Search results for "MAI"

A Generalised RBF Finite Difference Approach to Solve Nonlinear Heat Conduction Problems on Unstructured Datasets

2011

Radial Basis Functions have traditionally been used to provide a continuous interpolation of scattered data sets. However, this interpolation also allows for the reconstruction of partial derivatives throughout the solution field, which can then be used to drive the solution of a partial differential equation. Since the interpolation takes place on a scattered dataset with no local connectivity, the solution is essentially meshless. RBF-based methods have been successfully used to solve a wide variety of PDEs in this fashion. Such full-domain RBF methods are highly flexible and can exhibit spectral convergence rates Madych & Nelson (1990). However, in their traditional implementation the fu…

Hypoxia-induced reduction of sVEGFR-2 levels in human colonic microvascular endothelial cells in vitro: Comparative study with HUVEC.

2008

The functionality of large-vessel endothelial cells, such as human umbilical vein endothelial cells (HUVEC), may differ significantly from that in the microvasculature. We established a method for the isolation of human colonic microvascular endothelial cells (HCMEC). Since colonic diseases are often accompanied by hypoxia we examined its effects on HCMEC of five individuals in comparison with HUVEC, with respect to the secretion of the soluble form of the two important vascular endothelial growth factor (VEGF) receptors, VEGFR-1 and 2. After dissociation by dispase/collagenase of mucosal and submucosal tissue obtained from normal adult colon, HCMEC were isolated using CD31-coated magnetic …

The Cauchy problem for linear growth functionals

2003

In this paper we are interested in the Cauchy problem $$ \left\{ \begin{gathered} \frac{{\partial u}}{{\partial t}} = div a (x, Du) in Q = (0,\infty ) x {\mathbb{R}^{{N }}} \hfill \\ u (0,x) = {u_{0}}(x) in x \in {\mathbb{R}^{N}}, \hfill \\ \end{gathered} \right. $$ (1.1) where \( {u_{0}} \in L_{{loc}}^{1}({\mathbb{R}^{N}}) \) and \( a(x,\xi ) = {\nabla _{\xi }}f(x,\xi ),f:{\mathbb{R}^{N}}x {\mathbb{R}^{N}} \to \mathbb{R} \)being a function with linear growth as ‖ξ‖ satisfying some additional assumptions we shall precise below. An example of function f(x, ξ) covered by our results is the nonparametric area integrand \( f(x,\xi ) = \sqrt {{1 + {{\left\| \xi \right\|}^{2}}}} \); in this case …

Old and New on the Quasihyperbolic Metric

1998

Let D be a proper subdomain of \( {\mathbb{R}^d}\). Following Gehring and Palka [GP] we define the quasihyperbolic distance between a pair x 1, x 2 of points in D as the infimum of \( {\smallint _\gamma }\frac{{ds}}{{D\left( {x,\partial D} \right)}}\) over all rectifiable curves γ joining x 1, x 2 in D. We denote the quasihyperbolic distance between x 1, x 2 by k D (x 1, x 2). As pointed out by Gehring and Osgood [GO], x 1 and x 2 can be joined by a quasihyperbolic geodesic; also see [Mr]. The quasihyperbolic metric is comparable to the usual hyperbolic metric in a simply connected plane domain by the Koebe distortion theorem. For a multiply connected plane domain D these two metrics are co…

Quasi-Modes in Higher Dimension

2019

Recall that if a(x, ξ) and b(x, ξ) are two C1-functions defined on some domain in \({\mathbf {R}}^{2n}_{x,\xi }\), then we can define the Poisson bracket to be the C0-function on the same domain given by $$\displaystyle \{ a,b\} =a^{\prime }_\xi \cdot b^{\prime }_x-a^{\prime }_x \cdot b^{\prime }_\xi =H_a(b). $$ Here \(H_a=a^{\prime }_\xi \cdot \partial _x-a^{\prime }_x\cdot \partial _\xi \) denotes the Hamilton vector field of a. The following result is due to Zworski, who obtained it via a semi-classical reduction from the above mentioned result of Hormander. A direct proof was given in Dencker et al. and here we give a variant. We will assume some familiarity with symplectic geometry.

Product Integration for Weakly Singular Integral Equations In ℝm

1985

In this note we discuss the numerical solution of the second kind Fredholm integral equation: $$ y(t) = f(t) + \lambda \int\limits_{\Omega } {{{\psi }_{\alpha }}(|t - s|)g(t,s)y(s)ds,\;t \in \bar{\Omega },} $$ (1) Where \( \lambda \in ;\not{ \subset }\backslash \{ 0\} \) , the functions f,g are given and continuous, |.| denotes the Euclidean norm, and φα, 0 \alpha > 0} \\ {\left\{ {\begin{array}{*{20}{c}} {\ln (r),} & {j = 0} \\ {{{r}^{{ - j}}}} & {j > 0} \\ \end{array} } \right\},\alpha = m} \\ \end{array} ,} \right. $$ with Cj not depending on r. Here Ω _ is the closure of a bounded domain Ω⊂ℝm.

Absolute continuity of mappings with finite geometric distortion

2015

Suppose that ⊂ R n is a domain with n ≥ 2. We show that a continuous, sense-preserving, open and discrete mapping of finite geometric outer distortion with KO(·,f) ∈ L 1/(n 1) loc () is absolutely continuous on almost every line parallel to the coordinate axes. Moreover, if U ⊂ is an open set with N(f,U) 0 depends only on n and on the maximum multiplicity N(f,U).

La Communication des Institutions Culturelles dans le Domaine des Arts du Spectacle Vivant en France

2001

Spirals of Speaking Out? Effects of the “Suppressed Voice Rhetoric” on Audiences’ Willingness to Express Their Opinion

2020

A defining feature of counterpublics is to claim that their views are deliberately excluded from the mainstream public sphere. This rhetorical strategy – which we theorize as “suppressed voice rhet...

La didactique clinique comme mode d’accès aux savoirs des enseignants en ÉPS : le cas de l’enseignement du judo

2018

Cette étude à visée exploratoire et compréhensive met en évidence les savoirs personnels des enseignants transmis en cours d’ÉPS. La recherche présente trois vignettes didactiques cliniques d’enseignants spécialistes de judo. Les résultats montrent que ces savoirs personnels se sont construits pendant la pratique sportive du judo lorsque ceux-ci étaient de jeunes pratiquants. Le rôle du « déjà-là expérientiel » et ses effets sur les conceptions des professeurs sont mis en avant, en lien avec les savoirs personnels. Compte tenu des effets déterminants des « déjà-là expérientiels et conceptuels », nous proposons quelques pistes de travail pour la formation initiale des enseignants d’ÉPS.