Emerging topics on differential geometry and graph theory:
Gespeichert in:
| Format: | Elektronisch E-Book |
|---|---|
| Sprache: | English |
| Veröffentlicht: |
New York
Nova Science Publishers
©2010
|
| Schriftenreihe: | Mathematics research developments series
|
| Schlagworte: | |
| Online-Zugang: | FAW01 FAW02 |
| Beschreibung: | Includes bibliographical references and index ""EMERGING TOPICS ON DIFFERENTIALGEOMETRY AND GRAPH THEORY""; ""CONTENTS""; ""PREFACE""; ""APPLICATIONS OF GRAPH THEORY IN MECHANISMANALYSIS""; ""Abstract""; ""1. Introduction""; ""2 Graph Representation of Mechanisms""; ""2.1. Topological Graph Representation of Kcs with Simple Joints""; ""2.2. Bicolored Graph Representation of Kcs with Multiple Joints""; ""2.3. Tricolored Graph Representation of Glms""; ""2.4. Combinatorial Graph Representation of Glkcs""; ""3. Detection of Isomorphism Among Kcs and Glkcs""; ""3.1. Detection of Isomorphism Among Kcs"" ""(1) Theory to Detect Isomorphism among Kcs""""(2) Method to Detect Isomorphism among Kcs""; ""(3) Illustrations""; ""Example 1. Determination of Isomorphism of Kcs.""; ""Example 2: Determination of Isomorphism of Graphs""; ""3.2. Detection of Isomorphism among Glkcs""; ""(1) Theory to Detect Isomorphism Among Glkcs""; ""(2) Method to Detect Isomorphism Among Kcs""; ""(3) Illustrations""; ""Example 1: Determination of Isomorphism of the Glkcs, as Shown in Fig. 10(A) and (B)""; ""Example 2: Determination of isomorphism of the GLKCs, as shown in Fig. 11(a) and (b)."" ""4. Topology-Loop Characteristics of Kcs""""4.1. The Number of Topological Loops of Bicolored Graph""; ""4.2. The Number of Topological Loops of Tricolored Graph""; ""5. Structural Decomposition of Mechanisms""; ""5.1. Principle of Structural Decomposition""; ""5.2. Calculation of Transformation Number""; ""5.3. Types of Kinematic Units""; ""5.4. Criteria of Choosing the Sequential Circuits""; ""5.5. Examples of Structural Decomposition""; ""Example 1: Fig. 15(A) Shows A PLM with one DOF, and Fig. 15(B) the Weighted Graphand Fig. 15(C) the Decomposing Procedure."" ""Example 2: Fig. 16(A) Shows a Hydraulic Mechanism with one DOF, and Fig. 16(B) theWeighted Bicolored Graph and Fig. 16(C) the Decomposing Procedure.""""Example 3: Fig. 17(A) Shows a GLM with one DOF, and Fig. 17(B) the WeightedTricolored Graph and Fig. 17(C) the Decomposing Procedure.""; ""Example 4: Fig. 18 Shows a Complex GLM, its Tricolored Graph, and the DecomposingProcedure.""; ""6. Conclusion""; ""References""; ""A CATEGORICAL PERSPECTIVE ON CONNECTIONSWITH APPLICATION IN THE FORMULATION OFFUNCTORIAL PHYSICAL DYNAMICS""; ""Abstract""; ""1. Introduction"" ""2. The Extension/Restriction of Scalars Categorical Adjunction""""2.1. The Adjoint Pair of Extension/Restriction Functors""; ""2.2. The Universal Object of Differential 1-Forms""; ""2.3. The Notion of Connection""; ""2.4. The Algebraic De Rham Complex and the Notion of Curvature""; ""3. The Abstract Equivalent Monadic Notion of Connection""; ""3.1. The Extension/Restriction of Scalars Monad-Comonad Pair""; ""3.2. Categorical Monadic Reformulation of Connections""; ""4. General Theory of Relativity from the ClassicalExtension/Restriction Monad-Comonad Pair"" |
| Beschreibung: | x, 417 pages |
| ISBN: | 1611220696 9781611220698 9781607410119 1607410117 |
Internformat
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| 245 | 1 | 0 | |a Emerging topics on differential geometry and graph theory |c Lucas Bernard and François Roux, editors |
| 264 | 1 | |a New York |b Nova Science Publishers |c ©2010 | |
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| 500 | |a ""EMERGING TOPICS ON DIFFERENTIALGEOMETRY AND GRAPH THEORY""; ""CONTENTS""; ""PREFACE""; ""APPLICATIONS OF GRAPH THEORY IN MECHANISMANALYSIS""; ""Abstract""; ""1. Introduction""; ""2 Graph Representation of Mechanisms""; ""2.1. Topological Graph Representation of Kcs with Simple Joints""; ""2.2. Bicolored Graph Representation of Kcs with Multiple Joints""; ""2.3. Tricolored Graph Representation of Glms""; ""2.4. Combinatorial Graph Representation of Glkcs""; ""3. Detection of Isomorphism Among Kcs and Glkcs""; ""3.1. Detection of Isomorphism Among Kcs"" | ||
