the Banzhaf semivalue, in relation with the partnership formation, are derived.     

A maximal domain for strategy-proof and no-vetoer rules in the multi-object choice model

Following “Barberà et al. (1991, Econometrica 59:595–609)”, we study rules (or social choice functions) through which agents select a subset from a set of objects. We investigate domains on which there exist nontrivial strategy-proof rules. We establish that the set of separable preferences is a maximal domain for the existence of rules satisfying strategy-proofness and no-vetoer.     

A solution to the Baer splitting problem

Let be a commutative domain. We prove that an -module is projective if and only if for any torsion module . This answers in the affirmative a question raised by Kaplansky in 1962.

     

Host/Guest Interactions and NMR Spectroscopy. A Computer Program for Association Constant Determination

A computer program is presented for the computation of association constants for host/guest compounds based on experimental data obtained from the NMR spectra of samples with different host/guest ratios of known concentration.     

Ultraporous single phase iron oxide-silica nanostructured aerogels from ferrous precursors

Monoliths of iron oxide-silica aerogel nanocomposites have been synthesized using a novel synthesis route which consists of impregnating silica wet gels with anhydrous iron(II) precursors followed by ethanol supercritical drying of the gels. The process yields aerogels exhibiting high porosity, large surface areas (approximately 900 m2/g), rather low densities (approximately 0.6 g/cm3), and a homogeneous distribution of single-phase maghemite, gamma-Fe2O3, nanoparticles with average sizes in the 7-8 nm range. Remarkably, the gamma-Fe2O3 nanoparticles are obtained in the as-dried state without the need of postannealing. The nanoparticles are mostly superparamagnetic at room temperature but become blocked in a ferrimagnetic state at lower temperatures.     

Can Na(2)[B(12)H(12)] be a decomposition product of NaBH(4)?

We synthesized Na(2)[B(12)H(12)] by a solid state procedure and thermal decomposition of Na[B(3)H(8)], and calculated from a first-principles approach the thermodynamic and structural properties. In particular, the calculated enthalpy of formation of the monoclinic structure, at T = 0 K, of -1086.196 kJ mol(-1) showed that it is a very stable compound. Therefore, in case it were formed during the thermal decomposition of NaBH(4), it would be rather considered a product, which, in addition, prevents the subsequent re-hydrogenation process because of its low reactivity to hydrogen. We reported the isotherms of absorption of H(2), O(2), and H(2)O, calculated both theoretically and experimentally.