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An individual’s h-index corresponds to the number h of his/her papers that each has at least h citations. When the citation count of an article exceeds h, however, as is the case for the hundreds or even thousands of citations that accompany the most highly cited papers, no additional credit is given (these citations falling outside the so-called “Durfee square”). We propose a new bibliometric index, the “tapered h-index” (h T), that positively enumerates all citations, yet scoring them on an equitable basis with h. The career progression of h T and h are compared for six eminent scientists in contrasting fields. Calculated h T for year 2006 ranged between 44.32 and 72.03, with a corresponding range in h of 26 to 44. We argue that the h T-index is superior to h, both theoretically (it scores all citations), and because it shows smooth increases from year to year as compared with the irregular jumps seen in h. Conversely, the original h-index has the benefit of being conceptually easy to visualise. Qualitatively, the two indices show remarkable similarity (they are closely correlated), such that either can be applied with confidence.

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The nature of the empirical proportionality constant A in the relation L = Ah 2 between total number of citations L of the publication output of an author and his/her Hirsch index h is analyzed using data of the publication output and citations for six scientists elected to the membership of the Royal Society in 2006 and 199 professors working in different institutions in Poland. The main problem with the h index of different authors calculated by using the above relation is that it underestimates the ranking of scientists publishing papers receiving very high citations and results in high values of A. It was found that the value of the Hirsch constant A for different scientists is associated with the discreteness of h and is related to the tapered Hirsch index h T by A 1/2 ≈ 1.21h T. To overcome the drawback of a wide range of A associated with the discreteness of h for different authors, a simple index, the radius R of circular citation area, defined as R = (L/π)1/2h, is suggested. This circular citation area radius R is easy to calculate and improves the ranking of scientists publishing high-impact papers. Finally, after introducing the concept of citation acceleration a = L/t 2 = π(R/t)2 (t is publication duration of a scientist), some general features of citations of publication output of Polish professors are described in terms of their citability. Analysis of the data of Polish professors in terms of citation acceleration a shows that: (1) the citability of the papers of a majority of physics and chemistry professors is much higher than that of technical sciences professors, and (2) increasing fraction of conference papers as well as non-English papers and engagement in administrative functions of professors result in decreasing citability of their overall publication output.

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