Here we present a new proof of Blatter's result: a normed space is complete if every bounded closed convex subset has an element of minimum norm. We also present geometrical conditions for the existence of minimum-norm elements in bounded closed convex sets. Also, we characterize reflexivity in the class of Banach spaces by means of contraction functions. Furthermore, we study what happens if we remove the completeness hypothesis.
A sufficient condition for the strict insertion of a continuous function between two comparable upper and lower semicontinuous
functions on a normal space is given. Among immediate corollaries are the classical insertion theorems of Michael and Dowker.
Our insertion lemma also provides purely topological proofs of some standard results on closed subsets of normal spaces which
normally depend upon uniform convergence of series of continuous functions. We also establish a Tietze-type extension theorem
characterizing closed Gδ-sets in a normal space.
Here we show a longitudinal analysis of the overall prestige of first quartile journals during the period between 1999 and 2009, on the subject areas of Scopus. This longitudinal study allows us to analyse developmental trends over times in different subject areas with distinct citation and publication patterns. To this aim, we first introduce an axiomatic index of the overall prestige of journals with ranking score above a given threshold. Here we demonstrate that, between 1999 and 2009, there was high and increasing overall prestige of first quartile journals in only four areas of Scopus. Also, there was high and decreasing overall prestige of first quartile journals in five areas. Two subject areas showed high and oscillating overall prestige of first quartile journals. And there was low and increasing overall prestige in four areas, since the 1999.
Here we show a comparison of top economics departments in the US and EU based on a summary measure of the multidimensional prestige of influential papers in 2010. The multidimensional prestige takes into account that several indicators should be used for a distinct analysis of structural changes at the score distribution of paper prestige. We argue that the prestige of influential articles should not only consider one indicator as a single dimension, but in addition take into account further dimensions, since several different indicators have been developed to evaluate the impact of academic papers. After having identified the multidimensionally influential articles from an economics department, their prestige scores can be aggregated to produce a summary measure of the multidimensional prestige of research output of this department, which satisfies numerous properties.
We investigate the extension to Banach-space-valued functions of the classical inequalities due to Paley for the Fourier coefficients
with respect to a general orthonormal system Φ. This leads us to introduce the notions of Paley Φ-type and Φ-cotype for a
Banach space and some related concepts. We study the relations between these notions of type and cotype and those previously
defined. We also analyze how the interpolation spaces inherit these characteristics from the original spaces, and use them
to obtain sharp coefficient estimates for functions taking values in Lorentz spaces.
We characterize the supports of the measures having quadrature formulae with similar exactness as Gauss’ theorem. Indeed we
obtain the supports of the measures from which an m-point quadrature formula can be obtained such that it exactly integrates functions in the space ℙm−k,m−k[
Many aspects determine the quality of scientific journals. The impact factor is one of these quantitative parameters. However, the impact factor has a strong dependence on the journal discipline. This dependence forbids a direct comparison between different journals without introducing external considerations. In this paper, a renormalized impact factor, Fr, inspired in the definition of dimensionless physical parameters, is proposed. Fr allows a direct comparison among journals classified into different categories and, furthermore, the time evolution analysis of the journal's role in its field.