The Resource New trends in shape optimization, Also Pratelli, Günter Leugering, (electronic book)
New trends in shape optimization, Also Pratelli, Günter Leugering, (electronic book)
Resource Information
The item New trends in shape optimization, Also Pratelli, Günter Leugering, (electronic book) represents a specific, individual, material embodiment of a distinct intellectual or artistic creation found in Sydney Jones Library, University of Liverpool.This item is available to borrow from 1 library branch.
Resource Information
The item New trends in shape optimization, Also Pratelli, Günter Leugering, (electronic book) represents a specific, individual, material embodiment of a distinct intellectual or artistic creation found in Sydney Jones Library, University of Liverpool.
This item is available to borrow from 1 library branch.
 Language
 eng
 Extent
 1 online resource.
 Contents

 Introduction; On the Minimization of Area Among ChordConvex Sets; 1 Introduction and Setting of the Problem; 2 Definitions and Results; 2.1 Uniqueness of the Bisecting Chord of Given Direction; 2.2 Properties of the Extreme Points and of the Intersections Between Chords; 2.3 Zindler Sets and Their Properties; References; Optimization Problems Involving the First Dirichlet Eigenvalue and the Torsional Rigidity; 1 Introduction; 2 Statement of the Problem; 3 A Sharp Inequality Between Torsion and First Eigenvalue; 4 The Attainable Set; 5 Torsional Rigidity and the Heat Equation
 4.2 Parametrize Functions by Geometries5 Metric Structures via Characteristic Functions of Measurable Sets; 5.1 LinftyConvergence of Measurable Sets; 5.2 LpConvergence of Measurable Sets, 1lep<infty; 5.3 Compact Families; 6 Metric Structures via Distance Functions; 6.1 Pompéiu's Ecart Mutuel and Hausdorff Metric on Compact Sets; 6.2 Metric of Uniform Convergence; 6.3 Metric of Lipschitz Convergence; 6.4 Metric of W1,pConvergence, 1lep<infty; 6.5 Metrics Compatible with the Abelian Group Structure; 7 Metric Structures via Oriented Distance Functions
 7.1 Oriented Distance Function: Definition and Some Properties7.2 Some General Metrics on Cb(D); 7.3 Metrics Compatible with the Abelian Group Structure; 8 Boundary Properties of Sets in Cb0(D); 8.1 Finite Perimeter or Caccioppoli Sets; 8.2 Preliminary Considerations; 8.3 Sets of Bounded Curvature; 8.4 Metrics for Families of Sets with Smooth Boundaries; 9 Sets of Positive Reach, Submanifolds, Squared Distance Functions; 9.1 Sets of Positive Reach; 9.2 CkSubmanifolds, kge2; 9.3 Metric on Families of Submanifolds; 10 Metric Structure via the Support Function; 11 Some Concluding Remarks
 Isbn
 9783319175621
 Label
 New trends in shape optimization
 Title
 New trends in shape optimization
 Statement of responsibility
 Also Pratelli, Günter Leugering
 Language
 eng
 Cataloging source
 N$T
 Dewey number
 514/.24
 Index
 no index present
 LC call number
 QA612.7
 Literary form
 non fiction
 Nature of contents
 dictionaries
 http://library.link/vocab/relatedWorkOrContributorDate
 1953
 http://library.link/vocab/relatedWorkOrContributorName

 Pratelli, Aldo
 Leugering, Günter
 Series statement
 International series of numerical mathematics
 Series volume
 166
 http://library.link/vocab/subjectName

 Shape theory (Topology)
 Mathematical optimization
 Label
 New trends in shape optimization, Also Pratelli, Günter Leugering, (electronic book)
 Antecedent source
 unknown
 Bibliography note

