Search results for "Orff"

Gromov–Hausdorff convergence and Poincaré inequalities

2015

Power-law hereditariness of hierarchical fractal bones

2013

SUMMARY In this paper, the authors introduce a hierarchic fractal model to describe bone hereditariness. Indeed, experimental data of stress relaxation or creep functions obtained by compressive/tensile tests have been proved to be fit by power law with real exponent 0 ⩽ β ⩽1. The rheological behavior of the material has therefore been obtained, using the Boltzmann–Volterra superposition principle, in terms of real order integrals and derivatives (fractional-order calculus). It is shown that the power laws describing creep/relaxation of bone tissue may be obtained by introducing a fractal description of bone cross-section, and the Hausdorff dimension of the fractal geometry is then related …

Nonsymmetric conical upper density and $k$-porosity

2017

We study how the Hausdorff measure is distributed in nonsymmetric narrow cones in R n \mathbb {R}^n . As an application, we find an upper bound close to n − k n-k for the Hausdorff dimension of sets with large k k -porosity. With k k -porous sets we mean sets which have holes in k k different directions on every small scale.

Dimension of self-affine sets for fixed translation vectors

2016

An affine iterated function system is a finite collection of affine invertible contractions and the invariant set associated to the mappings is called self-affine. In 1988, Falconer proved that, for given matrices, the Hausdorff dimension of the self-affine set is the affinity dimension for Lebesgue almost every translation vectors. Similar statement was proven by Jordan, Pollicott, and Simon in 2007 for the dimension of self-affine measures. In this article, we have an orthogonal approach. We introduce a class of self-affine systems in which, given translation vectors, we get the same results for Lebesgue almost all matrices. The proofs rely on Ledrappier-Young theory that was recently ver…

Which measures are projections of purely unrectifiable one-dimensional Hausdorff measures

2008

We give a necessary and sufficient condition for a measure p, on the real line to be an orthogonal projection of XAl for some purely 1-unrectifiable planar set A.

Homogeneous Suslinian Continua

2011

AbstractA continuumis said to be Suslinian if it does not contain uncountably many mutually exclusive non-degenerate subcontinua. Fitzpatrick and Lelek have shown that a metric Suslinian continuum X has the property that the set of points at which X is connected im kleinen is dense in X. We extend their result to Hausdorff Suslinian continua and obtain a number of corollaries. In particular, we prove that a homogeneous, non-degenerate, Suslinian continuum is a simple closed curve and that each separable, non-degenerate, homogenous, Suslinian continuum is metrizable.

Mathematics and Music: a paradigmatic pair for basic learning

2012

The aim of the trial path described in this article is to highlight the possibility to develop intuition, analysis and synthesis abilities, which are typical of the logical - deductive mathematical thought, in primary school children (2nd class), through a significant approach to musical education, meant as systematic analysis of the sound parameters, which characterize and qualify its language. The Vygotskijan theoretical framework, which leads and interprets the didactic engineering proposed in class, emphasizes how the Mathematics - Music pair has promoted the changeover among different semiotic registers (Duval 2002), referred to Natural, iconographic, musical, geometric and pre - algeb…

MR2896126 Selmanogullari, T.; Savas, E.; Rhoades, B. E. On $q$-Hausdorff matrices. Taiwanese J. Math. 15 (2011), no. 6, 2429--2437

2011

The Henstock-Kurzweil-Stieltjes type integral for real functions on a fractal subset of the real line

2011

The aim of this paper is to introduce an Henstock-Kurzweil type integration process for real functions on a fractal subset E of the real line.

An enhanced random walk algorithm for delineation of head and neck cancers in PET studies

2017

An algorithm for delineating complex head and neck cancers in positron emission tomography (PET) images is presented in this article. An enhanced random walk (RW) algorithm with automatic seed detection is proposed and used to make the segmentation process feasible in the event of inhomogeneous lesions with bifurcations. In addition, an adaptive probability threshold and a k-means based clustering technique have been integrated in the proposed enhanced RW algorithm. The new threshold is capable of following the intensity changes between adjacent slices along the whole cancer volume, leading to an operator-independent algorithm. Validation experiments were first conducted on phantom studies:…