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 Chord-Convex 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 Linfty-Convergence of Measurable Sets; 5.2 Lp-Convergence 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,p-Convergence, 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 Ck-Submanifolds, 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 Medium---Phase 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 Chord-Convex 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 Linfty-Convergence of Measurable Sets; 5.2 Lp-Convergence 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,p-Convergence, 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 Ck-Submanifolds, 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 Medium---Phase 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 Chord-Convex 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 Linfty-Convergence of Measurable Sets; 5.2 Lp-Convergence 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,p-Convergence, 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 Ck-Submanifolds, 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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<div class="citation" vocab="http://schema.org/"><i class="fa fa-external-link-square fa-fw"></i> Data from <span resource="http://link.liverpool.ac.uk/portal/New-trends-in-shape-optimization-Also-Pratelli/kpKaWd5UPvs/" typeof="Book http://bibfra.me/vocab/lite/Item"><span property="name http://bibfra.me/vocab/lite/label"><a href="http://link.liverpool.ac.uk/portal/New-trends-in-shape-optimization-Also-Pratelli/kpKaWd5UPvs/">New trends in shape optimization, Also Pratelli, Günter Leugering, (electronic book)</a></span> - <span property="potentialAction" typeOf="OrganizeAction"><span property="agent" typeof="LibrarySystem http://library.link/vocab/LibrarySystem" resource="http://link.liverpool.ac.uk/"><span property="name http://bibfra.me/vocab/lite/label"><a property="url" href="http://link.liverpool.ac.uk/">Sydney Jones Library, University of Liverpool</a></span></span></span></span></div>
