Document (#35434)

Author

Egghe, L.

Title

¬A new short proof of Naranan's theorem, explaining Lotka's law and Zipf's law

Source

Journal of the American Society for Information Science and Technology. 61(2010) no.12, S.2581-2583

Year

2010

Series

Brief communication

Abstract

Naranan's important theorem, published in Nature in 1970, states that if the number of journals grows exponentially and if the number of articles in each journal grows exponentially (at the same rate for each journal), then the system satisfies Lotka's law and a formula for the Lotka's exponent is given in function of the growth rates of the journals and the articles. This brief communication re-proves this result by showing that the system satisfies Zipf's law, which is equivalent with Lotka's law. The proof is short and algebraic and does not use infinitesimal arguments.

Theme

Informetrie

Object

Naranan-Theorem
Zipf-Gesetz
Lotka-Gesetz

Similar documents (author)

1. Egghe, L.: Little science, big science and beyond (1994) 4.73

   4.727482 = sum of:
     4.727482 = weight(author_txt:egghe in 6883) [ClassicSimilarity], result of:
       4.727482 = fieldWeight in 6883, product of:
         1.0 = tf(freq=1.0), with freq of:
           1.0 = termFreq=1.0
         7.563971 = idf(docFreq=60, maxDocs=43254)
         0.625 = fieldNorm(doc=6883)
   

2. Egghe, L.: Expansion of the field of informetrics : the second special issue (2006) 4.73

   4.727482 = sum of:
     4.727482 = weight(author_txt:egghe in 119) [ClassicSimilarity], result of:
       4.727482 = fieldWeight in 119, product of:
         1.0 = tf(freq=1.0), with freq of:
           1.0 = termFreq=1.0
         7.563971 = idf(docFreq=60, maxDocs=43254)
         0.625 = fieldNorm(doc=119)
   

3. Egghe, L.: Expansion of the field of informetrics : origins and consequences (2005) 4.73

   4.727482 = sum of:
     4.727482 = weight(author_txt:egghe in 2979) [ClassicSimilarity], result of:
       4.727482 = fieldWeight in 2979, product of:
         1.0 = tf(freq=1.0), with freq of:
           1.0 = termFreq=1.0
         7.563971 = idf(docFreq=60, maxDocs=43254)
         0.625 = fieldNorm(doc=2979)
   

4. Egghe, L.: ¬The amount of actions needed for shelving and reshelving (1996) 4.73

   4.727482 = sum of:
     4.727482 = weight(author_txt:egghe in 5463) [ClassicSimilarity], result of:
       4.727482 = fieldWeight in 5463, product of:
         1.0 = tf(freq=1.0), with freq of:
           1.0 = termFreq=1.0
         7.563971 = idf(docFreq=60, maxDocs=43254)
         0.625 = fieldNorm(doc=5463)
   

5. Egghe, L.: Special features of the author - publication relationship and a new explanation of Lotka's law based on convolution theory (1994) 4.73

   4.727482 = sum of:
     4.727482 = weight(author_txt:egghe in 6137) [ClassicSimilarity], result of:
       4.727482 = fieldWeight in 6137, product of:
         1.0 = tf(freq=1.0), with freq of:
           1.0 = termFreq=1.0
         7.563971 = idf(docFreq=60, maxDocs=43254)
         0.625 = fieldNorm(doc=6137)
   

Similar documents (content)

1. Egghe, L.: ¬The power of power laws and an interpretation of Lotkaian informetric systems as self-similar fractals (2005) 0.24

