The Shapley value for arbitrary families of coalitions

We address the problem of finding a suitable definition of a value similar to that of Shapley’s, when the games are defined on a subfamily of coalitions with no structure. We present two frameworks: one based on the familiar efficiency, linearity and null player axioms, and the other on linearity and the behavior on unanimity games. We give several properties and examples in each case, and give necessary and sufficient conditions on the family of coalitions for the approaches to coincide.     

On the Lebesgue constant for the Xu interpolation formula

In the paper [Y. Xu, Lagrange interpolation on Chebyshev points of two variables, J. Approx. Theory 87 (1996) 220–238], the author introduced a set of Chebyshev-like points for polynomial interpolation (by a certain subspace of polynomials) in the square [-1,1]², and derived a compact form of the corresponding Lagrange interpolation formula. In [L. Bos, M. Caliari, S. De Marchi, M. Vianello, A numerical study of the Xu polynomial interpolation formula in two variables, Computing 76(3–4) (2005) 311–324], we gave an efficient implementation of the Xu interpolation formula and we studied numerically its Lebesgue constant, giving evidence that it grows like , n being the degree. The aim of the present paper is to provide an analytic proof to show that the Lebesgue constant does have this order of growth.     

Experimental test of two-way quantum key distribution in the presence of controlled noise

We describe the experimental test of a quantum key distribution performed with a two-way protocol without using entanglement. An individual incoherent eavesdropping is simulated and induces a variable amount of noise on the communication channel. This allows a direct verification of the agreement between theory and practice.     

Magnetic double resonance in force microscopy

Magnetic-resonance force microscopy is combined with cross-polarization and spin-decoupling NMR techniques to obtain double-resonance NMR signals of micrometer-scaled objects. The effective one-dimensional spatial resolution obtained in our experiments performed on a KPF6 single crystal sample is approximately 0.5 microm. The spectral linewidth of 900 Hz is sample limited. The described double-resonance techniques can introduce new chemical specificity to the magnetic-force sensor.     

Stochastic acceleration in turbulent electric fields generated by 3D reconnection

Electron and proton acceleration in three-dimensional electric and magnetic fields is studied through test particle simulations. The fields are obtained by a three-dimensional magnetohydrodynamic simulation of magnetic reconnection in slab geometry. The nonlinear evolution of the system is characterized by the growth of many unstable modes and the initial current sheet is fragmented with formation of small scale structures. We inject at random points inside the evolving current sheet a Maxwellian distribution of particles. In a relatively short time (less than a millisecond) the particles develop a power-law tail. The acceleration is extremely efficient and the electrons absorb a large percentage of the available energy in a small fraction of the characteristic time of the MHD simulation, suggesting that resistive MHD codes are unable to represent the full extent of particle acceleration.     

Double transverse-spin asymmetries in Drell–Yan processes with antiprotons

We present next-to-leading order predictions for double transverse-spin asymmetries in Drell–Yan dilepton production initiated by proton–antiproton scattering. The kinematic region of the proposed PAX experiment at GSI: 30?s?200 GeV²$30?s?200{\text{GeV}}^2$ and 2?M?7 GeV$2?M?7\text{GeV}$ is examined. The Drell–Yan asymmetries turn out to be large, in the range 20–40%. Measuring these asymmetries would provide the cleanest determination of the quark transversity distributions.     

A Three-component Extension of the Camassa–Holm Hierarchy

We introduce a bi-Hamiltonian hierarchy on the loop-algebra of endowed with a suitable Poisson pair. It gives rise to the usual Camassa–Holm (CH) hierarchy by means of a bi-Hamiltonian reduction, and its first nontrivial flow provides a three-component extension of the CH equation.     

Anisotropic multiplicative elastoplasticity for the prediction of earings in sheet forming

In this work, the simulation of earings in cup drawing by means of a recently developed anisotropic combined hardening material model is discussed. The model represents a multiplicative formulation of anisotropic elastoplasticity in the finite strain regime with nonlinear kinematic and isotropic hardening. Plastic anisotropy is described by the use of second-order structure tensors as additional arguments in the representation of the yield function and the plastic flow rule. The evolution equations are integrated by a form of the exponential map that preserves the plastic volume and the symmetry of the internal variables. Finite element simulations of cylindrical cup drawing processes are performed by means of ABAQUS/Standard where the discussed material model has been implemented into a user-defined reduced integration solid-shell element. (© 2010 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)