Results 71 to 80 of about 10,716 (231)
, 2016 SequencesThe Collatz sequence is built starting from the number n. If n is even, compute n/2; if n is odd, compute 3n+1. Repeat using the result. Here these sequences are shown using red spheres for even numbers and blue ones for odd numbers. Does this
Zizi, Jacqueline
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On the Hardness of Switching to a Small Number of Edges
Journal of Graph Theory, EarlyView.ABSTRACT Seidel's switching is a graph operation which makes a given vertex adjacent to precisely those vertices to which it was non‐adjacent before, while keeping the rest of the graph unchanged. Two graphs are called switching‐equivalent if one can be made isomorphic to the other one by a sequence of switches. Jelínková et al. [DMTCS 13, no. 2, 2011]
Vít Jelínek +2 more
wiley +1 more source
Advances in Nonlinear AnalysisIn this study, we explore the positive solutions of a nonlinear Choquard equation involving the Green kernel of the fractional operator (−ΔBN)−α⁄2{\left(-{\Delta }_{{{\mathbb{B}}}^{N}})}^{-\alpha /2} in the hyperbolic space, where ΔBN{\Delta }_{{{\mathbb{
Gupta Diksha, Sreenadh Konijeti
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The 3n+1-problem and holomorphic dynamics
, 1999 The 3n+1-problem is the following iterative procedure on the positive integers: the integer n maps to n/2 or 3n+1, depending on whether n is even or odd. It is conjectured that every positive integer will be eventually periodic, and the cycle it falls onto is $1\mapsto 4\mapsto 2\mapsto 1$.
Letherman, Simon +2 more
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This paper provides a formal solution to the Collatz Conjecture by defining the sequence as a Topological Super-Martingale. By establishing a "Metric Floor" and a "Scaling Gap" within a quantized manifold, we prove that infinite divergence is mathematically impossible.
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Cauchy problem for the non-newtonian viscous incompressible fluid [PDF]
, 1996 summary:We study the Cauchy problem for the non-Newtonian incompressible fluid with the viscous part of the stress tensor $\tau ^V(\mathbb{e}) = \tau (\mathbb{e}) - 2\mu _1 \Delta \mathbb{e}$, where the nonlinear function $\tau (\mathbb{e})$ satisfies ...
Pokorný, Milan
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Stable Cuts, NAC‐Colourings and Flexible Realisations of Graphs
Journal of Graph Theory, EarlyView.ABSTRACT A (2‐dimensional) realisation of a graph G $G$ is a pair ( G , p ) $(G,p)$, where p $p$ maps the vertices of G $G$ to R 2 ${{\mathbb{R}}}^{2}$. A realisation is flexible if it can be continuously deformed while keeping the edge lengths fixed, and rigid otherwise.
Katie Clinch +5 more
wiley +1 more source
Density Conditions for k $k$ Vertex‐Disjoint Triangles in Tripartite Graphs
Journal of Graph Theory, EarlyView.ABSTRACT Let n , k $n,k$ be positive integers such that n ≥ k $n\ge k$ and G $G$ be a tripartite graph with parts A , B , C $A,B,C$ such that ∣ A ∣ = ∣ B ∣ = ∣ C ∣ = n $| A| =| B| =| C| =n$. Denote the edge densities of G [ A , B ] , G [ A , C ] $G[A,B],G[A,C]$ and G [ B , C ] $G[B,C]$ by α , β $\alpha ,\beta $ and γ $\gamma $, respectively.
Mingyang Guo, Klas Markström
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On An Extremal Problem In The Class Of Bipartite 1-Planar Graphs
, 2016 A graph G = (V, E) is called 1-planar if it admits a drawing in the plane such that each edge is crossed at most once. In this paper, we study bipartite 1-planar graphs with prescribed numbers of vertices in partite sets.
Czap, Július +2 more
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The 3n+1 Collatz Problem and Functional Equations
, 1995 This paper reports on some functional equations, which arise in connection with the famous 3n + 1 Collatz problem. In particular, it reports on two analytic versions of the corresponding Collatz conjecture, which are contained in [1]
Lothar Berg, Günter Meinardus
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