 ReferencesOn a Classical Spectral Optimization Problem in Linear Elasticity; 1 Introduction; 2 The Eigenvalue Problems; 3 Analyticity Results ; 4 Isovolumetric Perturbations; References; Metric Spaces of Shapes and Geometries Constructed from Set Parametrized Functions; 1 Introduction; 2 Group, Symmetric Difference, and Characteristic Functions; 2.1 Group Structure Induced by the Symmetric Difference; 2.2 Metric Structures via Characteristic Functions; 3 Parametrize Geometries by Functions: Hypographs; 4 Analytical Representations of Geometries; 4.1 Parametrize Geometries by Functions
 ReferencesA Phase Field Approach for Shape and Topology Optimization in Stokes Flow; 1 Introduction; 2 Porous MediumPhase Field Formulation; 3 Sharp Interface Problem; 4 Sharp Interface Limit; References; An Overview on the Cheeger Problem; 1 Introduction; 2 Some Motivations; 2.1 Estimating the Smallest Eigenvalue of the Laplacian; 2.2 Existence of Graphs with Prescribed Mean Curvature; 2.3 Stable Shapes for Total Variation Minimization; 3 Some General Results on the Cheeger Problem; 3.1 The Cheeger Problem in Convex Domains; 3.2 Some Further Results About Cheeger Sets in mathbbR2
 Carrier category
 online resource
 Carrier category code

 cr
 Carrier MARC source
 rdacarrier
 Color
 multicolored
 Content category
 text
 Content type code

 txt
 Content type MARC source
 rdacontent
 Contents

 Introduction; On the Minimization of Area Among ChordConvex Sets; 1 Introduction and Setting of the Problem; 2 Definitions and Results; 2.1 Uniqueness of the Bisecting Chord of Given Direction; 2.2 Properties of the Extreme Points and of the Intersections Between Chords; 2.3 Zindler Sets and Their Properties; References; Optimization Problems Involving the First Dirichlet Eigenvalue and the Torsional Rigidity; 1 Introduction; 2 Statement of the Problem; 3 A Sharp Inequality Between Torsion and First Eigenvalue; 4 The Attainable Set; 5 Torsional Rigidity and the Heat Equation
 4.2 Parametrize Functions by Geometries5 Metric Structures via Characteristic Functions of Measurable Sets; 5.1 LinftyConvergence of Measurable Sets; 5.2 LpConvergence of Measurable Sets, 1lep<infty; 5.3 Compact Families; 6 Metric Structures via Distance Functions; 6.1 Pompéiu's Ecart Mutuel and Hausdorff Metric on Compact Sets; 6.2 Metric of Uniform Convergence; 6.3 Metric of Lipschitz Convergence; 6.4 Metric of W1,pConvergence, 1lep<infty; 6.5 Metrics Compatible with the Abelian Group Structure; 7 Metric Structures via Oriented Distance Functions
 7.1 Oriented Distance Function: Definition and Some Properties7.2 Some General Metrics on Cb(D); 7.3 Metrics Compatible with the Abelian Group Structure; 8 Boundary Properties of Sets in Cb0(D); 8.1 Finite Perimeter or Caccioppoli Sets; 8.2 Preliminary Considerations; 8.3 Sets of Bounded Curvature; 8.4 Metrics for Families of Sets with Smooth Boundaries; 9 Sets of Positive Reach, Submanifolds, Squared Distance Functions; 9.1 Sets of Positive Reach; 9.2 CkSubmanifolds, kge2; 9.3 Metric on Families of Submanifolds; 10 Metric Structure via the Support Function; 11 Some Concluding Remarks
 Control code
 SPR931873412
 Dimensions
 unknown
 Extent
 1 online resource.
 File format
 unknown
 Form of item
 online
 Isbn
 9783319175621
 Level of compression
 unknown
 Media category
 computer
 Media MARC source
 rdamedia
 Media type code

 c
 Quality assurance targets
 not applicable
 Reformatting quality
 unknown
 Reproduction note
 Electronic resource.
 Sound
 unknown sound
 Specific material designation
 remote
 Label
 New trends in shape optimization, Also Pratelli, Günter Leugering, (electronic book)
 Antecedent source
 unknown
 Bibliography note

