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Fractal geometry and dynamical systems in pure and applied mathematics II : fractals in applied mathematics /
| Clasificación: | Libro Electrónico |
|---|---|
| Autor Corporativo: | |
| Otros Autores: | |
| Formato: | Electrónico Congresos, conferencias eBook |
| Idioma: | Inglés |
| Publicado: |
Providence, Rhode Island :
American Mathematical Society,
2013.
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| Colección: | Contemporary mathematics (American Mathematical Society) ;
Volume 601. |
| Temas: | |
| Acceso en línea: | Texto completo |
Tabla de Contenidos:
- Preface; Statistical Mechanics and Quantum Fields on Fractals; 1. Introduction; 2. Discrete scaling symmetry
- Self similarity
- Definitions; 3. Heat kernel and spectral functions
- Generalities; 4. Laplacian on fractals
- Heat kernel and spectral zeta function; 5. Thermodynamics on photons : The fractal blackbody [34]; 6. Conclusion and some open questions; Acknowledgments; References; Spectral Algebra of the Chernov and Bogoslovsky Finsler Metric Tensors; Preliminaries; 1. Spectral theory prerequisites; 2. Spectral results for low dimensions; 3. Conclusions; References.
- Local Multifractal Analysis1. Introduction; 2. Properties of the local Hausdorff dimension and the local multifractal spectrum; 3. A local multifractal formalism for a dyadic family; 4. Measures with varying local spectrum; 5. Local spectrum of stochastic processes; 6. Other regularity exponents characterized by dyadic families; 7. A functional analysis point of view; Acknowledgement; References; Extreme Risk and Fractal Regularity in Finance; 1. Introduction; 2. Fractal Regularities in Financial Markets; 3. The Markov-Switching Multifractal (MSM); 4. Pricing Multifractal Risk; 5. Conclusion.
- 2. Functional equations for infinite graphsReferences; Vector Analysis on Fractals and Applications; 1. Introduction; 2. Dirichlet forms and energy measures; 3. 1-forms and vector fields; 4. Scalar PDE involving first order terms; 5. Navier-Stokes equations; 6. Magnetic Schrödinger equations; References; Non-Regularly Varying and Non-Periodic Oscillation of the On-Diagonal Heat Kernels on Self-Similar Fractals; 1. Introduction; 2. Framework and main results; 3. Proof of Theorems 2.17 and 2.18; 4. Post-critically finite self-similar fractals.
- 4.1. Harmonic structures and resulting self-similar Dirichlet spaces4.2. Cases with good symmetry and affine nested fractals; 4.3. Cases possibly without good symmetry; 5. Sierpiński carpets; References; Lattice Effects in the Scaling Limit of the Two-Dimensional Self-Avoiding Walk; 1. Introduction; 2. Lattice effects; 3. Simulations; 4. Conclusions and future work; References; The Casimir Effect on Laakso Spaces; 1. Introduction; 2. Laakso spaces; 3. Spectral Zeta Functions; 4. Casimir Effect; 5. Finite Approximations to Laakso Spaces; 6. Casimir Effect on L; 7. A Higher Dimensional Case.