Fundamentals of Numerical Computation by
Julia is an open-source and fast-growing programming language for scientific computing that offers clarity and ease of use for beginners but also speed and power for advanced applications. Fundamentals of Numerical Computation: Julia Edition provides a complete solution for teaching Julia in the context of numerical methods. It introduces the mathematics and use of algorithms for the fundamental problems of numerical computation: linear algebra, finding roots, approximating data and functions, and solving differential equations. A clear progression from simple to more advanced methods allows for use in either a one-semester course or a two-semester sequence. The book includes more than 40 functions and 160 examples fully coded in Julia and available for download, online supplemental content including tested source materials for student projects and in-class labs related to every chapter, and over 600 exercises, evenly split between mathematical and computational work, and solutions to most exercises for instructors.
Korteweg-De Vries Flows with General Initial Conditions by
Large numbers of studies of the KdV equation have appeared since the pioneering paper by Gardner, Greene, Kruskal, and Miura in 1967. Most of those works have employed the inverse spectral method for 1D Schrödinger operators or an advanced Fourier analysis. Although algebraic approaches have been discovered by Hirota-Sato and Marchenko independently, those have not been fully investigated and analyzed. The present book offers a new approach to the study of the KdV equation, which treats decaying initial data and oscillating data in a unified manner. The author's method is to represent the tau functions introduced by Hirota-Sato and developed by Segal-Wilson later in terms of the Weyl-Titchmarsh functions (WT functions, in short) for the underlying Schrödinger operators. The main result is stated by a class of WT functions satisfying some of the asymptotic behavior along a curve approaching the spectrum of the Schrödinger operators at +∞ in an order of -(n-1/2)for the nth KdV equation. This class contains many oscillating potentials (initial data) as well as decaying ones. Especially bounded smooth ergodic potentials are included, and under certain conditions on the potentials, the associated Schrödinger operators have dense point spectrum. This provides a mathematical foundation for the study of the soliton turbulence problem initiated by Zakharov, which was the author's motivation for extending the class of initial data in this book. A large class of almost periodic potentials is also included in these ergodic potentials. P. Deift has conjectured that any solutions to the KdV equation starting from nearly periodic initial data are almost periodic in time. Therefore, our result yields a foundation for this conjecture. For the reader's benefit, the author has included here (1) a basic knowledge of direct and inverse spectral problem for 1D Schrödinger operators, including the notion of the WT functions; (2)Sato's Grassmann manifold method revised by Segal-Wilson; and (3) basic results of ergodic Schrödinger operators.
Rethinking Urban Green Spaces by
Proposing and demonstrating the ways in which we need to rethink urban green spaces as cities, societies and environments evolve, renowned scholar Cecil C. Konijnendijk explores urban green spaces as essential parts of cities. Chapters offer a comprehensive look at how their roles have changed over time and will continue to do so, moving from their conventional purpose as areas for recreation to become spaces contributing to climate adaptation, biodiversity conservation and economic development. This timely and innovative book argues that we need to rethink the ways in which we govern, design, plan and manage green spaces, as well as the funding of different kinds of green spaces and the narratives around what green spaces can and cannot do. Using a diverse range of case studies from across the globe, Konijnendijk offers practical suggestions for change in the future to make cities greener and healthier, and introduces new green space concepts such as urban groves and streetwoods. This is an invigorating read for students and scholars of urban planning, landscape architecture, urban ecology and urban studies. Urban green space planners, designers and managers will also find the wealth of cases and practical suggestions make this an insightful read.
Einstein Constraints and Ricci Flow by
This book contains a self-consistent treatment of a geometric averaging technique, induced by the Ricci flow, that allows comparing a given (generalized) Einstein initial data set with another distinct Einstein initial data set, both supported on a given closed n-dimensional manifold. This is a case study where two vibrant areas of research in geometric analysis, Ricci flow and Einstein constraints theory, interact in a quite remarkable way. The interaction is of great relevance for applications in relativistic cosmology, allowing a mathematically rigorous approach to the initial data set averaging problem, at least when data sets are given on a closed space-like hypersurface. The book does not assume an a priori knowledge of Ricci flow theory, and considerable space is left for introducing the necessary techniques. These introductory parts gently evolve to a detailed discussion of the more advanced results concerning a Fourier-mode expansion and a sophisticated heat kernel representation of the Ricci flow, both of which are of independent interest in Ricci flow theory. This work is intended for advanced students in mathematical physics and researchers alike.
India Rising by
The book looks at the life of one of India's foremost scientists, Dr R. Chidambaram, who served as principal scientific advisor (PSA) to the Government of India and as chairman of the Scientific Advisory Committee to the Cabinet (SAC-C) from November 2001 to March 2018. As one of India's most distinguished experimental physicists, Dr Chidambaram has made outstanding contributions to many aspects of basic science and nuclear technology.
