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Progress on Fractal Dimensions of the Weierstrass Function and Weierstrass-Type Functions
Fractal and FractionalThe Weierstrass function W(x)=∑n=1∞ancos(2πbnx) is a function that is continuous everywhere and differentiable nowhere. There are many investigations on fractal dimensions of the Weierstrass function, and the investigation of its Hausdorff dimension is ...
Yue Qiu, Yongshun Liang
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Axioms, 2021 A refined asymptotics of the Jacobi theta functions and their logarithmic derivatives have been received. The asymptotics of the Nevanlinna characteristics of the indicated functions and the arbitrary elliptic function have been found.
Mykola Korenkov, Yurii Kharkevych
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A Dichotomy for the Weierstrass-type functions [PDF]
Inventiones mathematicae, 2020 For a real analytic periodic function ϕ:R→R\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt}
H. Ren, W. Shen
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Exact solutions for the Cahn-Hilliard equation in terms of Weierstrass-elliptic and Jacobi-elliptic functions. [PDF]
Sci RepDespite the historical position of the F-expansion method as a method for acquiring exact solutions to nonlinear partial differential equations (PDEs), this study highlights its superiority over alternative auxiliary equation methods.
Hussain A +5 more
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Weierstrass functions in Zygmund’s class [PDF]
Proceedings of the American Mathematical Society, 2005 Consider the function \[ f ( x ) =
Yanick Heurteaux
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Numerical calculations of Hölder exponents for the Weierstrass functions with (min,+)-wavelets
Trends in Computational and Applied Mathematics, 2014 For all function f : Rn to R one introduces (min; +)-wavelets which are lower and upper hulls build from (min; +) analysis.One shows at theoretical level and on numerical applications for the Weierstrass functions, that (min, +)-wavelets decomposition ...
Abdelouahab KENOUFI, Michel GONDRAN
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Fractional Weierstrass Function by Application of Jumarie Fractional Trigonometric Functions and Its Analysis [PDF]
Advances in Pure Mathematics, 2015 The classical example of no-where differentiable but everywhere continuous function is Weierstrass function. In this paper we define the fractional order Weierstrass function in terms of Jumarie fractional trigonometric functions. The Holder exponent and
Uttam Ghosh +2 more
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Rational Values of Weierstrass Zeta Functions [PDF]
Proceedings of the Edinburgh Mathematical Society, 2015 AbstractWe answer a question of Masser by showing that for the Weierstrass zeta function ζ corresponding to a given lattice Λ, the density of algebraic points of absolute multiplicative height bounded byTand degree bounded byklying on the graph of ζ, restricted to an appropriate domain, does not exceedc(logT)15for an effective constant c > 0 ...
G. Jones, M. Thomas
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LOCAL INTERDEFINABILITY OF WEIERSTRASS ELLIPTIC FUNCTIONS [PDF]
Journal of the Institute of Mathematics of Jussieu, 2014 We explain which Weierstrass ${\wp}$ -functions are locally definable from other ${\wp}$ -functions and exponentiation in the context of o-minimal structures.
G. Jones, Jonathan Kirby, Tamara Servi
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Rough Paths above Weierstrass Functions
Comptes Rendus. MathématiqueRough paths theory allows for a pathwise theory of solutions to differential equations driven by highly irregular signals. The fundamental observation of rough paths theory is that if one can define “iterated integrals” above a signal, then one can ...
Cellarosi, Francesco, Selk, Zachary
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