Search results for "Piecewise affine"

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Design, Control, and Analysis of Nonlinear Circuits with Tunnel Diode with Piecewise Affine Dynamics

2019

Computer scienceMechanical EngineeringDynamics (mechanics)Nonlinear circuitsEnergy Engineering and Power TechnologyDesign controlIndustrial and Manufacturing EngineeringNonlinear systemControl theoryLimit cycleAutomotive EngineeringTunnel diodePiecewise affineElectrical and Electronic EngineeringFormal verificationIEEJ Journal of Industry Applications
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Approximation of W1, Sobolev homeomorphism by diffeomorphisms and the signs of the Jacobian

2018

Abstract Let Ω ⊂ R n , n ≥ 4 , be a domain and 1 ≤ p [ n / 2 ] , where [ a ] stands for the integer part of a. We construct a homeomorphism f ∈ W 1 , p ( ( − 1 , 1 ) n , R n ) such that J f = det ⁡ D f > 0 on a set of positive measure and J f 0 on a set of positive measure. It follows that there are no diffeomorphisms (or piecewise affine homeomorphisms) f k such that f k → f in W 1 , p .

Sobolev homeomorphismGeneral Mathematicsta111010102 general mathematicsA domain01 natural sciencesMeasure (mathematics)Homeomorphism010101 applied mathematicsSobolev spaceCombinatoricssymbols.namesakeIntegerJacobian matrix and determinantsymbolsPiecewise affine0101 mathematicsapproximationJacobianMathematicsAdvances in Mathematics
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