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Plank theorems and their applications: A survey
Bulletin of the London Mathematical Society, Volume 58, Issue 1, January 2026.Abstract Plank problems concern the covering of convex bodies by planks in Euclidean space and are related to famous open problems in convex geometry. In this survey, we introduce plank problems and present surprising applications of plank theorems in various areas of mathematics.
William Verreault
wiley +1 more source
Powers in the Lucas sequence when the index is divisible by three [PDF]
, 2011 In this paper the m-powers with m ≥ 2 included in the Lucas sequences when the index satisfies some conditions are ...
Rodrigo Hitos, Javier +1 more
core
Exponential Diophantine equations [PDF]
Pacific Journal of Mathematics, 1982 Brenner, J. L., Foster, Lorraine L.
openaire +3 more sources
Stabilisation of hybrid stochastic differential equations by delay feedback control [PDF]
, 2008 This paper is concerned with the exponential mean-square stabilisation of hybrid stochastic differential equations (also known as stochastic dierential equations with Markovian switching) by delay feedback controls.
Lam, James +10 more
core +2 more sources
Exponential diophantine equations and the irrationality of certain real numbers [PDF]
, 1991 We apply Schlickewei's recent result on the S-unit equation to show that certain purely exponential diophantine equations have only finitely many solutions.
Paul-Georg Becker, Becker, Paul-Georg
core +1 more source
On a variant of Pillai's problem involving <i>S</i>-units and Fibonacci numbers. [PDF]
Bol Soc Mat Mex, 2022 Ziegler V.
europepmc +1 more source
Mixing Rates of the Geometrical Neutral Lorenz Model. [PDF]
J Stat Phys, 2023 Bruin H, Canales Farías HH.
europepmc +1 more source
On prime powers in linear recurrence sequences. [PDF]
Ann Math Quebec, 2023 Odjoumani J, Ziegler V.
europepmc +1 more source
Max–min of polynomials and exponential diophantine equations
Journal of Number Theory, 2010 In the first half of this paper, largely based on earlier work of \textit{R. Dvornicich, U. Zannier}, and the author [Acta Arith. 106, No. 2, 115--121 (2003; Zbl 1020.11018)], it is shown that for \(F \in {\mathbb Z}[x,y]\) one has \(\max_{x \in \mathbb Z \cap [-T,T]} \min_{y \in \mathbb Z} |F(x,y)| = o(T^{1/2})\) as \(T \to \infty\) if and only if ...
openaire +2 more sources
Counting Real Roots in Polynomial-Time via Diophantine Approximation. [PDF]
Found Comut Math, 2022 Rojas JM.
europepmc +1 more source