   0.23620372 = sum of:
     0.23620372 = product of:
       0.73813665 = sum of:
         0.012806349 = weight(abstract_txt:system in 5467) [ClassicSimilarity], result of:
           0.012806349 = score(doc=5467,freq=2.0), product of:
             0.043061294 = queryWeight, product of:
               1.0971326 = boost
               3.364676 = idf(docFreq=4064, maxDocs=43254)
               0.011664999 = queryNorm
             0.29739815 = fieldWeight in 5467, product of:
               1.4142135 = tf(freq=2.0), with freq of:
                 2.0 = termFreq=2.0
               3.364676 = idf(docFreq=4064, maxDocs=43254)
               0.0625 = fieldNorm(doc=5467)
         0.056944694 = weight(abstract_txt:1970 in 5467) [ClassicSimilarity], result of:
           0.056944694 = score(doc=5467,freq=1.0), product of:
             0.11644094 = queryWeight, product of:
               1.2757143 = boost
               7.8246975 = idf(docFreq=46, maxDocs=43254)
               0.011664999 = queryNorm
             0.4890436 = fieldWeight in 5467, product of:
               1.0 = tf(freq=1.0), with freq of:
                 1.0 = termFreq=1.0
               7.8246975 = idf(docFreq=46, maxDocs=43254)
               0.0625 = fieldNorm(doc=5467)
         0.01669526 = weight(abstract_txt:number in 5467) [ClassicSimilarity], result of:
           0.01669526 = score(doc=5467,freq=1.0), product of:
             0.064745404 = queryWeight, product of:
               1.3453028 = boost
               4.1257625 = idf(docFreq=1898, maxDocs=43254)
               0.011664999 = queryNorm
             0.25786015 = fieldWeight in 5467, product of:
               1.0 = tf(freq=1.0), with freq of:
                 1.0 = termFreq=1.0
               4.1257625 = idf(docFreq=1898, maxDocs=43254)
               0.0625 = fieldNorm(doc=5467)
         0.06992434 = weight(abstract_txt:proves in 5467) [ClassicSimilarity], result of:
           0.06992434 = score(doc=5467,freq=1.0), product of:
             0.1335229 = queryWeight, product of:
               1.3660873 = boost
               8.379008 = idf(docFreq=26, maxDocs=43254)
               0.011664999 = queryNorm
             0.523688 = fieldWeight in 5467, product of:
               1.0 = tf(freq=1.0), with freq of:
                 1.0 = termFreq=1.0
               8.379008 = idf(docFreq=26, maxDocs=43254)
               0.0625 = fieldNorm(doc=5467)
         0.08385922 = weight(abstract_txt:exponent in 5467) [ClassicSimilarity], result of:
           0.08385922 = score(doc=5467,freq=1.0), product of:
             0.15071994 = queryWeight, product of:
               1.451396 = boost
               8.902256 = idf(docFreq=15, maxDocs=43254)
               0.011664999 = queryNorm
             0.556391 = fieldWeight in 5467, product of:
               1.0 = tf(freq=1.0), with freq of:
                 1.0 = termFreq=1.0
               8.902256 = idf(docFreq=15, maxDocs=43254)
               0.0625 = fieldNorm(doc=5467)
         0.026403883 = weight(abstract_txt:articles in 5467) [ClassicSimilarity], result of:
           0.026403883 = score(doc=5467,freq=1.0), product of:
             0.087887146 = queryWeight, product of:
               1.5673943 = boost
               4.8068705 = idf(docFreq=960, maxDocs=43254)
               0.011664999 = queryNorm
             0.3004294 = fieldWeight in 5467, product of:
               1.0 = tf(freq=1.0), with freq of:
                 1.0 = termFreq=1.0
               4.8068705 = idf(docFreq=960, maxDocs=43254)
               0.0625 = fieldNorm(doc=5467)
         0.046233032 = weight(abstract_txt:journals in 5467) [ClassicSimilarity], result of:
           0.046233032 = score(doc=5467,freq=2.0), product of:
             0.101337865 = queryWeight, product of:
               1.6830672 = boost
               5.161615 = idf(docFreq=673, maxDocs=43254)
               0.011664999 = queryNorm
             0.45622662 = fieldWeight in 5467, product of:
               1.4142135 = tf(freq=2.0), with freq of:
                 2.0 = termFreq=2.0
               5.161615 = idf(docFreq=673, maxDocs=43254)
               0.0625 = fieldNorm(doc=5467)
         0.4252699 = weight(abstract_txt:lotka's in 5467) [ClassicSimilarity], result of:
           0.4252699 = score(doc=5467,freq=2.0), product of:
             0.5605185 = queryWeight, product of:
               5.597905 = boost
               8.583802 = idf(docFreq=21, maxDocs=43254)
               0.011664999 = queryNorm
             0.75870806 = fieldWeight in 5467, product of:
               1.4142135 = tf(freq=2.0), with freq of:
                 2.0 = termFreq=2.0
               8.583802 = idf(docFreq=21, maxDocs=43254)
               0.0625 = fieldNorm(doc=5467)
       0.32 = coord(8/25)
   

