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The critical exponent functions [PDF]
Comptes Rendus. Mathématique, 2022 The critical exponent of a finite or infinite word $w$ over a given alphabet is the supremum of the reals $\alpha $ for which $w$ contains an $\alpha $-power.
Corona, Dario, Della Corte, Alessandro
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The Critical Exponent is Computable for Automatic Sequences [PDF]
Electronic Proceedings in Theoretical Computer Science, 2011 The critical exponent of an infinite word is defined to be the supremum of the exponent of each of its factors. For k-automatic sequences, we show that this critical exponent is always either a rational number or infinite, and its value is computable ...
Jeffrey Shallit
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Solutions to Kirchhoff equations with critical exponent
Arab Journal of Mathematical Sciences, 2016 In this paper, we study the following problems {Δ2u−M(∫Ω|∇u|2dx)Δu=λf(x,u)+|u|2∗−2uinΩu=Δu=0on∂Ω, where 2∗=2NN−4 is the critical exponent. Under some conditions on M and f, we prove the existence of nontrivial solutions by using variational methods.
El Miloud Hssini +2 more
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Complementary symmetric Rote sequences: the critical exponent and the recurrence function [PDF]
Discrete Mathematics & Theoretical Computer Science, 2020 We determine the critical exponent and the recurrence function of complementary symmetric Rote sequences. The formulae are expressed in terms of the continued fraction expansions associated with the S-adic representations of the corresponding standard ...
Lubomíra Dvořáková +2 more
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Antisquares and Critical Exponents
Discrete Mathematics & Theoretical Computer Science, 2023 The (bitwise) complement $\overline{x}$ of a binary word $x$ is obtained by changing each $0$ in $x$ to $1$ and vice versa. An $\textit{antisquare}$ is a nonempty word of the form $x\, \overline{x}$. In this paper, we study infinite binary words that do not contain arbitrarily large antisquares.
Aseem R. Baranwal +5 more
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Geometrical Aspect of Compressibility Critical Exponent
Frontiers in Physics, 2022 Critical exponent γ ⪰ 1.1 characterizes the behavior of the mechanical compressibility of a real fluid when the temperature approaches the critical one.
J. S. Yu, W. K. Du, Q. H. Liu
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On the critical exponent of generalized Thue-Morse words [PDF]
Discrete Mathematics & Theoretical Computer Science, 2007 Automata, Logic and ...
Alexandre B. Massé +3 more
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Critical Relaxation and Critical Exponents [PDF]
Modern Physics Letters B, 1997 Dynamic relaxation of the XY model and fully frustrated XY model quenched from an initial ordered state to the critical temperature or below is investigated with Monte Carlo methods. Universal power law scaling behavior is observed. The dynamic critical exponent z and the static exponent η are extracted from the time-dependent Binder cumulant and ...
Luo, H. J., Zheng, B.
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On the Critical Exponent for k-Primitive Sets [PDF]
Combinatorica, 2021 A set of positive integers is primitive (or 1-primitive) if no member divides another. Erdős proved in 1935 that the weighted sum $\sum1/(n \log n)$ for $n$ ranging over a primitive set $A$ is universally bounded over all choices for $A$. In 1988 he asked if this universal bound is attained by the set of prime numbers.
Tsz Ho Chan +2 more
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On minimal critical exponent of balanced sequences [PDF]
Theoretical Computer Science, 2022 We study the threshold between avoidable and unavoidable repetitions in infinite balanced sequences over finite alphabets. The conjecture stated by Rampersad, Shallit and Vandomme says that the minimal critical exponent of balanced sequences over the alphabet of size $d \geq 5$ equals $\frac{d-2}{d-3}$. This conjecture is known to hold for $d\in \{5, 6,
L'ubomíra Dvoráková +3 more
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