[en] This paper seeks to identify the influence of the activities of the Agrupacion-Cluster de Conocimiento in the improvement of the Intellectual Capital of its partners, especially of their Relational Capital through the generation of inter-organizational spaces for our organizations in the Basque Country. The transmission of this knowledge requires the physical proximity of the people between whom the exchange can to be made. This exchange is facilitated when spaces are created with an atmosphere of total confidence and equality, in which one can express in complete liberty. (Author)

[en] In this paper an effective analytical-numerical approach to study the electromagnetic interaction between a bunch of particles and the drift tube of the vacuum chamber of a particle accelerator is presented. Particular attention is dedicated to the longitudinal coupling impedance, which is expanded as a Neumann series. Numerical calculations can be easily performed in a wide range of frequency

[en] In this note, it is proven that, given two perturbative constructions of time-ordered products via the Bogoliubov-Epstein-Glaser recursion, both sets of coupling functions are related by a local formal power series, recursively determined by causality.

[en] A representation of the coefficients of the expansion in series on powers of the activity z of density (first correlation function) is found. This representation allows one to compute, at least approximately, some of the initial coefficients of this expansion in series and it can be useful in investigation of the thermodynamic limit

[en] When f(z) is given by a known power series expansion, it is possible to construct the power series expansion for f(z; p) = e/sup -p/z f(z). We define p/sub opt/ to be the value of p for which the expansion for f(z; p) converges most rapidly. When f(z) is an entire function of order 1, we show that p/sub opt/ is uniquely defined and may be characterized in terms of the set of singularities z/sub i/ = 1/sigma/sub i/ of an associated function h(z). Specifically, it is the center of the smallest circle in the complex plane which contains all points sigma/sub i/

[en] The Pentagon Operator Product Expansion represents polygonal Wilson loops in planar N=4 super Yang-Mills in terms of a series of flux tube excitations for finite coupling. We demonstrate how to re-sum this series at the one loop level for the hexagonal Wilson loop dual to the six-point MHV amplitude. By summing over a series of effective excitations we find expressions which integrate to logarithms and polylogarithms, reproducing the known one-loop result.

[en] The large-n expansion is applied to the calculation of thermal critical exponents describing the critical behavior of spatially anisotropic d-dimensional systems at m-axial Lifshitz points. We derive the leading non-trivial 1/n correction for the perpendicular correlation-length exponent ν_L2 and hence several related thermal exponents to order O(1/n). The results are consistent with known large-n expansions for d-dimensional critical points and isotropic Lifshitz points, as well as with the second-order epsilon expansion about the upper critical dimension d^⁎=4+m/2 for generic m∈[0,d]. Analytical results are given for the special case d=4, m=1. For uniaxial Lifshitz points in three dimensions, 1/n coefficients are calculated numerically. The estimates of critical exponents at d=3, m=1 and n=3 are discussed.

[en] An iterative method for time-independent perturbation theory is presented. Lennard-Jones-Brillouin-Wigner (LBW) and Rayleigh-Schrodinger (RS) power series are shown to be particular cases of the iteration and the combined expansion-iteration. Improvements in convergence of the power series are suggested and analyzed. The iterative method gives considerable insight into the nature and relative convergence of the currently used time-independent perturbation methods

[en] A model representing scalar hysteretic systems with wipe-out memory is proposed. In this model a hysteresis operator is represented as a power series expansion containing an infinite number of terms in general. It is shown that this representation converges to any given hysteresis relation having wipe-out memory as long as the output of the given hysteresis varies sufficiently smoothly with input history. [copyright] 2001 American Institute of Physics

[en] We present a consistent nonequilibrium theory for the production of molecular dimers from a two-component quantum-degenerate atomic Fermi gas, via a linear downward sweep of a magnetic field across a Feshbach resonance. This problem raises interest because it is presently unclear as to why deviations from the universal Landau-Zener formula for the transition probability at two-level crossing are observed in the experimentally measured production efficiencies. We show that the molecular conversion efficiency is represented by a power series in terms of a dimensionless parameter which, in the zero-temperature limit, depends solely on the initial gas density and the Landau-Zener parameter. Our result reveals a hindrance of the canonical Landau-Zener transition probability due to many-body effects, and presents an explanation for the experimentally observed deviations [K.E. Strecker, et al., Phys. Rev. Lett. 91 (2003) 080406]