 ReferencesOn a Classical Spectral Optimization Problem in Linear Elasticity; 1 Introduction; 2 The Eigenvalue Problems; 3 Analyticity Results ; 4 Isovolumetric Perturbations; References; Metric Spaces of Shapes and Geometries Constructed from Set Parametrized Functions; 1 Introduction; 2 Group, Symmetric Difference, and Characteristic Functions; 2.1 Group Structure Induced by the Symmetric Difference; 2.2 Metric Structures via Characteristic Functions; 3 Parametrize Geometries by Functions: Hypographs; 4 Analytical Representations of Geometries; 4.1 Parametrize Geometries by Functions
 ReferencesA Phase Field Approach for Shape and Topology Optimization in Stokes Flow; 1 Introduction; 2 Porous MediumPhase Field Formulation; 3 Sharp Interface Problem; 4 Sharp Interface Limit; References; An Overview on the Cheeger Problem; 1 Introduction; 2 Some Motivations; 2.1 Estimating the Smallest Eigenvalue of the Laplacian; 2.2 Existence of Graphs with Prescribed Mean Curvature; 2.3 Stable Shapes for Total Variation Minimization; 3 Some General Results on the Cheeger Problem; 3.1 The Cheeger Problem in Convex Domains; 3.2 Some Further Results About Cheeger Sets in mathbbR2
 Carrier category
 online resource
 Carrier category code

 cr
 Carrier MARC source
 rdacarrier
 Color
 multicolored
 Content category
 text
 Content type code

 txt
 Content type MARC source
 rdacontent
 Contents

 Introduction; On the Minimization of Area Among ChordConvex Sets; 1 Introduction and Setting of the Problem; 2 Definitions and Results; 2.1 Uniqueness of the Bisecting Chord of Given Direction; 2.2 Properties of the Extreme Points and of the Intersections Between Chords; 2.3 Zindler Sets and Their Properties; References; Optimization Problems Involving the First Dirichlet Eigenvalue and the Torsional Rigidity; 1 Introduction; 2 Statement of the Problem; 3 A Sharp Inequality Between Torsion and First Eigenvalue; 4 The Attainable Set; 5 Torsional Rigidity and the Heat Equation
 4.2 Parametrize Functions by Geometries5 Metric Structures via Characteristic Functions of Measurable Sets; 5.1 LinftyConvergence of Measurable Sets; 5.2 LpConvergence of Measurable Sets, 1lep<infty; 5.3 Compact Families; 6 Metric Structures via Distance Functions; 6.1 Pompéiu's Ecart Mutuel and Hausdorff Metric on Compact Sets; 6.2 Metric of Uniform Convergence; 6.3 Metric of Lipschitz Convergence; 6.4 Metric of W1,pConvergence, 1lep<infty; 6.5 Metrics Compatible with the Abelian Group Structure; 7 Metric Structures via Oriented Distance Functions
 7.1 Oriented Distance Function: Definition and Some Properties7.2 Some General Metrics on Cb(D); 7.3 Metrics Compatible with the Abelian Group Structure; 8 Boundary Properties of Sets in Cb0(D); 8.1 Finite Perimeter or Caccioppoli Sets; 8.2 Preliminary Considerations; 8.3 Sets of Bounded Curvature; 8.4 Metrics for Families of Sets with Smooth Boundaries; 9 Sets of Positive Reach, Submanifolds, Squared Distance Functions; 9.1 Sets of Positive Reach; 9.2 CkSubmanifolds, kge2; 9.3 Metric on Families of Submanifolds; 10 Metric Structure via the Support Function; 11 Some Concluding Remarks
 Control code
 SPR931873412
 Dimensions
 unknown
 Extent
 1 online resource.
 File format
 unknown
 Form of item
 online
 Isbn
 9783319175621
 Level of compression
 unknown
 Media category
 computer
 Media MARC source
 rdamedia
 Media type code

 c
 Quality assurance targets
 not applicable
 Reformatting quality
 unknown
 Reproduction note
 Electronic resource.
 Sound
 unknown sound
 Specific material designation
 remote
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