Results 81 to 90 of about 9,714 (169)

On the Glide of the 3x+1 Problem

IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences, 2019
Yuyin Yu, Zongxiang Yi, Chuanming Tang, Jian Gao 0001   +3 more
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Integer Representations and Trajectories of the 3x+1 Problem

, 2019
This paper studies certain trajectories of the Collatz function. I show that if for each odd number $n$, $n\sim 3n+2$ then every positive integer $n \in \mathbb{N}\setminus 2^{\mathbb{N}}$ has the representation $$n=\left(2^{a_{k+1}}-\sum_{i=0}^{k}{2^{a_i}3^{k-i}}\right)/ 3^{k+1}$$ where $0\le a_0 \le a_1 \le \cdot \cdot \cdot \le a_{k+1}$.
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A New Way to Proof 3x+1 Problem

, 2015
Under the 3x+1 problem, classified the number into four kind by mod 4. The four kind number can form a cycle base on 3x+b1 problem. Base on this cycle, if the number of kind number is zero the 3x+1 will be proofed.
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Deterministic Structures in the Stopping Time Dynamics of the 3x + 1 Problem

, 2017
27 pages, 3 figures, 4 tables, 9 programs in PARI ...
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A Solution to the 3x + 1 Problem

American Journal of Computational Mathematics, 2023
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Collatz's "3x+1" problem and iterative maps on interval

, 2006
In this paper, we convert Collatz map into a simple conjugate iterative maps defined in [0,1]. Such maps are more familiar to us and easier to deal with. Some new features of this map are observed by this method. An interesting heuristic proof is also presented. This research may provide a new venture to crack the "3x+1" problem.
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Iteration Steps of 3x+1 Problem

On the 3x+1 problem, given a positive integer $N$, let $D\left( N \right) $, $O\left( N \right) $, $E\left( N \right) $ be the total iteration steps, the odd iteration steps and the even iteration steps when $N$ iterates to 1(except 1) respectively. Trivially, we have $D\left( N \right) =O\left( N \right) +E\left( N \right) $. In this paper, we propose
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TNF alpha unmasks enteric malate aspartate shuttle dysfunction bridging Parkinson disease and intestinal inflammation. [PDF]

Nat Commun
Ghirotto B, Gonçalves LE, Ruder V, James C, Gerasimova E, Rizo T, Wend H, Farrell M, Gerez JA, Prymaczok NC, Kuijs M, Shulman M, Hartebrodt A, Prots I, Gessner A, Vieth M, Zunke F, Winkler J, Blumenthal DB, Theis FJ, Riek R, Günther C, Neurath M, Gupta P, Winner B.   +24 more
europepmc   +1 more source

Screening Children for Risk of Frequent Substance Use in Young Adulthood: A 17-Year Prospective, National Study. [PDF]

J Stud Alcohol Drugs
Nooney A, Dontha M, Pelham WE.
europepmc   +1 more source

The impact of physical activity on cognitive, behavioral, and academic performance in children with ADHD: a systematic review. [PDF]

Dement Neuropsychol
Porfirio GB, Bardella MDC, Oliani MM, de Moraes C.   +3 more
europepmc   +1 more source