Results 51 to 60 of about 3,294 (223)

Progress on Fractal Dimensions of the Weierstrass Function and Weierstrass-Type Functions

Fractal and Fractional
The 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
doaj   +1 more source

On fractal faithfulness and fine fractal properties of random variables with independent ${\mathit{Q}}^{\ast }$-digits

Modern Stochastics: Theory and Applications, 2016
We develop a new technique to prove the faithfulness of the Hausdorff–Besicovitch dimension calculation of the family $\varPhi ({Q}^{\ast })$ of cylinders generated by ${Q}^{\ast }$-expansion of real numbers.
Muslem Ibragim, Grygoriy Torbin
doaj   +1 more source

Hearing the Serre Invariant of a Compact p‐Adic Analytic Manifold

Mathematische Nachrichten, EarlyView.
ABSTRACT Using a previous novel way of defining kernel functions for Laplacian integral operators on a compact p$p$‐adic analytic manifold X$X$, one such operator Δ0s$\Delta _0^s$ with s∈R$s\in \mathbb {R}$ is applied to hearing the Serre invariant i(X)$i(X)$ by showing that a wavelet eigenvalue (with the wavelet having small support) is always ...
Patrick Erik Bradley, Ángel Morán Ledezma   +1 more
wiley   +1 more source

Numerical estimates of Hausdorff dimension [PDF]

Journal of Computational Physics, 1982
Numerical methods for estimating Hausdorff dimension, useful in the analysis of turbulence, are explained and applied to a specific example. In particular, methods involving rescaling and approximation by Cantor sets are discussed.
openaire   +3 more sources

Regularity Estimates for Fully Nonlinear Dead‐Core Problems With a Hamiltonian Term

Mathematische Nachrichten, EarlyView.
ABSTRACT In this paper, we present a problem involving fully nonlinear elliptic operators with Hamiltonian, which can present a singularity or degenerate as the gradient approaches the origin. The model studied here, allows the appearance of plateau zones, i.e., unknown regions of the domain in which the non‐negative solutions vanishes.
Rafael R. Costa, Ginaldo S. Sá
wiley   +1 more source

On the Dimension of Paracompact Hausdorff Spaces [PDF]

Nagoya Mathematical Journal, 1955
This short note gives the generalized sum theorem for Lebesgue dimension of paracompact Hausdorff spaces. Our theorem, though it is a generalization of Mr. Morita’s sum theorem for fully normal spaces [3, Theorem 3. 2] which is essentially based on his generalized sum theorem for normal spaces [3, Theorem 3.1], is obtained by very brief arguments ...
openaire   +3 more sources

Gradient‐ and Newton‐Based Unit Vector Extremum Seeking Control

International Journal of Robust and Nonlinear Control, EarlyView.
ABSTRACT This paper proposes new methods for stable and efficient convergence in multivariable extremum seeking control (ESC) using sliding mode techniques. Inspired by classical sliding modes and finite‐time control, the approach integrates these ideas into gradient‐ and Newton‐based ESC schemes with sinusoidal perturbations.
Roberto Luo, Victor Hugo Pereira Rodrigues, Tiago Roux Oliveira, Miroslav Krstic   +3 more
wiley   +1 more source

Errata to ‘Hausdorff dimension for horseshoes’ [PDF]

Ergodic Theory and Dynamical Systems, 1985
In our paper ‘Hausdorff dimension for horseshoes’ (H. McCluskey and A. Manning, Ergod. Th. & Dynam. Sys. (1983) 3, 251–260), § 3 entitled ‘Continuity across a bifurcation’ should be deleted since the proof of theorem 3 there is wrong.The mistake is that does not in fact imply that δs → 1.
openaire   +1 more source

Drifting to the top? The effects of category erraticism on status mobility in the U.S. venture capital industry

Strategic Management Journal, EarlyView.
Abstract Research Summary We examine the effects of category erraticism, that is, having moved across socio‐cognitively distant industry categories over time, on status mobility. We argue that it is not the breadth of the categories that a firm spans or the overall distance among those categories, but whether its movement across categories forms a ...
Danyang Li, Michael Jensen
wiley   +1 more source

Hausdorff Dimension and mean porosity [PDF]

Mathematische Annalen, 1997
Let \(E \subset R^n\) be a compact set and assume that there exists \(c \in (0, 1/2)\) such that for every \(x \in E\) and all \(r \in (0, d(E)/2),\) the ball \(B^n(x,r)\) contains a ball of radius \(cr\) not meeting \(E \). Then no point of \(E\) can be a point of density and hence \(E \) has \(n\)-dimensional Lebesgue measure equal to \(0\). In fact,
Koskela, Pekka, Rohde, Steffen
openaire   +3 more sources