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Abstract  

The weighted averages of a sequence (c k), c k ∈ ℂ, with respect to the weights (p k), p k ≥ 0, with {fx135-1} are defined by {fx135-2} while the weighted average of a measurable function f: ℝ+ → ℂ with respect to the weight function p(t) ≥ 0 with {fx135-3}. Under mild assumptions on the weights, we give necessary and sufficient conditions under which the finite limit σ nL as n → ∞ or σ(t) → L as t → ∞ exists, respectively. These characterizations may find applications in probability theory.

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Abstract

In our previous work (Scientometrics 87:293–301, 2011), a numerical model of over-competitive research funding in “peer-group-assessed-grant-based-funding-system” was proposed and the process was firstly investigated quantitatively. The simulation results show that the mainstream of a very complicated research topic could obtain monopoly supremacy with only the aid of the mechanism the model described. Here, the numbers of publications of cosmology back to 1950 are utilized to empirically test this positive feedback mechanism. The development of three main theories of cosmology, Big Bang, Steady State and Plasma Universe, are revisited. The later two, which are non-mainstream opinions, both state in their peer reviewed papers, that their theories fit the phenomena that support the standard theory. The ratios of publications of the orthodox theory, Big Bang, approximately satisfy the numeric calculating results of our model. The reason for the discrepancy between the model and actual situation is discussed. A further question about the controversy is presented.

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Abstract

The aim of peer review is to separate the wheat from the chaff for publication and research funding. In the excessive competition, this mechanism would only select the wheat of mainstream. Up to now, almost all discussions on the consequence of the short-comings of peer review are limited to qualitatively description. I propose a model of “peer-group-assessed-grant-based-funding-system” combined with tenure system and over-competitive research funding review process. It is the first on the quantitatively investigation which dramatizes the current short-comings of the process. My simulation shows that it takes about two or three generations of researchers for the mainstream of a complicated research topic obtaining monopoly supremacy, with only the aid of the mechanism the model described. Based on the computation results, suggestions are proposed to avoid loss of self-correction capability on popularity determined single research direction which could be wrong on very complicated research topics.

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