Noncompactness and noncompleteness in isometries of Lipschitz spaces

We solve the following three questions concerning surjective linear isometries between spaces of Lipschitz functions $\mathrm{Lip}(X,E)$ and $\mathrm{Lip}(Y,F)$, for strictly convex normed spaces $E$ and $F$ and metric spaces $X$ and $Y$: \begin{enumerate} \item Characterize those base spaces $X$ and $Y$ for which all isometries are weighted composition maps. \item Give a condition independent of base spaces under which all isometries are weighted composition maps. \item Provide the general form of an isometry, both when it is a weighted composition map and when it is not. \end{enumerate} In particular, we prove that requirements of completeness on $X$ and $Y$ are not necessary when $E$ and $F$ are not complete, which is in sharp contrast with results known in the scalar context.Comment: 25 pages, no figures, \documentclass[12pt]{amsart} Changes with respect to the first version include the description of isometries that are not weighted composition, and a complete characterization of spaces admitting the

An estimation of the pattern of diffusion of mobile phones: the case of Colombia

In this paper we fond that the difusion pattern of mobile telephony in Colombia can be best haracterised as following a Logistic curve. Although in recent years the rate of growth of mobile phone subscribers has started to slow down, we find evidence that there is still room for further expansion as thesaturation level is expected to be reached in five years time. The estimated saturation level is consistent with some individuals possessing more than one mobile device.Technology di¤usion; Mobile telecommunications; Gompertzcurve; Logistic curve; Colombia.

Complex networks analysis in socioeconomic models

This chapter aims at reviewing complex networks models and methods that were either developed for or applied to socioeconomic issues, and pertinent to the theme of New Economic Geography. After an introduction to the foundations of the field of complex networks, the present summary adds insights on the statistical mechanical approach, and on the most relevant computational aspects for the treatment of these systems. As the most frequently used model for interacting agent-based systems, a brief description of the statistical mechanics of the classical Ising model on regular lattices, together with recent extensions of the same model on small-world Watts-Strogatz and scale-free Albert-Barabasi complex networks is included. Other sections of the chapter are devoted to applications of complex networks to economics, finance, spreading of innovations, and regional trade and developments. The chapter also reviews results involving applications of complex networks to other relevant socioeconomic issues, including results for opinion and citation networks. Finally, some avenues for future research are introduced before summarizing the main conclusions of the chapter.Comment: 39 pages, 185 references, (not final version of) a chapter prepared for Complexity and Geographical Economics - Topics and Tools, P. Commendatore, S.S. Kayam and I. Kubin Eds. (Springer, to be published

Border cities: economic competitors or complements?

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