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Abstract

Using a power-law model, the two best-known topics in citation analysis, namely the impact factor and the Hirsch index, are unified into one relation (not a function). The validity of our model is, at least in a qualitative way, confirmed by real data.

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Abstract

Fundamental mathematical properties of rhythm sequences are studied. In particular, a set of three axioms for valid rhythm indicators is proposed, and it is shown that the R-indicator satisfies only two out of three but that the R-indicator satisfies all three. This fills a critical, logical gap in the study of these indicator sequences. Matrices leading to a constant R-sequence are called baseline matrices. They are characterized as matrices with constant w-year diachronous impact factors. The relation with classical impact factors is clarified. Using regression analysis matrices with a rhythm sequence that is on average equal to 1 (smaller than 1, larger than 1) are characterized.