7,079 research outputs found
Noncompactness and noncompleteness in isometries of Lipschitz spaces
We solve the following three questions concerning surjective linear
isometries between spaces of Lipschitz functions and
, for strictly convex normed spaces and and metric
spaces and : \begin{enumerate} \item Characterize those base spaces
and 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 and are not
necessary when and 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
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