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Let S be a set of n points distributed uniformly and independently in a convex, bounded set in the plane. A four-gon is called empty if it contains no points of S in its interior. We show that the expected number of empty non-convex four-gons with vertices from S is 12n 2logn + o(n 2logn) and the expected number of empty convex four-gons with vertices from S is Θ(n 2).

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This paper attempts an exposition of the connection between valuation theory and hyperstructure theory. In this regards, by considering the notion of totally ordered canonical hypergroup we define a hypervaluation of a hyperfield onto a totally ordered canonical hypergroup and obtain some related basic results.

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We provide sufficient conditions for a mapping acting between two Banach spaces to be a diffeomorphism. We get local diffeomorhism by standard method while in making it global we employ a critical point theory and a duality mapping. We provide application to integro-differential initial value problem for which we get differentiable dependence on parameters.

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We obtain new lower and upper bounds for probabilities of unions of events. These bounds are sharp. They are stronger than earlier ones. General bounds may be applied in arbitrary measurable spaces. We have improved the method that has been introduced in previous papers. We derive new generalizations of the first and second parts of the Borel-Cantelli lemma.

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It is proved that there exists an NI ring R over which the polynomial ring R[x] is not an NLI ring. This answers an open question of Qu and Wei (Stud. Sci. Math. Hung., 51(2), 2014) in the negative. Moreover a sufficient condition of R[x] to be an NLI ring is included for an NLI ring R.

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A space X is almost star countable (weakly star countable) if for each open cover U of X there exists a countable subset F of X such that \documentclass{aastex} \usepackage{amsbsy} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{bm} \usepackage{mathrsfs} \usepackage{pifont} \usepackage{stmaryrd} \usepackage{textcomp} \usepackage{upgreek} \usepackage{portland,xspace} \usepackage{amsmath,amsxtra} \usepackage{bbm} \pagestyle{empty} \DeclareMathSizes{10}{9}{7}{6} \begin{document} $\bigcup {_{x \in F}\overline {St\left( {x,U} \right)} } = X$ \end{document} (respectively, \documentclass{aastex} \usepackage{amsbsy} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{bm} \usepackage{mathrsfs} \usepackage{pifont} \usepackage{stmaryrd} \usepackage{textcomp} \usepackage{upgreek} \usepackage{portland,xspace} \usepackage{amsmath,amsxtra} \usepackage{bbm} \pagestyle{empty} \DeclareMathSizes{10}{9}{7}{6} \begin{document} $\overline {\bigcup {_{x \in F}} St\left( {x,U} \right)} = X$ \end{document}. In this paper, we investigate the relationships among star countable spaces, almost star countable spaces and weakly star countable spaces, and also study topological properties of almost star countable spaces.

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Abstract

In this paper we present a compilation of journal impact properties in relation to other bibliometric indicators as found in our earlier studies together with new results. We argue that journal impact, even calculated in a sufficiently advanced way, becomes important in evaluation practices based on bibliometric analysis only at an aggregate level. In the relation between average journal impact and actual citation impact of groups, the influence of research performance is substantial. Top-performance as well as lower performance groups publish in more or less the same range of journal impact values, but top-performance groups are, on average, more successful in the entire range of journal impact. We find that for the high field citation-density groups a larger size implies a lower average journal impact. For groups in the low field citation-density regions however a larger size implies a considerably higher average journal impact. Finally, we found that top-performance groups have relatively less self-citations than the lower performance groups and this fraction is decreasing with journal impact.

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Abstract

In this study the issue of the validity of the argument against the applied length of citation windows in Journal Impact Factors calculations is critically re-analyzed. While previous studies argued against the relatively short citation window of 1–2 years, this study shows that the relative short term citation impact measured in the window underlying the Journal Impact Factor is a good predictor of the citation impact of the journals in the next years to come. Possible exceptions to this observation relate to journals with relatively low numbers of publications, and the citation impact related to publications in the year of publication. The study focuses on five Journal Subject Categories from the science and social sciences, on normal articles published in these journals, in the 2 years 2000 and 2004.

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Abstract

Journal impact factors (IFs) can be considered historically as the first attempt to normalize citation distributions by using averages over 2 years. However, it has been recognized that citation distributions vary among fields of science and that one needs to normalize for this. Furthermore, the mean—or any central-tendency statistics—is not a good representation of the citation distribution because these distributions are skewed. Important steps have been taken to solve these two problems during the last few years. First, one can normalize at the article level using the citing audience as the reference set. Second, one can use non-parametric statistics for testing the significance of differences among ratings. A proportion of most-highly cited papers (the top-10% or top-quartile) on the basis of fractional counting of the citations may provide an alternative to the current IF. This indicator is intuitively simple, allows for statistical testing, and accords with the state of the art.

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Abstract

It is shown that the age-independent index based on h-type index per decade, called hereafter an α index instead of the a index, suggested by Kosmulski (Journal of Informetrics 3, 341–347, ) and Abt (Scientometrics ) is related to the square-root of the ratio of citation acceleration a to the Hirsch constant A.

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