Results 21 to 30 of about 10,716 (231)
The 3x+1 problem: new lower bounds on nontrivial cycle lengths
Discrete Mathematics, 1993 Let T:N → N be the function defined by T(n)=n2 if n is even, T(n)=(3n+1)2 if n is odd. We show, among other things, that any nontrivial cyclic orbit under iteration of T must contain at least 17087915 ...
Eliahou, Shalom
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International Journal of Applied MathematicsCollatz conjecture, a longstanding problem in number theory, has intrigued mathematicians due to its simple formulation yet complex behavior. In this study, Moussa Model of Positive Integers is introduced, a novel mathematical framework that extends and generalizes the Collatz conjecture.
Ahmad A. Moussa
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Advanced Nonlinear Studies, 2023 We consider the existence and nonexistence of the positive solution for the following Brézis-Nirenberg problem with logarithmic perturbation: −Δu=∣u∣2∗−2u+λu+μulogu2x∈Ω,u=0x∈∂Ω,\left\{\phantom{\rule[-1.25em]{}{0ex}}\begin{array}{ll}-\Delta u={| u| }^{{2}^
Deng Yinbin +3 more
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A Preliminary Study: Why Develop High Order Thinking Skills Worksheets Based on the 3N
Journal of Medives: Journal of Mathematics Education IKIP Veteran Semarang, 2021 This qualitative research is a preliminary study of a 4-D model development research that aims to describe the basic problems, student characteristics, the formulation of learning outcomes, and specific learning goals as the initial stage of developing a
Fitria Sulistyowati, Esti Harini
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Scale-free behavior in hailstone sequences generated by the Collatz map
Physical Review Research, 2021 The Collatz conjecture, perhaps the most elementary unsolved problem in mathematics, claims that for all positive integers n, the map n↦n/2 (n even) and n↦3n+1 (n odd) reaches 1 after a finite number of iterations.
M. G. E. da Luz +3 more
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Abstract and Applied Analysis, 2014 We consider the fourth-order difference equation: Δ(z(k+1)Δ3u(k-1))=w(k)f(k,u(k)), k∈{1,2,…,n-1} subject to the boundary conditions: u(0)=u(n+2)=∑i=1n+1g(i)u(i), aΔ2u(0)-bz(2)Δ3u(0)=∑i=3n+1h(i)Δ2u(i-2), aΔ2u(n)-bz(n+1)Δ3u(n-1)=∑i=3n+1h(i)Δ2u(i-2), where
Yanping Guo +3 more
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Discharging Approach for Double Roman Domination in Graphs
IEEE Access, 2018 The discharging method is most well-known for its central role in the proof of the Four Color Theorem. This proof technique was extensively applied to study various graph coloring problems, in particular on planar graphs.
Zehui Shao +5 more
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, 2004 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.
P. B. Konstadinidis
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International Journal of Robust and Nonlinear Control, EarlyView., 2023 Abstract We propose a hierarchical energy management scheme for aggregating Distributed Energy Resources (DERs) for grid flexibility services. To prevent a direct participation of numerous prosumers in the wholesale electricity market, aggregators, as self‐interest agents in our scheme, incentivize prosumers to provide flexibility. We firstly model the
Xiupeng Chen +3 more
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Algorithms for the discrete Fréchet distance under translation
Journal of Computational Geometry, 2020 $\newcommand{\frechet}{Fréchet}$The (discrete) \frechet\ distance (DFD) is a popular similarity measure for curves. Often the input curves are not aligned, so one of them must undergo some transformation for the distance computation to be meaningful ...
Omrit Filtser, Matthew Katz
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