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β-Turn Mimicking Crosslinking Provides Hyperstability and Fast Folding Kinetics for Short Collagen Triple Helices. [PDF]
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Distinct aneuploid karyotypes are universally selected for across cancers
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A Polynomial Analogue of the 3n+ 1 Problem
The American Mathematical Monthly, 2008viewed as mapping the integers to itself. The famous 3n + I conjecture postulates that after a finite number of iterations one always arrives at the value 1. This has been shown to be true for all n < 240. Whether it converges to 1 for every positive integer n is an open problem, see Lagarias [3].
Kenneth Hicks +3 more
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An Analytic Approach to the Collatz $$3n+1$$ 3 n + 1 Problem for Negative Start Values
Computational Methods and Function Theory, 2013In three papers, Meinardus (Uber das Syracuse-Problem, Preprint Nr. 67, Universitat Mannheim, 1987) and Berg and Meinardus (Results Math 25:1–12, 1994; Rostock Math Kolloq 48:11–18, 1995) have shown that the Collatz $$3n+1$$
Lothar Berg, Gerhard Opfer
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Analysis of a Collatz Game and Other Variants of the $$3n+1$$ Problem
Advances in Computer Games, 2023Ingo Althöfer +2 more
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On the Glide of the 3x+1 Problem
IEICE Transactions on Fundamentals of Electronics Communications and Computer Sciences, 2017For any positive integer $n$, define an iterated function $$ f(n)=\left\{\begin{array}{ll} n/2, & \mbox{$n$ even,} \\ 3n+1, & \mbox{$n$ odd.} \end{array} \right. $$ Suppose $k$ (if it exists) is the lowest number such that $f^{k}(n)
Yuyin Yu +3 more
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