Representing non-weakly compact operators

For each $S \in L(E)$ (with $E$ a Banach space) the operator $R(S) \in L(E^{**}/E)$ is defined by $R(S)(x^{**}+E) = S^{**}x^{**}+E$ \quad ($x^{**}\in E^{**}$). We study mapping properties of the correspondence $S\to R(S),$ which provides a representation $R$ of the weak Calkin algebra $L(E)/W(E)$ (here $W(E)$ denotes the weakly compact operators on $E$). Our results display strongly varying behaviour of $R.$ For instance, there are no non--zero compact operators in Im$(R)$ in the case of $L^1$ and $C(0,1),$ but $R(L(E)/W(E))$ identifies isometrically with the class of lattice regular operators on $\ell^2$ for $E=\ell^2(J)$ (here $J$ is the James' space). Accordingly, there is an operator $T \in L(\ell^2(J))$ such that $R(T)$ is invertible but $T$ fails to be invertible modulo $W(\ell^2(J)).

Masses of the Goldstone modes in the CFL phase of QCD at finite density

We construct the U_L(3) x U_R(3) effective lagrangian which encodes the dynamics of the low energy pseudoscalar excitations in the Color-Flavor-Locking superconducting phase of QCD at finite quark density. We include the effects of instanton-induced interactions and study the mass pattern of the pseudoscalar mesons. A tentative comparison with the analytical estimate for the gap suggests that some of these low energy momentum modes are not stable for moderate values of the quark chemical potential.Comment: 15 pages, 5 figures; Discussion of quark mass effects at very large densities amended, references adde

Underlying events in Herwig++

In this contribution we describe the new model of multiple partonic interactions (MPI) that has been implemented in Herwig++. Tuning its two free parameters is enough to find a good description of CDF underlying event data. We show extrapolations to the LHC and compare them to results from other models.Comment: 4 pages, 3 figures, to appear in the proceedings of the "HERA and the LHC" worksho

Multiple Interactions in Herwig++

In this contribution we describe a new model of multiple partonic interactions that has been implemented in Herwig++. Tuning its two free parameters we find a good description of CDF underlying event data. We show extrapolations to the LHC and discuss intrinsic PDF uncertainties.Comment: 4 pages, 2 figures, to appear in the proceedings of the DIS 2008 workshop, 7-11 April 2008, University College Londo

Uncovering GPTS with Patent Data

This paper asks the question: Can we see evidence of General Purpose Technologies in patent data? Using data on three million US patents granted between 1967 and 1999, and their citations received between 1975 and 2002, we construct a number of measures of GPTs, including generality, number of citations, and patent class growth, for patents themselves and for the patents that cite the patents. A selection of the top twenty patents in the tails of the distribution of several of these measures yields a set of mostly ICT technologies, of which the most important are those underlying transactions on the internet and object-oriented software. We conclude with a brief discussion of the problems we encountered in developing our measures and suggestions for future work in this area.