Results 11 to 20 of about 4,903,854 (193)

Supervised and Unsupervised Learning with Numerical Computation for the Wolfram Cellular Automata [PDF]

Entropy
The local rules of elementary cellular automata (ECA) with one-dimensional three-cell neighborhoods are represented by eight-bit binary numbers that encode deterministic update rules.
Kui Tuo, Shengfeng Deng, Yuxiang Yang, Yanyang Wang, Qiuping Wang, Wei Li, Wenjun Zhang   +6 more
doaj   +2 more sources

ASYMPTOTIC DENSITY OF UNHAPPY NUMBERS

Bukovinian Mathematical Journal
For a number   $n\in\mathbb N$ we consider the sum of squares of all digits of $n$ and denote it by   $S^2(n)$. Let $T_0(n)=n$, $T_1(n)=S^2(n)$, \dots, $T_{k+1}(n)=T_1(T_k(n))$ for $k\ge 1$.
M. Hordei, S. Horoshkevych, O. Karlova
semanticscholar   +2 more sources

Asymptotic Density and the Asymptotics of Partition Functions

Acta Mathematica Hungarica, 2000
Let A be a set of positive integers with gcd (A) = 1, and let pA(n) be the partition function of A. Let c0 = π√2/3. If A has lower asymptotic density α and upper asymptotic density β, then lim inf log pA(n)/c0 √n ≧ √α and lim sup log pA(n)/c0 √n ≦ √β. In
M. Nathanson
semanticscholar   +3 more sources

Asymptotic Density and the Theory of Computability: A Partial Survey [PDF]

Computability and Complexity, 2016
The purpose of this paper is to survey recent work on how classical asymptotic density interacts with the theory of computability. We have tried to make the survey accessible to those who are not specialists in computability theory and we mainly state ...
C. Jockusch, P. Schupp
semanticscholar   +3 more sources

The asymptotic density of sequences [PDF]

Bulletin of the American Mathematical Society, 1951
I. Niven
semanticscholar   +3 more sources

Quasi-Density of Sets, Quasi-Statistical Convergence and the Matrix Summability Method

Axioms, 2022
In this paper, we define the quasi-density of subsets of the set of natural numbers and show several of the properties of this density. The quasi-density dp(A) of the set A⊆N is dependent on the sequence p=(pn). Different sequences (pn), for the same set
Renata Masarova, Tomas Visnyai, Robert Vrabel   +2 more
doaj   +1 more source

A variation of the class of statistical γ covers

Topological Algebra and its Applications, 2023
In this article, we introduce s-s-γ\gamma cover using the notion of star operator, which is an extension of the previous results on s-γ\gamma covers.
Bal Prasenjit, Rakshit Debjani
doaj   +1 more source

On the Asymptotic Density of Prime k-tuples and a Conjecture of Hardy and Littlewood [PDF]

Computational Methods in Science and Technology, 2019
In 1922 Hardy and Littlewood proposed a conjecture on the asymptotic density of admissible prime k-tuples. In 2011 Wolf computed the "Skewes number" for twin primes, i.e., the first prime at which a reversal of the Hardy-Littlewood inequality occurs.
L. T'oth
semanticscholar   +1 more source

Undecidable problems concerning densities of languages [PDF]

Discrete Mathematics & Theoretical Computer Science, 2005
In this paper we prove that the question whether a language presented by a context free grammar has density, is undecidable. Moreover we show that there is no algorithm which, given two unambiguous context free grammars on input, decides whether the ...
Jakub Kozik
doaj   +1 more source

On the density and the structure of the Peirce-like formulae [PDF]

Discrete Mathematics & Theoretical Computer Science, 2008
Within the language of propositional formulae built on implication and a finite number of variables $k$, we analyze the set of formulae which are classical tautologies but not intuitionistic (we call such formulae - Peirce's formulae).
Antoine Genitrini, Jakub Kozik, Grzegorz Matecki   +2 more
doaj   +1 more source