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QL-implications versus D-implications

Margarita Mas, Miquel Monserrat, Joan Torrens (2006)

Kybernetika

This paper deals with two kinds of fuzzy implications: QL and Dishkant implications. That is, those defined through the expressions I ( x , y ) = S ( N ( x ) , T ( x , y ) ) and I ( x , y ) = S ( T ( N ( x ) , N ( y ) ) , y ) respectively, where T is a t-norm, S is a t-conorm and N is a strong negation. Special attention is due to the relation between both kinds of implications. In the continuous case, the study of these implications is focused in some of their properties (mainly the contrapositive symmetry and the exchange principle). Finally, the case of non continuous t-norms...

Quantization Dimension Estimate of Inhomogeneous Self-Similar Measures

Mrinal Kanti Roychowdhury (2013)

Bulletin of the Polish Academy of Sciences. Mathematics

We consider an inhomogeneous measure μ with the inhomogeneous part a self-similar measure ν, and show that for a given r ∈ (0,∞) the lower and the upper quantization dimensions of order r of μ are bounded below by the quantization dimension D r ( ν ) of ν and bounded above by a unique number κ r ∈ ( 0 , ∞ ) , related to the temperature function of the thermodynamic formalism that arises in the multifractal analysis of μ.

Quantization Dimension Function and Ergodic Measure with Bounded Distortion

Mrinal Kanti Roychowdhury (2009)

Bulletin of the Polish Academy of Sciences. Mathematics

The quantization dimension function for the image measure of a shift-invariant ergodic measure with bounded distortion on a self-conformal set is determined, and its relationship to the temperature function of the thermodynamic formalism arising in multifractal analysis is established.

Quasiconvex relaxation of multidimensional control problems with integrands f(t, ξ, v)

Marcus Wagner (2011)

ESAIM: Control, Optimisation and Calculus of Variations

We prove a general relaxation theorem for multidimensional control problems of Dieudonné-Rashevsky type with nonconvex integrands f(t, ξ, v) in presence of a convex control restriction. The relaxed problem, wherein the integrand f has been replaced by its lower semicontinuous quasiconvex envelope with respect to the gradient variable, possesses the same finite minimal value as the original problem, and admits a global minimizer. As an application, we provide existence theorems for the image registration...

Quasiconvex relaxation of multidimensional control problems with integrands f(t, ξ, v)

Marcus Wagner (2011)

ESAIM: Control, Optimisation and Calculus of Variations

We prove a general relaxation theorem for multidimensional control problems of Dieudonné-Rashevsky type with nonconvex integrands f(t, ξ, v) in presence of a convex control restriction. The relaxed problem, wherein the integrand f has been replaced by its lower semicontinuous quasiconvex envelope with respect to the gradient variable, possesses the same finite minimal value as the original problem, and admits a global minimizer. As an application, we provide existence theorems for the image registration...

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