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Weak notions of Jacobian determinant and relaxation
"... In this paper we study two weak notions of Jacobian determinant for Sobolev maps, namely the distributional Jacobian and the relaxed total variation, which in general could be different. We show some cases of equality and use them to give an explicit expression for the relaxation of some polyconvex ..."
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In this paper we study two weak notions of Jacobian determinant for Sobolev maps, namely the distributional Jacobian and the relaxed total variation, which in general could be different. We show some cases of equality and use them to give an explicit expression for the relaxation of some polyconvex
Topological degree, Jacobian determinants and relaxation
 Unione Mat. Ital. Sez. B
"... In English: a characterization of the total variation TV (u,Ω) of the Jacobian determinant detDu is obtained for some classes of functions u: Ω → Rn outside the traditional regularity space W 1,n(Ω;Rn). In particular, explicit formulas are deduced for functions that are locally Lipschitz continuous ..."
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Cited by 5 (3 self)
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In English: a characterization of the total variation TV (u,Ω) of the Jacobian determinant detDu is obtained for some classes of functions u: Ω → Rn outside the traditional regularity space W 1,n(Ω;Rn). In particular, explicit formulas are deduced for functions that are locally Lipschitz continuous
NewtonPuiseux Roots Of Jacobian Determinants
"... Let f(x;y); g(x; y) denote either a pair of holomorphic function germs, or a pair of monic polynomials in x whose coefficients are Laurent series in y. A (relative) polar arc is a NewtonPuiseux root, x = fl(y), of the Jacobian J = fygx \Gamma fxgy . ..."
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Cited by 3 (0 self)
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Let f(x;y); g(x; y) denote either a pair of holomorphic function germs, or a pair of monic polynomials in x whose coefficients are Laurent series in y. A (relative) polar arc is a NewtonPuiseux root, x = fl(y), of the Jacobian J = fygx \Gamma fxgy .
The Characterization of the Regularity of the Jacobian Determinant in the framework of Potential spaces
 J. London Math. Soc
"... . We give necessary and sufficient conditions on the parameters s 1 ; s 2 ; : : : ; s m ; p 1 ; p 2 ; : : : ; pm such that the Jacobian determinant extends to a bounded operator from H s1 p1 \Theta H s2 p2 \Theta : : : \Theta H sm pm into Z 0 . Here all spaces are defined on R n and 2 ..."
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. We give necessary and sufficient conditions on the parameters s 1 ; s 2 ; : : : ; s m ; p 1 ; p 2 ; : : : ; pm such that the Jacobian determinant extends to a bounded operator from H s1 p1 \Theta H s2 p2 \Theta : : : \Theta H sm pm into Z 0 . Here all spaces are defined on R n and 2
Efficient Jacobian Determination by StructureRevealing Automatic Differentiation
"... I hereby declare that I am the sole author of this thesis. This is a true copy of the thesis, including any required final revisions, as accepted by my examiners. I understand that my thesis may be made electronically available to the public. ii This thesis is concerned with the efficient computatio ..."
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tem. This allows for the efficient determination of the Jacobian matrix using AD software. We will illustrate the promise of this approach with computational experiments. iii Acknowledgements I am heartily thankful to my supervisor, Thomas F. Coleman, whose encouragement, guidance and support from the initial
Tetrahedral element shape optimization via the jacobian determinant and condition number
 IN PROCEEDINGS OF THE 8TH INTERNATIONAL MESHING ROUNDTABLE
, 1999
"... We present a new shape measure for tetrahedral elements that is optimal in the sense that it gives the distance of a tetrahedron from the set of inverted elements. This measure is constructed from the condition number of the linear transformation between a unit equilateral tetrahedron and any tetra ..."
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Cited by 45 (6 self)
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condition number is not defined for tetrahedral with negative volume, these objective functions can be used only when the initial mesh is valid. Therefore, we formulate a third objective function using the determinant of the element Jacobian that is suitable for mesh untangling. We review the optimization
Tetrahedral Element Shape Optimization via the Jacobian Determinant and Condition Number
 in Proceedings of the 8th International Meshing Roundtable
, 1999
"... . We present a new shape measure for tetrahedral elements that is optimal in the sense that it gives the distance of a tetrahedron from the set of inverted elements. This measure is constructed from the condition number of the linear transformation between a unit equilateral tetrahedron and any tetr ..."
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condition number is not defined for tetrahedra with negative volume, these objective functions can be used only when the initial mesh is valid. Therefore, we formulate a third objective function using the determinant of the element Jacobian that is suitable for mesh untangling. We review the optimization
Reversible jump Markov chain Monte Carlo computation and Bayesian model determination
 Biometrika
, 1995
"... Markov chain Monte Carlo methods for Bayesian computation have until recently been restricted to problems where the joint distribution of all variables has a density with respect to some xed standard underlying measure. They have therefore not been available for application to Bayesian model determi ..."
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Cited by 1330 (24 self)
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determination, where the dimensionality of the parameter vector is typically not xed. This article proposes a new framework for the construction of reversible Markov chain samplers that jump between parameter subspaces of di ering dimensionality, which is exible and entirely constructive. It should therefore
A Tutorial on Visual Servo Control
 IEEE Transactions on Robotics and Automation
, 1996
"... This paper provides a tutorial introduction to visual servo control of robotic manipulators. Since the topic spans many disciplines our goal is limited to providing a basic conceptual framework. We begin by reviewing the prerequisite topics from robotics and computer vision, including a brief review ..."
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Cited by 822 (25 self)
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This paper provides a tutorial introduction to visual servo control of robotic manipulators. Since the topic spans many disciplines our goal is limited to providing a basic conceptual framework. We begin by reviewing the prerequisite topics from robotics and computer vision, including a brief review of coordinate transformations, velocity representation, and a description of the geometric aspects of the image formation process. We then present a taxonomy of visual servo control systems. The two major classes of systems, positionbased and imagebased systems, are then discussed. Since any visual servo system must be capable of tracking image features in a sequence of images, we include an overview of featurebased and correlationbased methods for tracking. We conclude the tutorial with a number of observations on the current directions of the research field of visual servo control. 1 Introduction Today there are over 800,000 robots in the world, mostly working in factory environment...
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