2. Yan, S.; Rousseau, R.; Huang, S.: Contributions of chinese authors in PLOS ONE (2016) 0.16

   0.15582721 = sum of:
     0.15582721 = product of:
       0.55652577 = sum of:
         0.057626113 = weight(abstract_txt:arguments in 4230) [ClassicSimilarity], result of:
           0.057626113 = score(doc=4230,freq=1.0), product of:
             0.08956855 = queryWeight, product of:
               1.1188667 = boost
               6.8626604 = idf(docFreq=122, maxDocs=43254)
               0.011664999 = queryNorm
             0.64337444 = fieldWeight in 4230, product of:
               1.0 = tf(freq=1.0), with freq of:
                 1.0 = termFreq=1.0
               6.8626604 = idf(docFreq=122, maxDocs=43254)
               0.09375 = fieldNorm(doc=4230)
         0.02504289 = weight(abstract_txt:number in 4230) [ClassicSimilarity], result of:
           0.02504289 = score(doc=4230,freq=1.0), product of:
             0.064745404 = queryWeight, product of:
               1.3453028 = boost
               4.1257625 = idf(docFreq=1898, maxDocs=43254)
               0.011664999 = queryNorm
             0.38679022 = fieldWeight in 4230, product of:
               1.0 = tf(freq=1.0), with freq of:
                 1.0 = termFreq=1.0
               4.1257625 = idf(docFreq=1898, maxDocs=43254)
               0.09375 = fieldNorm(doc=4230)
         0.056011092 = weight(abstract_txt:articles in 4230) [ClassicSimilarity], result of:
           0.056011092 = score(doc=4230,freq=2.0), product of:
             0.087887146 = queryWeight, product of:
               1.5673943 = boost
               4.8068705 = idf(docFreq=960, maxDocs=43254)
               0.011664999 = queryNorm
             0.637307 = fieldWeight in 4230, product of:
               1.4142135 = tf(freq=2.0), with freq of:
                 2.0 = termFreq=2.0
               4.8068705 = idf(docFreq=960, maxDocs=43254)
               0.09375 = fieldNorm(doc=4230)
         0.04903753 = weight(abstract_txt:journals in 4230) [ClassicSimilarity], result of:
           0.04903753 = score(doc=4230,freq=1.0), product of:
             0.101337865 = queryWeight, product of:
               1.6830672 = boost
               5.161615 = idf(docFreq=673, maxDocs=43254)
               0.011664999 = queryNorm
             0.48390138 = fieldWeight in 4230, product of:
               1.0 = tf(freq=1.0), with freq of:
                 1.0 = termFreq=1.0
               5.161615 = idf(docFreq=673, maxDocs=43254)
               0.09375 = fieldNorm(doc=4230)
         0.0697106 = weight(abstract_txt:journal in 4230) [ClassicSimilarity], result of:
           0.0697106 = score(doc=4230,freq=2.0), product of:
             0.10168929 = queryWeight, product of:
               1.685983 = boost
               5.170557 = idf(docFreq=667, maxDocs=43254)
               0.011664999 = queryNorm
             0.6855255 = fieldWeight in 4230, product of:
               1.4142135 = tf(freq=2.0), with freq of:
                 2.0 = termFreq=2.0
               5.170557 = idf(docFreq=667, maxDocs=43254)
               0.09375 = fieldNorm(doc=4230)
         0.06987731 = weight(abstract_txt:short in 4230) [ClassicSimilarity], result of:
           0.06987731 = score(doc=4230,freq=1.0), product of:
             0.12832466 = queryWeight, product of:
               1.8939593 = boost
               5.808377 = idf(docFreq=352, maxDocs=43254)
               0.011664999 = queryNorm
             0.54453534 = fieldWeight in 4230, product of:
               1.0 = tf(freq=1.0), with freq of:
                 1.0 = termFreq=1.0
               5.808377 = idf(docFreq=352, maxDocs=43254)
               0.09375 = fieldNorm(doc=4230)
         0.22922021 = weight(abstract_txt:exponentially in 4230) [ClassicSimilarity], result of:
           0.22922021 = score(doc=4230,freq=1.0), product of:
             0.28330523 = queryWeight, product of:
               2.8141217 = boost
               8.630322 = idf(docFreq=20, maxDocs=43254)
               0.011664999 = queryNorm
             0.80909276 = fieldWeight in 4230, product of:
               1.0 = tf(freq=1.0), with freq of:
                 1.0 = termFreq=1.0
               8.630322 = idf(docFreq=20, maxDocs=43254)
               0.09375 = fieldNorm(doc=4230)
       0.28 = coord(7/25)
   

