The full basis theorem does not imply analytic wellordering

A finite support product of ${\omega }_1$ clones of Jensen's minimal ${\Pi }_2^1$ singleton forcing is used to define a model in which any non-empty analytically definable set of reals contains an analytically definable real (the full basis theorem), but there is no analytically definable wellordering of the reals.     

Stability of O3 + N2, O3 + O2 and O3 + CO2 double hydrates: DFT study

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Approximation of bandlimited functions

Many signals encountered in science and engineering are approximated well by bandlimited functions. We provide suitable error bounds for the approximation of bandlimited functions by linear combinations of certain special functions—the prolate spheroidal wave functions of order 0. The coefficients in the approximating linear combinations are given explicitly via appropriate quadrature formulae.     

Room temperature Ni-catalyzed reduction of aryl tosylates by borane hydrides

Mild Ni-catalyzed homogeneous reductions of aryl tosylates are described for the first time. The catalytic system Ni(PPh₃)₂Cl₂ and PCy₃ is shown to be general for hydrogenolysis of a wide range of tosylates, including hindered, deactivated, heterocyclic, and bifunctional examples.     

Some new results on superimposed codes

A (w,r) cover‐free family is a family of subsets of a finite set such that no intersection of w members of the family is covered by a union of r others. A (w,r) superimposed code is the incidence matrix of such a family. Such a family also arises in cryptography as the concept of key distribution pattern. In the present paper, we give some new results on superimposed codes. First we construct superimposed codes from super‐simple designs which give us results better than superimposed codes constructed by other known methods. Next we prove the uniqueness of the (1,2) superimposed code of size 9 × 12, the (2,2) superimposed code of size 14 × 8, and the (2,3) superimposed code of size 30 × 10. Finally, we improve numerical values of upper bounds for the asymptotic rate of some (w,r) superimposed codes. © 2004 Wiley Periodicals, Inc.     

Quasi-wavelet calculations of sound scattering behind barriers

Quasi-wavelets (QWs) are a representation of turbulence consisting of self-similar, eddy-like structures with random orientations and positions in space. They are used in this paper to calculate the scattering, due to turbulent velocity fluctuations, of sound behind noise barriers as a function of the size and spatial location of the eddies. The sound scattering cross-section for QWs of an individual size class (eddy size) is derived and shown to reproduce results for the von Kármán spectrum when the scattered energies from a continuous distribution of QW sizes are combined. A Bragg resonance condition is derived for the eddy size that scatters most strongly for a given acoustic wavenumber and scattering angle. Results for scattering over barriers show that, for typical barrier conditions, most of the scattered energy originates from eddies in the size range of approximately one-half to twice the size of the eddies responsible for maximum scattering. The results also suggest that scattering over the barrier due to eddies with a line of sight to both the source and receiver is generally significant only for frequencies above several kilohertz, for sources and receivers no more than a few meters below the top of the barrier, and for very turbulent atmospheric conditions.     

Large N phase transition in the heat kernel on the U (N) group

The large N phase transition point is investigated in the heat kernel on the U(N) group with respect to arbitrary boundary conditions. A simple functional relation is found relating the density of eigenvalues of the boundary field to the saddle point shape of the typical Young tableaux in the large N limit of the character expansion of the heat kernel. Both strong coupling and weak coupling phases are investigated for some particular cases of the boundary holonomy.     

Aqueous solution and solid state interactions of lanthanide ions with a methacrylic ester polymer bearing pendant 15‐crown‐5 moieties

The interaction between trivalent lanthanide ions and poly(1,4,7,10,13‐pentaoxacyclopentadecan‐2‐yl‐methyl methacrylate), PCR5, in aqueous solution and in the solid state have been studied. In aqueous solution, evidence of a weak interaction between the lanthanides and PCR5 comes from the small red shift of the Ce(III) emission spectra and the slight broadening of the Gd(III) EPR spectra. From the Tb(III) lifetimes in the presence of H₂O and D₂O the loss of one or two water coordinated molecules is confirmed when Tb(III) is bound to PCR5. An association constant of the order of 200 M^?1 was obtained for a 1:1 (lanthanide:15‐crown‐5) complex from the shift of the polymer NMR signals induced by Tb(III). A similar association constant is obtained from the differences of the molar conductivity of Ce(III) solution at various concentrations in presence and absence of PCR5. When Tb(III) is adsorbed on PCR5 membranes, lifetime experiments in H₂O and D₂O confirm the loss of 5 or 6 water coordinated molecules indicating that in solid state the lanthanide(III)‐PCR5 interaction is stronger than in solution. The adsorption of Ce(III) in PCR5 membranes shows a Langmuir type isotherm, from which an equilibrium constant of 39 M^?1 has been calculated. SEM shows that the membrane morphology is not much affected by lanthanide adsorption. Support for lanthanide ion–crown interactions comes from ab initio calculations on 15‐crown‐5/La(III) complex. © 2007 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 45: 1788–1799, 2007     

Efficiency and effectiveness of Spanish football teams: a three-stage-DEA approach

In this paper, we apply a three-stage-DEA model to the Spanish Professional Football League, which means separating the teams’ economic behaviour into three components: operating efficiency—of the offence and defence—athletic or operating effectiveness, and social effectiveness. The results showed that the technical inefficiency of the defence is greater than that of the offence, both being caused by aspects linked to the poor management of players’ abilities and by the football team’s size. Teams showed a favourable evolution of their offensive and defensive efficiency during the 2004/2005 season and to a lesser extent in the season before. The point system assigned by the professional football league regulations evaluates the teams’ athletic effectiveness, but we detected that the teams with the most experience perform athletically in a more effective manner. Their social effectiveness is strongly related to the level of play in itself and to factors linked to their PFL ranking: participation in international competitions for important football teams; or the struggle of minor football teams to stay in the first division.