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Computing upper bounds on Friedrichs’ constant

Vejchodský, Tomáš (2012)

Applications of Mathematics 2012

This contribution shows how to compute upper bounds of the optimal constant in Friedrichs’ and similar inequalities. The approach is based on the method of a p r i o r i - a p o s t e r i o r i i n e q u a l i t i e s [9]. However, this method requires trial and test functions with continuous second derivatives. We show how to avoid this requirement and how to compute the bounds on Friedrichs’ constant using standard finite element methods. This approach is quite general and allows variable coefficients and mixed boundary conditions. We use the computed...

Condorcet, mathématique sociale et vérité

Bernard Bru (1994)

Mathématiques et Sciences Humaines

A l'occasion du bicentenaire de la mort de Condordet, nous rappelons la théorie du motif de croire du fondateur de la Mathématique sociale, théorie qui seule peut nous assurer de la «réalité» des vérités auxquelles nous conduit le calcul des probabilités , comme de toute autre espèce de vérités, s'il s'en trouve.

Contents

(2013)

Applications of Mathematics 2013

Contents

(2012)

Applications of Mathematics 2012

Convergence and stability constant of the theta-method

Faragó, István (2013)

Applications of Mathematics 2013

The Euler methods are the most popular, simplest and widely used methods for the solution of the Cauchy problem for the first order ODE. The simplest and usual generalization of these methods are the so called theta-methods (notated also as θ -methods), which are, in fact, the convex linear combination of the two basic variants of the Euler methods, namely of the explicit Euler method (EEM) and of the implicit Euler method (IEM). This family of the methods is well-known and it is introduced almost...

Convergence and stability of higher-order finite element solution of reaction-diffusion equation with Turing instability

Kůs, Pavel (2015)

Application of Mathematics 2015

In this contribution, higher-order finite element method is used for the solution of reaction-diffusion equation with Turing instability. Some aspects concerning convergence of the method for this particular problem are discussed. Our numerical tests confirm the convergence of the method, but for some very special choices of parameters, this convergence has very uncommon properties.

Counting triangles that share their vertices with the unit n -cube

Brandts, Jan, Cihangir, Apo (2013)

Applications of Mathematics 2013

This paper is about 0 / 1 -triangles, which are the simplest nontrivial examples of 0 / 1 -polytopes: convex hulls of a subset of vertices of the unit n -cube I n . We consider the subclasses of right 0 / 1 -triangles, and acute 0 / 1 -triangles, which only have acute angles. They can be explicitly counted and enumerated, also modulo the symmetries of I n .

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