[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] 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] 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] 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^-pz f(z). We define p_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_opt is uniquely defined and may be characterized in terms of the set of singularities z_i = 1/sigma_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_i

[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 convenient method is presented for the evaluation in the asymptotic limit of the ratio of two entire functions of the same order and type. The coefficients in the power series must be positive, which restricts the applications to scattering theory to repulsive potentials only

[en] This paper describes some methods for calculating derivative terms in the one loop effective action for a quantum field theory. The functional approach and background field method are first used to derive the general form of the one loop determinant. Then the determinant is expanded in powers of derivatives of the background fields. The form of this expansion is described for the simple case of an interacting scalar field, and then for the more complicated problem of a non-abelian gauge field. Finally, the expansion is applied to the task of calculating Higgs mass dependent effects in the Glashow-Weinberg-Salam model, and all terms which grow with the Higgs mass M_H are found in the one loop approximation. The result of this calculation is used to find the dependence of the gauge boson mass ratio ρ on M_H, and also to estimate the size of corrections to W and Z scattering theorems

[en] Von Neumann's method of generating random variables with the exponential distribution and Forsythe's method for obtaining distributions with densities of the form e/sup -G//sup( x/) are generalized to apply to certain power series representations. The flexibility of the power series methods is illustrated by algorithms for the Cauchy and geometric distributions