دانلود کتاب Complex Variable Methods in Plane Elasticity

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This monograph is a synthesis of the theory of the pairwise coupling of the angular momenta of arbitrarily many independent systems to the total angular momentum in which the universal role of doubly stochastic matrices and their quantum-mechanical probabilistic interpretation is a major theme. A uniform viewpoint is presented based on the structure of binary trees. This includes a systematic method for the evaluation of all 3n-j coefficients and their relationship to cubic graphs. A number of topical subjects that emerge naturally are also developed, such as the algebra of permutation matrices, the properties of magic squares and an associated generalized Regge form, the Zeilberger counting formula for alternating sign matrices, and the Heisenberg ring problem, viewed as a composite system in which the total angular momentum is conserved. The readership is intended to be advanced graduate students and researchers interested in learning about the relationship between unitary symmetry and combinatorics and challenging unsolved problems. The many examples serve partially as exercises, but this monograph is not a textbook. It is hoped that the topics presented promote further and more rigorous developments that lead to a deeper understanding of the angular momentum properties of complex systems viewed as composite wholes 1. Basic Concepts and Formulas -- 2. Stress Functions -- 3. The Stresses and Displacements under Transformation of Coordinate System -- 4. Complex Expressions for Certain Mechanical Quantities -- 5. Boundary Conditions of Fundamental Problems: The Case of Bounded and Simply Connected Regions -- 6. The Case of Bounded and Multi-connected Regions -- 7. The Case of Unbounded Regions -- 8. Modified Second Fundamental Problems under General Relative Displacements -- 9. First Fundamental Problems for Bounded and Simply Connected Regions -- 10. First Fundamental Problems for the Infinite Plane with a Hole -- 11. First Fundamental Problems for Multi-connected Regions -- 12. The General Method of Solution for Second Fundamental Problems -- 13. The Method of Solution for Modified Second Fundamental Problems -- 14. The Case of Circular Region -- 15. The Case of Infinite Plane with a Circular Hole -- 16. The Case of Circular Ring Region -- 17. Applications of Conformal Mapping