3. Egghe, L.: Zipfian and Lotkaian continuous concentration theory (2005) 0.14

   0.1425218 = sum of:
     0.1425218 = product of:
       0.89076126 = sum of:
         0.052278586 = weight(abstract_txt:equivalent in 5679) [ClassicSimilarity], result of:
           0.052278586 = score(doc=5679,freq=1.0), product of:
             0.094786406 = queryWeight, product of:
               1.1509954 = boost
               7.0597243 = idf(docFreq=100, maxDocs=43254)
               0.011664999 = queryNorm
             0.551541 = fieldWeight in 5679, product of:
               1.0 = tf(freq=1.0), with freq of:
                 1.0 = termFreq=1.0
               7.0597243 = idf(docFreq=100, maxDocs=43254)
               0.078125 = fieldNorm(doc=5679)
         0.10482402 = weight(abstract_txt:exponent in 5679) [ClassicSimilarity], result of:
           0.10482402 = score(doc=5679,freq=1.0), product of:
             0.15071994 = queryWeight, product of:
               1.451396 = boost
               8.902256 = idf(docFreq=15, maxDocs=43254)
               0.011664999 = queryNorm
             0.69548875 = fieldWeight in 5679, product of:
               1.0 = tf(freq=1.0), with freq of:
                 1.0 = termFreq=1.0
               8.902256 = idf(docFreq=15, maxDocs=43254)
               0.078125 = fieldNorm(doc=5679)
         0.3577696 = weight(abstract_txt:zipf's in 5679) [ClassicSimilarity], result of:
           0.3577696 = score(doc=5679,freq=2.0), product of:
             0.34166393 = queryWeight, product of:
               3.090403 = boost
               9.47762 = idf(docFreq=8, maxDocs=43254)
               0.011664999 = queryNorm
             1.0471389 = fieldWeight in 5679, product of:
               1.4142135 = tf(freq=2.0), with freq of:
                 2.0 = termFreq=2.0
               9.47762 = idf(docFreq=8, maxDocs=43254)
               0.078125 = fieldNorm(doc=5679)
         0.37588906 = weight(abstract_txt:lotka's in 5679) [ClassicSimilarity], result of:
           0.37588906 = score(doc=5679,freq=1.0), product of:
             0.5605185 = queryWeight, product of:
               5.597905 = boost
               8.583802 = idf(docFreq=21, maxDocs=43254)
               0.011664999 = queryNorm
             0.67060953 = fieldWeight in 5679, product of:
               1.0 = tf(freq=1.0), with freq of:
                 1.0 = termFreq=1.0
               8.583802 = idf(docFreq=21, maxDocs=43254)
               0.078125 = fieldNorm(doc=5679)
       0.16 = coord(4/25)
   

