This text, now in its second edition, presents the mathematical background needed to design many optical combinations that are used in astronomical telescopes and cameras. It uses a novel approach to third-order aberration theory based on Fermat’s principle and the use of particular optical paths (called stigmatic paths) instead of rays, allowing for easier derivation of third-order formulae…
This volume tackles Gödel's two-stage project of first using Husserl's transcendental phenomenology to reconstruct and develop Leibniz' monadology, and then founding classical mathematics on the metaphysics thus obtained. The author analyses the historical and systematic aspects of that project, and then evaluates it, with an emphasis on the second stage. The book is organised around Gödel…
This monograph presents, in an attractive and self-contained form, techniques based on the L1 stability theory derived at the end of the 1990s by A. Bressan, T.-P. Liu and T. Yang that yield original error estimates for so-called well-balanced numerical schemes solving 1D hyperbolic systems of balance laws. Rigorous error estimates are presented for both scalar balance laws and a position-depen…
This biography sheds light on all facets of the life and the achievements of Ernst Zermelo (1871-1953). Zermelo is best-known for the statement of the axiom of choice and his axiomatization of set theory. However, he also worked in applied mathematics and mathematical physics. His dissertation, for example, promoted the calculus of variations, and he created the pivotal method in the theory of …
This text provides a framework in which the main objectives of the field of uncertainty quantification (UQ) are defined and an overview of the range of mathematical methods by which they can be achieved. Complete with exercises throughout, the book will equip readers with both theoretical understanding and practical experience of the key mathematical and algorithmic tools underlying the treatme…
The book presents pedagogical reviews of important topics on high energy physics to the students and researchers in particle physics. The book also discusses topics on the Quark–Gluon plasma, thermal field theory, perturbative quantum chromodynamics, anomalies and cosmology. Students of particle physics need to be well-equipped with basic understanding of many concepts underlying the standard…
Most interesting and difficult problems in equilibrium statistical mechanics concern models which exhibit phase transitions. For graduate students and more experienced researchers this book provides an invaluable reference source of approximate and exact solutions for a comprehensive range of such models. Part I contains background material on classical thermodynamics and statistical mechanics…
The present volume aims to be a comprehensive survey on the derivation of the equations of motion, both in General Relativity as well as in alternative gravity theories. The topics covered range from the description of test bodies, to self-gravitating (heavy) bodies, to current and future observations. Emphasis is put on the coverage of various approximation methods (e.g., multipolar, post-N…
The book reports on the latest theoretical and experimental advances in the field of active flow and combustion control. It covers new developments in actuator technology and sensing, in robust and optimal open- and closed-loop control, as well as in model reduction for control. It collects contributions presented during the third edition of the Active Flow and Combustion Control conference, he…
In this book, a modified improved LMS algorithm is employed for weight adaptation of dipole array for the generation of beam pattern in multiple signal environments. In phased arrays, the generation of adapted pattern according to the signal scenario requires an efficient adaptive algorithm. The antenna array is expected to maintain sufficient gain towards each of the desired source while at th…