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Completely generalized nonlinear variational inclusions for fuzzy mappings

Nan-jing Huang (1999)

Czechoslovak Mathematical Journal

In this paper, we introduce and study a new class of completely generalized nonlinear variational inclusions for fuzzy mappings and construct some new iterative algorithms. We prove the existence of solutions for this kind of completely generalized nonlinear variational inclusions and the convergence of iterative sequences generated by the algorithms.

Complex calculus of variations

Michel Gondran, Rita Hoblos Saade (2003)

Kybernetika

In this article, we present a detailed study of the complex calculus of variations introduced in [M. Gondran: Calcul des variations complexe et solutions explicites d’équations d’Hamilton–Jacobi complexes. C.R. Acad. Sci., Paris 2001, t. 332, série I]. This calculus is analogous to the conventional calculus of variations, but is applied here to 𝐂 n functions in 𝐂 . It is based on new concepts involving the minimum and convexity of a complex function. Such an approach allows us to propose explicit solutions...

Complex Ginzburg-Landau equations in high dimensions and codimension two area minimizing currents

Fanghua Lin, Tristan Rivière (1999)

Journal of the European Mathematical Society

There is an obvious topological obstruction for a finite energy unimodular harmonic extension of a S 1 -valued function defined on the boundary of a bounded regular domain of R n . When such extensions do not exist, we use the Ginzburg-Landau relaxation procedure. We prove that, up to a subsequence, a sequence of Ginzburg-Landau minimizers, as the coupling parameter tends to infinity, converges to a unimodular harmonic map away from a codimension-2 minimal current minimizing the area within the homology...

Computation of the distance to semi-algebraic sets

Christophe Ferrier (2010)

ESAIM: Control, Optimisation and Calculus of Variations

This paper is devoted to the computation of distance to set, called S, defined by polynomial equations. First we consider the case of quadratic systems. Then, application of results stated for quadratic systems to the quadratic equivalent of polynomial systems (see [5]), allows us to compute distance to semi-algebraic sets. Problem of computing distance can be viewed as non convex minimization problem: d ( u , S ) = inf x S x - u 2 , where u is in n . To have, at least, lower approximation of distance, we consider the dual...

Concentrated monotone measures with non-unique tangential behavior in 3

Robert Černý, Jan Kolář, Mirko Rokyta (2011)

Czechoslovak Mathematical Journal

We show that for every ε > 0 there is a set A 3 such that 1 A is a monotone measure, the corresponding tangent measures at the origin are non-conical and non-unique and 1 A has the 1 -dimensional density between 1 and 2 + ε everywhere in the support.

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