| Description |
1 online resource (x, 417 pages) : illustrations |
| Series |
Mathematics research developments series |
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Mathematics research developments series.
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| Contents |
""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"" |
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""(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)."" |
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""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."" |
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""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"" |
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""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"" |
| Bibliography |
Includes bibliographical references and index |
| Notes |
Print version record |
| Subject |
Geometry, Differential.
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Graph theory.
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MATHEMATICS -- Geometry -- Differential.
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Geometry, Differential
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Graph theory
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| Form |
Electronic book
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| Author |
Bernard, Lucas, 1962-
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Roux, François, 1960-
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| LC no. |
2009016576 |
| ISBN |
1611220696 |
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9781611220698 |
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