Related papers: Benford's law from 1881 to 2006
A statistical model for the fragmentation of a conserved quantity is analyzed, using the principle of maximum entropy and the theory of partitions. Upper and lower bounds for the restricted partitioning problem are derived and applied to…
Correction to Annals of Probability 29 (2001) 1612--1624 [doi:10.1214/aop/1015345764].
This note announces recent exciting progress on the frontier between algebraic topology and probability theory. It is intended for a journal which publishes such announcements (without an abstract, typically in Russian). A description of a…
Numerical data for the distribution of citations are examined for: (i) papers published in 1981 in journals which are catalogued by the Institute for Scientific Information (783,339 papers) and (ii) 20 years of publications in Physical…
In our study we analysed 3.889 records which were indexed in the Library and Information Science Abstracts (LISA) database in the research field of informetrics. We can show the core journals of the field via a Bradford (power law)…
This paper was withdrawn by the author.
Benford's Law predicts that the first significant digit on the leftmost side of numbers in real-life data is proportioned between all possible 1 to 9 digits approximately as in LOG(1 + 1/digit), so that low digits occur much more frequently…
This paper has been withdrawn by the author as a more general result is known and could be referenced at "Combinatorial Enumeration" by Ian P. Goulden, David M. Jackson - Dover Publication 2004 - Section 3.3.13, Page 176.
An interpretation of selected parts of Newton's Principia, with modern notation and methods. Keplers Laws are derived from an inverse square law using Newton's methods.
This survey presents an overview of the advances around Tverberg's theorem, focusing on the last two decades. We discuss the topological, linear-algebraic, and combinatorial aspects of Tverberg's theorem and its applications. The survey…
This paper is an exposition and review of the research related to the Riemann Hypothesis starting from the work of Riemann and ending with a description of the work of G. Spencer-Brown, culminating in his Denjoy proof of the RH.
This paper presents a brief account of the important milestones in the historical development of the theory of differential equations. The paper begins with a discussion on the date of birth of differential equations and then touches upon…
We study the statistics of citations from all Physical Review journals for the 110-year period 1893 until 2003. In addition to characterizing the citation distribution and identifying publications with the highest citation impact, we…
During the last years the authors have studied the number of limit cycles of several families of planar vector fields. The common tool has been the use of an extended version of the celebrated Bendixson-Dulac Theorem. The aim of this work…
This paper from 2008 is the first in a series of three related papers on modal methods in interpretability logics and applications. In this first paper the foundations are laid for later results. These foundations consist of a thorough…
Annotated bibliography of 18th, 19th, and early 20th century works involving Lambert series. A tour of 19th and early 20th century analytic number theory.
The scope of this paper is twofold. First, to emphasize the use of the mod 1 map in exploring the digit distribution of random variables. We show that the well-known base- and scale-invariance of Benford variables are consequences of their…
The suggestion in 1986 of a possible gravity-like ``fifth" fundamental force renewed interest in the question of whether new macroscopic forces are present in nature. Such forces are predicted in many theories which unify gravity with the…
This article is an extended version of a talk given in Oxford in June 2021 as part of an online meeting `Ninety minutes of CCC' to mark the 90th birthday of Sir Roger Penrose. I assemble some questions that I have been asked or have asked…
Short review article on quantum computation accepted for Supplement III, Encyclopaedia of Mathematics (publication expected Summer 2001). See also http://www.wkap.nl/series.htm/ENM