125,257 research outputs found
Erdos Conjecture I.
Get PDFIn this short paper I show how it is related to other famous unsolved problems in
prime number theory. In order to do this, I formulate the main hypothetical result of this paper - a useful upper bound conjecture (Conjecture 3.), describing one aspect of the distribution of primes in various special forms, paying a brief attention to Fermat, Mersenne, Fibonacci, Lucas and Smarandache sequences, and I debate some side effects of the most surprising results it implies. At
the end I also give connections of the questions discussed to other important areas of prime number theory, such as topics from the theory of distribution of primes in denser sequences, and along the way I mention some further conjectures of Erdos that have relevant applications there
On the Erdos-Straus Conjecture
Get PDFPaul Erdos conjectured that for every n ∈ N, n ≥ 2, there exist a, b, c natural numbers, not necessarily distinct, so that 4 n = 1 a + 1 b + 1 c (see [3]). In this paper we prove an extension of Mordell’s theorem and formulate a conjecture which is stronger than Erdos’ conjecture
Going Beyond Counting First Authors in Author Co-citation Analysis
Get PDFThe present study examines one of the fundamental aspects of author co-citation analysis (ACA) - the way co-citation
counts are defined. Co-citation counting provides the data on which all subsequent statistical analyses and mappings
are based, and we compare ACA results based on two different types of co-citation counting - the traditional type that
only counts the first one among a cited work's authors on the one hand and a non-traditional type that takes into
account the first 5 authors of a cited work on the other hand. Results indicate that the picture produced through this non-traditional author co-citation counting contains more coherent author groups and is therefore considerably clearer. However, this picture represents fewer specialties in the research field being studied than that produced through the traditional first-author co-citation counting when the same number of top-ranked authors is selected and analyzed. Reasons for these effects are discussed
Dispelling the Myths Behind First-author Citation Counts
Get PDFWe conducted a full-scale evaluative citation analysis study of scholars in the XML research field to explore just how different from each other author rankings resulting from different citation counting methods actually are, and to demonstrate the capability of emerging data and tools on the Web in supporting more realistic citation counting methods. Our results contest some common arguments for the continued
use of first-author citation counts in the evaluation of scholars, such as high correlations between author rankings by first-author citation counts and other citation
counting methods, and high costs of using more realistic citation counting methods that are not well-supported by the ISI databases. It is argued that increasingly available digital full text research papers make it possible for citation analysis studies to go beyond what the ISI databases have directly supported and to employ more
sophisticated methods
The Cameron-Erdos Conjecture
No full textA set A of integers is said to be sum-free if there are no solutions to the equation x + y = z with x,y and z all in A. Answering a question of Cameron and Erdos, we show that the number of sum-free subsets of {1,...,N} is O(2^(N/2))
Dynamical formation of correlations in a Bose-Einstein condensate
No full textWe consider the evolution of N bosons interacting with a repulsive short range pair potential in three dimensions. The potential is scaled according to the Gross-Pitaevskii scaling, i.e. it is given by N 2 V(N(x i − x j )). We monitor the behaviour of the solution to the N-particle Schrödinger equation in a spatial window where two particles are close to each other. We prove that within this window a short-scale interparticle structure emerges dynamically. The local correlation between the particles is given by the two-body zero energy scattering mode. This is the characteristic structure that was expected to form within a very short initial time layer and to persist for all later times, on the basis of the validity of the Gross-Pitaevskii equation for the evolution of the Bose-Einstein condensate. The zero energy scattering mode emerges after an initial time layer where all higher energy modes disperse out of the spatial window. We can prove the persistence of this structure up to sufficiently small times before three-particle correlations could develop
Copeland-erdos and champernowne numbers for small bases
No full textKnowledge about Number Bases, Prime Numbers and Number TheoryThe Copeland–Erdos and Champernowne numbers for small bases are shown. They are formed by concatenating the sequences of positive integers and of primes, represented in base b. Both definitions can be modified by requiring the base b representations to be reversedComponente Curricular::Educação Superior::Ciências Exatas e da Terra::Matemátic
Copeland-erdos and champernowne numbers for small bases
No full textKnowledge about Number Bases, Prime Numbers and Number TheoryThe Copeland–Erdos and Champernowne numbers for small bases are shown. They are formed by concatenating the sequences of positive integers and of primes, represented in base b. Both definitions can be modified by requiring the base b representations to be reversedComponente Curricular::Educação Superior::Ciências Exatas e da Terra::Matemátic
Copeland-erdos and champernowne numbers for small bases
No full textKnowledge about Number Bases, Prime Numbers and Number TheoryThe Copeland–Erdos and Champernowne numbers for small bases are shown. They are formed by concatenating the sequences of positive integers and of primes, represented in base b. Both definitions can be modified by requiring the base b representations to be reversedComponente Curricular::Educação Superior::Ciências Exatas e da Terra::Matemátic
Copeland-erdos and champernowne numbers for small bases
No full textKnowledge about Number Bases, Prime Numbers and Number TheoryThe Copeland–Erdos and Champernowne numbers for small bases are shown. They are formed by concatenating the sequences of positive integers and of primes, represented in base b. Both definitions can be modified by requiring the base b representations to be reversedComponente Curricular::Educação Superior::Ciências Exatas e da Terra::Matemátic
- …
