This book introduces the fundamental concepts, methods, and applications of Hausdorff calculus, with a focus on its applications in fractal systems. Topics such as the Hausdorff diffusion equation, Hausdorff radial basis function, Hausdorff derivative nonlinear systems, PDE modeling, statistics on fractals, etc. are discussed in detail. It is an essential reference for researchers in mathematics, physics, geomechanics, and mechanics.

Fills a gap in the field of second language teaching, especially in the Chinese as a second language teaching field. includes both research and pedagogical aspects that would attract both practitioners and researchers exploring pedagogical approaches to teaching Chinese listening based on a comparative view of Chinese listening and that of other languages.

Fills a gap in the field of second language teaching, especially in the Chinese as a second language teaching field. includes both research and pedagogical aspects that would attract both practitioners and researchers exploring pedagogical approaches to teaching Chinese listening based on a comparative view of Chinese listening and that of other languages.

This text is aimed at professionals and students working on random processes in various areas, including physics and finance. The first author, Melvin Lax (1922-2002), was a distinguished Professor of Physics at City College of New York and a member of the U. S. National Academy of Sciences, widely known for his contribution on random processes in physics. Most chapters of this book are the outcome of the class notes which Lax taught at the City University of New York from 1985 to 2001. The material is unique as it presents the theoretical framework of Lax's treatment of random processes, starting from basic probability theory, to Fokker-Planck and Langevin Processes, and includes diverse applications, such as explanation of very narrow laser width and analytical solution of the elastic Boltzmann transport equation. Lax's critical viewpoint on mathematics currently used in the financial world is also presented in this book.

This book presents a broad collection of models and computational methods - from atomistic to continuum - applied to crystal dislocations. Its purpose is to help students and researchers in computational materials sciences to acquire practical knowledge of relevant simulation methods. Because their behavior spans multiple length and time scales, crystal dislocations present a common ground for an in-depth discussion of a variety of computational approaches, including their relative strengths, weaknesses and inter-connections. The details of the covered methods are presented in the form of 'numerical recipes' and illustrated by case studies. A suite of simulation codes and data files is made available on the book's website to help the reader 'to learn-by-doing' through solving the exercise problems offered in the book.

A unique and comprehensive graduate text and reference on numerical methods for electromagnetic phenomena, from atomistic to continuum scales, in biology, optical-to-micro waves, photonics, nanoelectronics and plasmas. The state-of-the-art numerical methods described include: * Statistical fluctuation formulae for the dielectric constant * Particle-Mesh-Ewald, Fast-Multipole-Method and image-based reaction field method for long-range interactions * High-order singular/hypersingular (Nystrom collocation/Galerkin) boundary and volume integral methods in layered media for Poisson-Boltzmann electrostatics, electromagnetic wave scattering and electron density waves in quantum dots * Absorbing and UPML boundary conditions * High-order hierarchical Nedelec edge elements * High-order discontinuous Galerkin (DG) and Yee finite difference time-domain methods * Finite element and plane wave frequency-domain methods for periodic structures * Generalized DG beam propagation method for optical waveguides * NEGF(Non-equilibrium Green's function) and Wigner kinetic methods for quantum transport * High-order WENO and Godunov and central schemes for hydrodynamic transport * Vlasov-Fokker-Planck and PIC and constrained MHD transport in plasmas"

This textbook provides students with a complete working knowledge of the properties of imperfections in crystalline solids. Readers will learn how to apply the fundamental principles of mechanics and thermodynamics to defect properties in materials science, gaining all the knowledge and tools needed to put this into practice in their own research. Beginning with an introduction to defects and a brief review of basic elasticity theory and statistical thermodynamics, the authors go on to guide the reader in a step-by-step way through point, line, and planar defects, with an emphasis on their structural, thermodynamic, and kinetic properties. Numerous end-of-chapter exercises enable students to put their knowledge into practice, and with solutions for instructors and MATLAB (R) programs available online, this is an essential text for advanced undergraduate and introductory graduate courses in crystal defects, as well as being ideal for self-study.

This book presents a broad collection of models and computational methods - from atomistic to continuum - applied to crystal dislocations. Its purpose is to help students and researchers in computational materials sciences to acquire practical knowledge of relevant simulation methods. Because their behavior spans multiple length and time scales, crystal dislocations present a common ground for an in-depth discussion of a variety of computational approaches, including their relative strengths, weaknesses and inter-connections. The details of the covered methods are presented in the form of "numerical recipes" and illustrated by case studies. A suite of simulation codes and data files is made available on the book's website to help the reader "to learn-by-doing" through solving the exercise problems offered in the book.

This respected high-level text is aimed at students and professionals working on random processes in various areas, including physics and finance. The first author, Melvin Lax (1922-2002) was a distinguished Professor of Physics at City College of New York and a member of the U. S. National Academy of Sciences, and is widely known for his contributions to our understanding of random processes in physics. Most chapters of this book are outcomes of the class notes which Lax taught at the City University of New York from 1985 to 2001. The material is unique as it presents the theoretical framework of Lax's treatment of random processes, from basic probability theory to Fokker-Planck and Langevin Processes, and includes diverse applications, such as explanations of very narrow laser width, analytical solutions of the elastic Boltzmann transport equation, and a critical viewpoint of mathematics currently used in the world of finance.

A compilation of articles and photos by Ng Wai Choy, a Singaporean journalist who was living in Beijing shared his life experience in Beijing.