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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 The relaxed problem, wherein the integrand f has been replaced by its lower semicontinuous quasiconvex envelope with respect to the gradient variable, possesses the same finite minimal value as the original problem, and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 The relaxed problem, wherein the integrand f has been replaced by its lower semicontinuous quasiconvex envelope with respect to the gradient variable, possesses the same finite minimal value as the original problem, and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...

Random perturbations of exponential Riesz bases in L 2 ( - π , π )

Gennadii Chistyakov, Yura Lyubarskii (1997)

Annales de l'institut Fourier

Let a sequence { λ n } be given such that the exponential system { exp ( i λ n x ) } forms a Riesz basis in L 2 ( - π , π ) and { ξ n } be a sequence of independent real-valued random variables. We study the properties of the system { exp ( i ( λ n + ξ n ) x ) } as well as related problems on estimation of entire functions with random zeroes and also problems on reconstruction of bandlimited signals with bandwidth 2 π via their samples at the random points { λ n + ξ n } .

Recobriments i grafs distància-regulars.

Josep Rifà Coma, Jaume Pujol Capdevila (1988)

Qüestiió

Uno de los aspectos claves en las telecomunicaciones está relacionado con el uso de los códigos correctores de errores para la transmisión de información. Actualmente se utiliza una clase muy simple de códigos; la implementación física de un código corrector de errores es complicada y costosa. En el campo de la Informática Teórica se intenta abordar el problema de los códigos correctores de errores desde diferentes ángulos. Uno de ellos es el de la Combinatoria Algebraica y, en particular, los grafos...

Recognition of atherosclerotic plaques and their extended dimensioning with computerized tomography angiography imaging

Tomasz Markiewicz, Mirosław Dziekiewicz, Marek Maruszyński, Romana Bogusławska-Walecka, Wojciech Kozłowski (2014)

International Journal of Applied Mathematics and Computer Science

In this paper the authors raise the issue of automatic discrimination of atherosclerotic plaques within an artery lumen based on numerical and statistical thresholding of Computerized Tomography Angiographic (CTA) images and their advanced dimensioning as a support for preoperative vessel assessment. For the study, a set of tomograms of the aorta, as well as the ilio-femoral and femoral arteries were examined. In each case a sequence of about 130-480 images of the artery cutoff planes were analyzed...

Reconstructibility of Boolean control networks with time delays in states

Ping Sun, Lijun Zhang, Kuize Zhang (2018)

Kybernetika

This paper deals with the reconstructibility of Boolean control networks (BCNs) with time delays in states. First, a survey on the semi-tensor product, weighted pair graph, constructed forest and finite automata is given. Second, by using the weighted pair graph, constructed forest and finite automata, an algorithm is designed to judge whether a Boolean control network with time delays in states is reconstructable or not under a mild assumption. Third, an algorithm is proposed to determine the current...

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