Related papers: Benford's law from 1881 to 2006
This is the first scientific article since 2010 counting the words which are effective and permanent federal law in the United States (US) Code. The latest version of the US Code --published in 2025-- is the largest since 1991, encompassing…
Benford's law, or the law of the first significant digit, has been subjected to numerous studies due to its unique applications in financial fields, especially accounting and auditing. However, studies that addressed the law's establishment…
The purpose of this note consists of discrete rational reconstruction which took place during the years 1609-1630 and 1630-1666, ie, the year of the publication of their Astronomia Nova and the year of death of the great German astronomer…
During the last ten years or so, derivations of the Born rule based on decision theory have been proposed and developed, and it is claimed that these are valid in the context of the Everett interpretation. This claim is critically assessed…
Benford's law is the statement that in many real world data sets, the probability of having digit $d$ in base $B$ as the first digit is \log_{B}\!\left(\frac{d+1}{d}\right) for all $1 \leq d \leq B$. We sometimes refer to this as weak…
It is known that if X is uniformly distributed modulo 1 and Y is an arbitrary random variable independent of X then Y+X is also uniformly distributed modulo 1. We prove a converse for any continuous random variable Y (or a reasonable…
Purpose. In this study, we want to identify current possible causes for citing and referencing errors in scholarly literature to compare if something changed from the snapshot provided Sweetland in his 1989 paper.…
An anecdotal account of the author's role in the origins of lattice gauge theory, prepared for delivery on the thirtieth anniversary of the publication of "Confinement of Quarks" [Phys. Rev. D10 (1974) 2445].
We found that in transition arrays of complex atomic spectra, the strengths of electric-dipolar lines obey Benford's law, which means that their significant digits follow a logarithmic distribution favoring the smallest values. This…
This article describes the third law of thermodynamics. This law is often poorly known and is often decried, or even considered optional and irrelevant to describe weather and climate phenomena. This, however, is inaccurate and contrary to…
This article was originally published in Topology 22 (1983). The present hyperTeXed redaction includes references to post-1983 results as Addenda, and corrects a few typographical errors. (See math.GT/0411115 for a more comprehensive…
This is an extended version of a talk given at the conference "Algebra and Topology in Interaction" on the occasion of the 70th Anniversary of D.B. Fuchs at UC Davis in September 2009. It is a brief survey of an area originated around 1995…
We carry out a thorough bibliometric analysis of recent publications in mathematics based on the database Web of Science. The individual relations between various features and the citations are provided, and the importance of the features…
In an earlier paper we introduced the notion of 'bifurcating continued fractions' in a heuristic manner. In this paper a formal theory is developed for the 'bifurcating continued fractions'.
I comment on some theoretical work presented at QCD Moriond 2006.
A partly autobiographical survey of the development of enumerative and algebraic combinatorics in the 1960's and 1970's.
This work aims to test the Verdoorn Law, with the alternative specifications of (1)Kaldor (1966), for five regions (NUTS II) Portuguese from 1986 to 1994 and for the 28 NUTS III Portuguese in the period 1995 to 1999. Will, therefore, to…
For arbitrary Borel probability measures with compact support on the real line, characterizations are established of the best finitely supported approximations, relative to three familiar probability metrics (Levy, Kantorovich, and…
A concise presentation of Schrodinger's ancilla theorem (1936 Proc. Camb. Phil. Soc. 32, 446) and its several recent rediscoveries.
Using the sum invariance property of Benford random variables, we prove that an $n$-digit Benford variable converges to a Benford variable as $n$ approaches infinity.