Search results for " Geometry."

Introducing Golden Section in the Mathematics Class to Develop Critical Thinking from the STEAM Perspective

2021

The Golden Section is a mathematical concept that is one of the most famous examples of connections between mathematics and the arts. Despite its widespread references in various areas of nature, art, architecture, literature, music, or aesthetics, discussions of the golden ratio often turn out to be false or misleading. Most of the incorrect statements are based on approximations or stem from the lack of checking the facts, making scientific mistakes in verifying the original scientific, historical, cultural context, or performing arbitrary operations in the measurements. This article offers geometric data and measurements, which allow the students to explore the golden ratio in various co…

Long-Time Behaviour for the Brownian Heat Kernel on a Compact Riemannian Manifold and Bismut’s Integration-by-Parts Formula

2007

We give a probabilistic proof of the classical long-time behaviour of the heat kernel on a compact manifold by using Bismut’s integration-by-parts formula.

EXPERIMENTAL INVESTIGATION OF DILUTE SOLID-LIQUID SUSPENSION IN AN UNBAFFLED STIRRED VESSELS BY A NOVEL PULSED LASER BASED IMAGE ANALYSIS TECHNIQUE

2009

The availability of experimental information on solid distribution inside stirred tanks is a topic of great importance in several industrial applications. The measurement of solid particle distribution in turbulent multiphase flow is not simple and the development of suitable measurement techniques is still in progress. In this work a novel non-intrusive technique for measuring particle concentration fields in solid-liquid systems is employed. The technique makes use of a laser sheet, a high sensitivity digital camera for image acquisition and a Matlab procedure for post-processing the acquired images. Experimental data are here obtained for the case of an unbaffled stirred tank. Stable tor…

The elite judo female athlete's heart.

2022

Purpose: There is a paucity of data on physiological heart adaptation in elite-level judo female athletes. This study aimed to assess left ventricular morphology and function in highly trained elite female judokas.Methods: The study prospectively included 18 females aged 23.5 ± 2.25 years, nine elite level judokas, and nine healthy non-athlete volunteers. All participants underwent a medical examination, electrocardiogram, and transthoracic 2D echocardiogram. Left ventricular diastolic and systolic diameters and volumes were determined, and parameters of left heart geometry and function (systolic and diastolic) were measured, calculated, and compared between groups.Results: When groups were…

Voisinages tubulaires épointés et homotopie stable à l'infini

2022

We initiate a study of punctured tubular neighborhoods and homotopy theory at infinity in motivic settings. We use the six functors formalism to give an intrinsic definition of the stable motivic homotopy type at infinity of an algebraic variety. Our main computational tools include cdh-descent for normal crossing divisors, Euler classes, Gysin maps, and homotopy purity. Under-adic realization, the motive at infinity recovers a formula for vanishing cycles due to Rapoport-Zink; similar results hold for Steenbrink's limiting Hodge structures and Wildeshaus' boundary motives. Under the topological Betti realization, the stable motivic homotopy type at infinity of an algebraic variety recovers…

Aménités urbaines et périurbaines dans une aire métropolitaine de forme fractale

2002

In the THÜNEN tradition, Urban Economy is a striking abstraction, giving models that keep the main features of the wide diversity of real word cities. Nevertheless, this paradigm less suits the modern urban spatial structures (polycentrism, weak centripetal forces, etc.), particularly the peri-urban form of metropolitan areas, which are an urban/rural integrated space. In this paper, we propose a classical micro-economic urban model combined with a " SIERPINSKI's carpet " geometry, a fractal form which suits for fit together urban and rural areas in a hierarchical structure. Subject to a budget constraint, a household maximises a Cobb-Douglas/CES function, where household's taste for divers…

Neuromuscular function and bone geometry and strength in aging

2010

An Inverse Problem for the Relativistic Boltzmann Equation

2020

We consider an inverse problem for the Boltzmann equation on a globally hyperbolic Lorentzian spacetime $(M,g)$ with an unknown metric $g$. We consider measurements done in a neighbourhood $V\subset M$ of a timelike path $\mu$ that connects a point $x^-$ to a point $x^+$. The measurements are modelled by a source-to-solution map, which maps a source supported in $V$ to the restriction of the solution to the Boltzmann equation to the set $V$. We show that the source-to-solution map uniquely determines the Lorentzian spacetime, up to an isometry, in the set $I^+(x^-)\cap I^-(x^+)\subset M$. The set $I^+(x^-)\cap I^-(x^+)$ is the intersection of the future of the point $x^-$ and the past of th…

A blow-up result for a nonlinear wave equation on manifolds: the critical case

2021

We consider a inhomogeneous semilinear wave equation on a noncompact complete Riemannian manifold (Formula presented.) of dimension (Formula presented.), without boundary. The reaction exhibits the combined effects of a critical term and of a forcing term. Using a rescaled test function argument together with appropriate estimates, we show that the equation admits no global solution. Moreover, in the special case when (Formula presented.), our result improves the existing literature. Namely, our main result is valid without assuming that the initial values are compactly supported.

A remark on two notions of flatness for sets in the Euclidean space

2021

In this note we compare two ways of measuring the $n$-dimensional "flatness" of a set $S\subset \mathbb{R}^d$, where $n\in \mathbb{N}$ and $d>n$. The first one is to consider the classical Reifenberg-flat numbers $\alpha(x,r)$ ($x \in S$, $r>0$), which measure the minimal scaling-invariant Hausdorff distances in $B_r(x)$ between $S$ and $n$-dimensional affine subspaces of $\mathbb{R}^d$. The second is an `intrinsic' approach in which we view the same set $S$ as a metric space (endowed with the induced Euclidean distance). Then we consider numbers ${\sf a}(x,r)$'s, that are the scaling-invariant Gromov-Hausdorff distances between balls centered at $x$ of radius $r$ in $S$ and the $n$-dimensi…