| 500 | |a ""(1) Theory to Detect Isomorphism among Kcs""""(2) Method to Detect Isomorphism among Kcs""; ""(3) Illustrations""; ""Example 1. Determination of Isomorphism of Kcs.""; ""Example 2: Determination of Isomorphism of Graphs""; ""3.2. Detection of Isomorphism among Glkcs""; ""(1) Theory to Detect Isomorphism Among Glkcs""; ""(2) Method to Detect Isomorphism Among Kcs""; ""(3) Illustrations""; ""Example 1: Determination of Isomorphism of the Glkcs, as Shown in Fig. 10(A) and (B)""; ""Example 2: Determination of isomorphism of the GLKCs, as shown in Fig. 11(a) and (b)."" | ||
| 500 | |a ""4. Topology-Loop Characteristics of Kcs""""4.1. The Number of Topological Loops of Bicolored Graph""; ""4.2. The Number of Topological Loops of Tricolored Graph""; ""5. Structural Decomposition of Mechanisms""; ""5.1. Principle of Structural Decomposition""; ""5.2. Calculation of Transformation Number""; ""5.3. Types of Kinematic Units""; ""5.4. Criteria of Choosing the Sequential Circuits""; ""5.5. Examples of Structural Decomposition""; ""Example 1: Fig. 15(A) Shows A PLM with one DOF, and Fig. 15(B) the Weighted Graphand Fig. 15(C) the Decomposing Procedure."" | ||
| 500 | |a ""Example 2: Fig. 16(A) Shows a Hydraulic Mechanism with one DOF, and Fig. 16(B) theWeighted Bicolored Graph and Fig. 16(C) the Decomposing Procedure.""""Example 3: Fig. 17(A) Shows a GLM with one DOF, and Fig. 17(B) the WeightedTricolored Graph and Fig. 17(C) the Decomposing Procedure.""; ""Example 4: Fig. 18 Shows a Complex GLM, its Tricolored Graph, and the DecomposingProcedure.""; ""6. Conclusion""; ""References""; ""A CATEGORICAL PERSPECTIVE ON CONNECTIONSWITH APPLICATION IN THE FORMULATION OFFUNCTORIAL PHYSICAL DYNAMICS""; ""Abstract""; ""1. Introduction"" | ||
| 500 | |a ""2. The Extension/Restriction of Scalars Categorical Adjunction""""2.1. The Adjoint Pair of Extension/Restriction Functors""; ""2.2. The Universal Object of Differential 1-Forms""; ""2.3. The Notion of Connection""; ""2.4. The Algebraic De Rham Complex and the Notion of Curvature""; ""3. The Abstract Equivalent Monadic Notion of Connection""; ""3.1. The Extension/Restriction of Scalars Monad-Comonad Pair""; ""3.2. Categorical Monadic Reformulation of Connections""; ""4. General Theory of Relativity from the ClassicalExtension/Restriction Monad-Comonad Pair"" | ||
| 650 | 4 | |a Geometry, Differential | |
| 650 | 4 | |a Graph theory | |
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| 650 | 4 | |a Geometry, Differential | |
| 650 | 4 | |a Graph theory | |
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| 650 | 0 | 7 | |a Graphentheorie |0 (DE-588)4113782-6 |2 gnd |9 rswk-swf |
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Datensatz im Suchindex
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| any_adam_object | |
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| dewey-full | 516.3/6 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 516 - Geometry |
| dewey-raw | 516.3/6 |
| dewey-search | 516.3/6 |
| dewey-sort | 3516.3 16 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Electronic eBook |
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| record_format | marc |
| series2 | Mathematics research developments series |
| spelling | Emerging topics on differential geometry and graph theory Lucas Bernard and François Roux, editors New York Nova Science Publishers ©2010 x, 417 pages txt rdacontent c rdamedia cr rdacarrier Mathematics research developments series Includes bibliographical references and index ""EMERGING TOPICS ON DIFFERENTIALGEOMETRY AND GRAPH THEORY""; ""CONTENTS""; ""PREFACE""; ""APPLICATIONS OF GRAPH THEORY IN MECHANISMANALYSIS""; ""Abstract""; ""1. Introduction""; ""2 Graph Representation of Mechanisms""; ""2.1. Topological Graph Representation of Kcs with Simple Joints""; ""2.2. Bicolored Graph Representation of Kcs with Multiple Joints""; ""2.3. Tricolored Graph Representation of Glms""; ""2.4. Combinatorial Graph Representation of Glkcs""; ""3. Detection of Isomorphism Among Kcs and Glkcs""; ""3.1. Detection of Isomorphism Among Kcs"" ""(1) Theory to Detect Isomorphism among Kcs""""(2) Method to Detect Isomorphism among Kcs""; ""(3) Illustrations""; ""Example 1. Determination of Isomorphism of Kcs.""; ""Example 2: Determination of Isomorphism of