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The structure of the 3x + 1 problem [PDF]
Electronic Journal of Graph Theory and Applications, 2021 Paul Erdös said about the 3x+1 problem, "Mathematics is not yet ready for such problems". And he is seemingly right. Although we cannot solve this problem either, we provide some results about its structure.
Alf Kimms
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Long-Term Donor Chimerism Monitoring for Relapse Risk Assessment After Pediatric Allo-HSCT [PDF]
The Application of Clinical GeneticsAnna Prażmo,1 Paulina Skowera,2 Agnieszka Zaucha-Prazmo,3,* Monika Lejman2,* 1Student Scientific Society of Independent Laboratory of Genetic Diagnostics, Medical University of Lublin, Lublin, Poland; 2Independent Laboratory of ...
Prażmo A +3 more
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The convergence of power iteration method for tournament matrices and its applications [PDF]
ریاضی و جامعه, 2023 In this paper, we prove that for every tournament matrix with nonzero spectral radius, the power iteration method converges to a nonzero eigenvector corresponding to the eigenvalue with the maximum magnitude. An application of this result for ranking the
Amirhosein Nokhodkar, Rasool Kazemi
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THE EFFECT OF KANGAROO METHOD ON IMPROVEMENT BODY WEIGHT ON LOW BIRTH WEIGHT
Indonesian Midwifery and Health Sciences Journal, 2021 Background: In Indonesia the Neonatal mortality rate was 15 infants per 1000 births and in Surabaya in 2018 LBW deaths were 50 per 1000 live births, while in Haji General Hospital the LBW deaths were 12 babies in 1 year.
Yeni Riskawati +2 more
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Discrete Mathematics & Theoretical Computer Science, 2002 We use Conway's \emphFractran language to derive a function R:\textbfZ^+ → \textbfZ^+ of the form R(n) = r_in if n ≡ i \bmod d where d is a positive integer, 0 ≤ i < d and r_0,r_1, ...
Kenneth G. Monks
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A binomial representation of the 3x + 1 problem [PDF]
Acta Arithmetica, 1999 Let \(f(x)=(3x+1)/2\) if \(x\) is odd, and \(f(x)=x/2\) if \(x\) is even, and define \(g\) recursively by \(g(a,0)=a\) and \(g(a,k+1)=f(g(a,k))\). Then the \(3x+1\) problem is to prove that, for any positive integer \(a\), there is some \(k\) such that \(g(a,k)=1\). The relation \(\text{Syr}(a,b)\) is defined to hold when there is some \(m\) satisfying
Margenstern, Maurice, Matiyasevich, Yuri
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On special integer linear combinations of terms of rational cycles for the generalized 3x+1 problem [PDF]
Notes on Number Theory and Discrete MathematicsIn the paper, some special linear combinations of the terms of rational cycles of generalized Collatz sequences are studied. It is proved that for specific choice of the coefficients these linear combinations are integers.
Yagub N. Aliyev
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Differentiated surgical treatment of rectovaginal fistulae
GMS Interdisciplinary Plastic and Reconstructive Surgery DGPW, 2012 Objective: Rectovaginal fistulae (RVF) are a serious and debilitating problem for patients and a challenge for the treating surgeons. We present our experiences in the surgical treatment of these patients.
Kröpil, Feride +5 more
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Acta Arithmetica, 2006 In this work, we introduce another extension U of the 3n+1 function to the real line. We propose a conjecture about the U-trajectories that generalizes the famous 3n+1 (or Collatz) conjecture. We then prove our main result about the iterates of U (which is directly related to both of these conjectures).
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A New Approach on Proving Collatz Conjecture
Journal of Mathematics, 2019 Collatz Conjecture (3x+1 problem) states any natural number x will return to 1 after 3⁎x+1 computation (when x is odd) and x/2 computation (when x is even). In this paper, we propose a new approach for possibly proving Collatz Conjecture (CC). We propose
Wei Ren
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