4. Kretschmer, H.; Kretschmer, T.: Well-ordered collaboration structures of co-author pairs in journals (2006) 0.12

   0.116354726 = sum of:
     0.116354726 = product of:
       0.7272171 = sum of:
         0.05247566 = weight(abstract_txt:formula in 1151) [ClassicSimilarity], result of:
           0.05247566 = score(doc=1151,freq=1.0), product of:
             0.11026613 = queryWeight, product of:
               1.2414283 = boost
               7.614402 = idf(docFreq=57, maxDocs=43254)
               0.011664999 = queryNorm
             0.4759001 = fieldWeight in 1151, product of:
               1.0 = tf(freq=1.0), with freq of:
                 1.0 = termFreq=1.0
               7.614402 = idf(docFreq=57, maxDocs=43254)
               0.0625 = fieldNorm(doc=1151)
         0.01669526 = weight(abstract_txt:number in 1151) [ClassicSimilarity], result of:
           0.01669526 = score(doc=1151,freq=1.0), product of:
             0.064745404 = queryWeight, product of:
               1.3453028 = boost
               4.1257625 = idf(docFreq=1898, maxDocs=43254)
               0.011664999 = queryNorm
             0.25786015 = fieldWeight in 1151, product of:
               1.0 = tf(freq=1.0), with freq of:
                 1.0 = termFreq=1.0
               4.1257625 = idf(docFreq=1898, maxDocs=43254)
               0.0625 = fieldNorm(doc=1151)
         0.056623664 = weight(abstract_txt:journals in 1151) [ClassicSimilarity], result of:
           0.056623664 = score(doc=1151,freq=3.0), product of:
             0.101337865 = queryWeight, product of:
               1.6830672 = boost
               5.161615 = idf(docFreq=673, maxDocs=43254)
               0.011664999 = queryNorm
             0.5587612 = fieldWeight in 1151, product of:
               1.7320508 = tf(freq=3.0), with freq of:
                 3.0 = termFreq=3.0
               5.161615 = idf(docFreq=673, maxDocs=43254)
               0.0625 = fieldNorm(doc=1151)
         0.6014225 = weight(abstract_txt:lotka's in 1151) [ClassicSimilarity], result of:
           0.6014225 = score(doc=1151,freq=4.0), product of:
             0.5605185 = queryWeight, product of:
               5.597905 = boost
               8.583802 = idf(docFreq=21, maxDocs=43254)
               0.011664999 = queryNorm
             1.0729753 = fieldWeight in 1151, product of:
               2.0 = tf(freq=4.0), with freq of:
                 4.0 = termFreq=4.0
               8.583802 = idf(docFreq=21, maxDocs=43254)
               0.0625 = fieldNorm(doc=1151)
       0.16 = coord(4/25)
   

5. Falkowski, B.-J.: On certain generalizations of inner product similarity measures (1998) 0.12

   0.11582013 = sum of:
     0.11582013 = product of:
       0.96516776 = sum of:
         0.13984868 = weight(abstract_txt:proves in 5556) [ClassicSimilarity], result of:
           0.13984868 = score(doc=5556,freq=1.0), product of:
             0.1335229 = queryWeight, product of:
               1.3660873 = boost
               8.379008 = idf(docFreq=26, maxDocs=43254)
               0.011664999 = queryNorm
             1.047376 = fieldWeight in 5556, product of:
               1.0 = tf(freq=1.0), with freq of:
                 1.0 = termFreq=1.0
               8.379008 = idf(docFreq=26, maxDocs=43254)
               0.125 = fieldNorm(doc=5556)
         0.23159747 = weight(abstract_txt:proof in 5556) [ClassicSimilarity], result of:
           0.23159747 = score(doc=5556,freq=1.0), product of:
             0.23547748 = queryWeight, product of:
               2.5656078 = boost
               7.8681827 = idf(docFreq=44, maxDocs=43254)
               0.011664999 = queryNorm
             0.98352283 = fieldWeight in 5556, product of:
               1.0 = tf(freq=1.0), with freq of:
                 1.0 = termFreq=1.0
               7.8681827 = idf(docFreq=44, maxDocs=43254)
               0.125 = fieldNorm(doc=5556)
         0.5937216 = weight(abstract_txt:theorem in 5556) [ClassicSimilarity], result of:
           0.5937216 = score(doc=5556,freq=3.0), product of:
             0.30582643 = queryWeight, product of:
               2.9238365 = boost
               8.966795 = idf(docFreq=14, maxDocs=43254)
               0.011664999 = queryNorm
             1.941368 = fieldWeight in 5556, product of:
               1.7320508 = tf(freq=3.0), with freq of:
                 3.0 = termFreq=3.0
               8.966795 = idf(docFreq=14, maxDocs=43254)
               0.125 = fieldNorm(doc=5556)
       0.12 = coord(3/25)