Graphs""; ""3.2. Detection of Isomorphism among Glkcs""; ""(1) Theory to Detect Isomorphism Among Glkcs""; ""(2) Method to Detect Isomorphism Among Kcs""; ""(3) Illustrations""; ""Example 1: Determination of Isomorphism of the Glkcs, as Shown in Fig. 10(A) and (B)""; ""Example 2: Determination of isomorphism of the GLKCs, as shown in Fig. 11(a) and (b)."" ""4. Topology-Loop Characteristics of Kcs""""4.1. The Number of Topological Loops of Bicolored Graph""; ""4.2. The Number of Topological Loops of Tricolored Graph""; ""5. Structural Decomposition of Mechanisms""; ""5.1. Principle of Structural Decomposition""; ""5.2. Calculation of Transformation Number""; ""5.3. Types of Kinematic Units""; ""5.4. Criteria of Choosing the Sequential Circuits""; ""5.5. Examples of Structural Decomposition""; ""Example 1: Fig. 15(A) Shows A PLM with one DOF, and Fig. 15(B) the Weighted Graphand Fig. 15(C) the Decomposing Procedure."" ""Example 2: Fig. 16(A) Shows a Hydraulic Mechanism with one DOF, and Fig. 16(B) theWeighted Bicolored Graph and Fig. 16(C) the Decomposing Procedure.""""Example 3: Fig. 17(A) Shows a GLM with one DOF, and Fig. 17(B) the WeightedTricolored Graph and Fig. 17(C) the Decomposing Procedure.""; ""Example 4: Fig. 18 Shows a Complex GLM, its Tricolored Graph, and the DecomposingProcedure.""; ""6. Conclusion""; ""References""; ""A CATEGORICAL PERSPECTIVE ON CONNECTIONSWITH APPLICATION IN THE FORMULATION OFFUNCTORIAL PHYSICAL DYNAMICS""; ""Abstract""; ""1. Introduction"" ""2. The Extension/Restriction of Scalars Categorical Adjunction""""2.1. The Adjoint Pair of Extension/Restriction Functors""; ""2.2. The Universal Object of Differential 1-Forms""; ""2.3. The Notion of Connection""; ""2.4. The Algebraic De Rham Complex and the Notion of Curvature""; ""3. The Abstract Equivalent Monadic Notion of Connection""; ""3.1. The Extension/Restriction of Scalars Monad-Comonad Pair""; ""3.2. Categorical Monadic Reformulation of Connections""; ""4. General Theory of Relativity from the ClassicalExtension/Restriction Monad-Comonad Pair"" Geometry, Differential Graph theory MATHEMATICS / Geometry / Differential bisacsh Geometry, Differential fast Graph theory fast Differentialgeometrie (DE-588)4012248-7 gnd rswk-swf Graphentheorie (DE-588)4113782-6 gnd rswk-swf 1\p (DE-588)4143413-4 Aufsatzsammlung gnd-content Graphentheorie (DE-588)4113782-6 s 2\p DE-604 Differentialgeometrie (DE-588)4012248-7 s 3\p DE-604 Bernard, Lucas 1962- Sonstige oth Roux, François 1960- Sonstige oth 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 2\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 3\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Emerging topics on differential geometry and graph theory Geometry, Differential Graph theory MATHEMATICS / Geometry / Differential bisacsh Geometry, Differential fast Graph theory fast Differentialgeometrie (DE-588)4012248-7 gnd Graphentheorie (DE-588)4113782-6 gnd |
| subject_GND | (DE-588)4012248-7 (DE-588)4113782-6 (DE-588)4143413-4 |
| title | Emerging topics on differential geometry and graph theory |
| title_auth | Emerging topics on differential geometry and graph theory |
| title_exact_search | Emerging topics on differential geometry and graph theory |
| title_full | Emerging topics on differential geometry and graph theory Lucas Bernard and François Roux, editors |
| title_fullStr | Emerging topics on differential geometry and graph theory Lucas Bernard and François Roux, editors |
| title_full_unstemmed | Emerging topics on differential geometry and graph theory Lucas Bernard and François Roux, editors |
| title_short | Emerging topics on differential geometry and graph theory |
| title_sort | emerging topics on differential geometry and graph theory |
| topic | Geometry, Differential Graph theory MATHEMATICS / Geometry / Differential bisacsh Geometry, Differential fast Graph theory fast Differentialgeometrie (DE-588)4012248-7 gnd Graphentheorie (DE-588)4113782-6 gnd |
| topic_facet | Geometry, Differential Graph theory MATHEMATICS / Geometry / Differential Differentialgeometrie Graphentheorie Aufsatzsammlung |
| work_keys_str_mv | AT bernardlucas emergingtopicsondifferentialgeometryandgraphtheory AT rouxfrancois emergingtopicsondifferentialgeometryandgraphtheory |