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Scientometrics
Authors: P. Weingart, R. Sehringer, and M. Winterhager

Abstract  

Scientific reality is a multi-sided phenomenon which cannot be described in a single and authoritative way. The descriptions of scientific research areas differ if one compares the definitions of science policy programmes with expert judgments in the peer-review process. Bibliometric measurements function as an intermediate representation of science. To make them useful and compatible with other representations they have to be translated. The difficulties of mutual translation of these different delineations of scientific research areas are demonstrated in two case studies (marine sciences and multiple sclerosis research) where each of these three different representations of science is supported by empirical results.

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Abstract  

We construct a translation invariant σ-ideal T(κ) (where κ is an infinite cardinal number) such that covt (T(κ)) = 2κ while cov (T(κ)) = cof (T(κ)) = ω1. The constructions can be carried out in R as well.

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Abstract  

An asymmetric operator of generalized translation is introduced in this paper. Using this operator, we define a generalized modulus of smoothness and prove direct and inverse theorems of approximation theory for it.

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Abstract  

It is shown that the group of isometries of the 3-dimensional space with respect to taxicab metric is the semi-direct product of octahedral group O h and T(3), where O h is the (Euclidean) symmetry group of the regular octahedron and T(3) is the group of all translations of the 3-dimensional space.

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Summary  

We introduce a new characterization of linear isometries. More precisely, we prove that if a one-to-one mapping f:ℝn→ℝn(2≦n<∞) maps every regular pentagon of side length a> 0 onto a pentagon with side length b> 0, then there exists a linear isometry I :ℝn→ℝnup to translation such that f(x) = (b/a) I(x).

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Abstract  

Let GC be a domain which is bounded by a finite number of pairwise disjoint Jordan curves. We prove the existence of a function which is holomorphic exactly on G and has universal translates with respect to a prescribed set E ⊂∂G and which in addition is continuous on G -\E.

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Abstract  

We prove that there exists a special homeomorphism of the Cantor space such that every noncancellable composition of finite powers and translations of rational numbers has no fixed point. For this homeomorphism there exists both a Vitali and Bernstein subset of the Cantor set such that the image of this set is equal to its complement. There exists a Bernstein and Vitali set such that there is no Borel isomorphism between this set and its complement.

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Abstract  

Based on the concept of so-called (total) omnipresence of operators, several results on the generity of (translation-dilation) universal functions are proved. Mainly to have a unified approach to holomorphic and harmonic functions, in the first part operators on spaces of P-holomorphic functions are considered. The second part is devoted to holomorphic functions having lacunary power series structure and to holomorphic functions which are univalent in certain prescribed sets.

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Abstract  

Fix k, d, 1 ≤ kd + 1. Let
\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} \pagestyle{empty} \DeclareMathSizes{10}{9}{7}{6} \begin{document} $$\mathcal{F}$$ \end{document}
be a nonempty, finite family of closed sets in ℝd, and let L be a (dk + 1)-dimensional flat in ℝd. The following results hold for the set T ≡ ∪{F: F in
\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} \pagestyle{empty} \DeclareMathSizes{10}{9}{7}{6} \begin{document} $$\mathcal{F}$$ \end{document}
}. Assume that, for every k (not necessarily distinct) members F 1, …, F k of
\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} \pagestyle{empty} \DeclareMathSizes{10}{9}{7}{6} \begin{document} $$\mathcal{F}$$ \end{document}
,∪{F i: 1 ≤ ik} is starshaped and the corresponding kernel contains a translate of L. Then T is starshaped, and its kernel also contains a translate of L. Assume that, for every k (not necessarily distinct) members F 1, …, F k of
\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} \pagestyle{empty} \DeclareMathSizes{10}{9}{7}{6} \begin{document} $$\mathcal{F}$$ \end{document}
,∪{F i: 1 ≤ ik} is starshaped and there is a translate of L meeting each set ker F i, 1 ≤ ik − 1. Then there is a translate L 0 of L such that every point of T sees via T some point of L 0. If k = 2 or d = 2, improved results hold.
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Abstract  

This article presents a scientometric procedure which assists in the production of bibliometric indicators for conducting international comparisons about transdisciplinary research field. The procedure aims at the analysis of how a nomenclature in the field of the environment, established by public research administrators, translates into subsets of scientific journals. Relations between the nomenclature and scientific disciplines were obtained through analysis of reviews. The environmental field's structure has been analysed by using journal cross-citation data.

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