Search (6 results, page 1 of 1)

0.025732353 = product of:
  0.051464707 = sum of:
    0.051464707 = product of:
      0.10292941 = sum of:
        0.10292941 = weight(_text_:t in 271) [ClassicSimilarity], result of:
          0.10292941 = score(doc=271,freq=14.0), product of:
            0.17876579 = queryWeight, product of:
              3.9394085 = idf(docFreq=2338, maxDocs=44218)
              0.04537884 = queryNorm
            0.575778 = fieldWeight in 271, product of:
              3.7416575 = tf(freq=14.0), with freq of:
                14.0 = termFreq=14.0
              3.9394085 = idf(docFreq=2338, maxDocs=44218)
              0.0390625 = fieldNorm(doc=271)
      0.5 = coord(1/2)
  0.5 = coord(1/2)

Abstract

Herdan's law in linguistics and Heaps' law in information retrieval are different formulations of the same phenomenon. Stated briefly and in linguistic terms they state that vocabularies' sizes are concave increasing power laws of texts' sizes. This study investigates these laws from a purely mathematical and informetric point of view. A general informetric argument shows that the problem of proving these laws is, in fact, ill-posed. Using the more general terminology of sources and items, the author shows by presenting exact formulas from Lotkaian informetrics that the total number T of sources is not only a function of the total number A of items, but is also a function of several parameters (e.g., the parameters occurring in Lotka's law). Consequently, it is shown that a fixed T(or A) value can lead to different possible A (respectively, T) values. Limiting the T(A)-variability to increasing samples (e.g., in a text as done in linguistics) the author then shows, in a purely mathematical way, that for large sample sizes T~ A**phi, where phi is a constant, phi < 1 but close to 1, hence roughly, Heaps' or Herdan's law can be proved without using any linguistic or informetric argument. The author also shows that for smaller samples, a is not a constant but essentially decreases as confirmed by practical examples. Finally, an exact informetric argument on random sampling in the items shows that, in most cases, T= T(A) is a concavely increasing function, in accordance with practical examples.

0.01945183 = product of:
  0.03890366 = sum of:
    0.03890366 = product of:
      0.07780732 = sum of:
        0.07780732 = weight(_text_:t in 2009) [ClassicSimilarity], result of:
          0.07780732 = score(doc=2009,freq=8.0), product of:
            0.17876579 = queryWeight, product of:
              3.9394085 = idf(docFreq=2338, maxDocs=44218)
              0.04537884 = queryNorm
            0.43524727 = fieldWeight in 2009, product of:
              2.828427 = tf(freq=8.0), with freq of:
                8.0 = termFreq=8.0
              3.9394085 = idf(docFreq=2338, maxDocs=44218)
              0.0390625 = fieldNorm(doc=2009)
      0.5 = coord(1/2)
  0.5 = coord(1/2)

Abstract

The article studies the influence of the query formulation of a topic on its h-index. In order to generate pure random sets of documents, we used N-grams (N variable) to measure this influence: strings of zeros, truncated at the end. The used databases are WoS and Scopus. The formula h=T**1/alpha, proved in Egghe and Rousseau (2006) where T is the number of retrieved documents and is Lotka's exponent, is confirmed being a concavely increasing function of T. We also give a formula for the relation between h and N the length of the N-gram: h=D10**(-N/alpha) where D is a constant, a convexly decreasing function, which is found in our experiments. Nonlinear regression on h=T**1/alpha gives an estimation of , which can then be used to estimate the h-index of the entire database (Web of Science [WoS] and Scopus): h=S**1/alpha, , where S is the total number of documents in the database.

0.01925633 = product of:
  0.03851266 = sum of:
    0.03851266 = product of:
      0.07702532 = sum of:
        0.07702532 = weight(_text_:t in 243) [ClassicSimilarity], result of:
          0.07702532 = score(doc=243,freq=4.0), product of:
            0.17876579 = queryWeight, product of:
              3.9394085 = idf(docFreq=2338, maxDocs=44218)
              0.04537884 = queryNorm
            0.4308728 = fieldWeight in 243, product of:
              2.0 = tf(freq=4.0), with freq of:
                4.0 = termFreq=4.0
              3.9394085 = idf(docFreq=2338, maxDocs=44218)
              0.0546875 = fieldNorm(doc=243)
      0.5 = coord(1/2)
  0.5 = coord(1/2)

Abstract

Based on earlier results about the shifted Lotka function, we prove an implicit functional relation between the Hirsch index (h-index) and the total number of sources (T). It is shown that the corresponding function, h(T), is concavely increasing. Next, we construct an implicit relation between the h-index and the impact factor IF (an average number of items per source). The corresponding function h(IF) is increasing and we show that if the parameter C in the numerator of the shifted Lotka function is high, then the relation between the h-index and the impact factor is almost linear.

0.015370517 = product of:
  0.030741034 = sum of:
    0.030741034 = product of:
      0.06148207 = sum of:
        0.06148207 = weight(_text_:22 in 4992) [ClassicSimilarity], result of:
          0.06148207 = score(doc=4992,freq=2.0), product of:
            0.15890898 = queryWeight, product of:
              3.5018296 = idf(docFreq=3622, maxDocs=44218)
              0.04537884 = queryNorm
            0.38690117 = fieldWeight in 4992, product of:
              1.4142135 = tf(freq=2.0), with freq of:
                2.0 = termFreq=2.0
              3.5018296 = idf(docFreq=3622, maxDocs=44218)
              0.078125 = fieldNorm(doc=4992)
      0.5 = coord(1/2)
  0.5 = coord(1/2)

Date

14. 2.2012 12:53:22

0.00922231 = product of:
  0.01844462 = sum of:
    0.01844462 = product of:
      0.03688924 = sum of:
        0.03688924 = weight(_text_:22 in 7659) [ClassicSimilarity], result of:
          0.03688924 = score(doc=7659,freq=2.0), product of:
            0.15890898 = queryWeight, product of:
              3.5018296 = idf(docFreq=3622, maxDocs=44218)
              0.04537884 = queryNorm
            0.23214069 = fieldWeight in 7659, product of:
              1.4142135 = tf(freq=2.0), with freq of:
                2.0 = termFreq=2.0
              3.5018296 = idf(docFreq=3622, maxDocs=44218)
              0.046875 = fieldNorm(doc=7659)
      0.5 = coord(1/2)
  0.5 = coord(1/2)

Source

Journal of information science. 22(1996) no.3, S.165-170

0.00922231 = product of:
  0.01844462 = sum of:
    0.01844462 = product of:
      0.03688924 = sum of:
        0.03688924 = weight(_text_:22 in 2558) [ClassicSimilarity], result of:
          0.03688924 = score(doc=2558,freq=2.0), product of:
            0.15890898 = queryWeight, product of:
              3.5018296 = idf(docFreq=3622, maxDocs=44218)
              0.04537884 = queryNorm
            0.23214069 = fieldWeight in 2558, product of:
              1.4142135 = tf(freq=2.0), with freq of:
                2.0 = termFreq=2.0
              3.5018296 = idf(docFreq=3622, maxDocs=44218)
              0.046875 = fieldNorm(doc=2558)
      0.5 = coord(1/2)
  0.5 = coord(1/2)

Date

14. 8.2004 19:17:22