Konrad Schöbel aims to lay the foundations for a consequent algebraic geometric treatment of variable Separation, which is one of the oldest and most powerful methods to construct exact solutions for the fundamental equations in classical and quantum physics. The present work reveals a surprising algebraic geometric structure behind the famous list of separation coordinates, bringing together …
This book makes good background reading for much of modern magnetospheric physics. Its origin was a Festspiel for Professor Jim Dungey, former professor in the Physics Department at Imperial College on the occasion of his 90th birthday, 30 January 2013. Remarkably, although he retired 30 years ago, his pioneering and, often, maverick work in the 50’s through to the 70’s on solar terrestrial…
Now in its second edition, this monograph explores the Monge-Ampère equation and the latest advances in its study and applications. It provides an essentially self-contained systematic exposition of the theory of weak solutions, including regularity results by L. A. Caffarelli. The geometric aspects of this theory are stressed using techniques from harmonic analysis, such as covering lemmas …
All kinds of singular interactions described by potentials supported on small sets (like the Dirac δ-potentials, fractals, singular measures, high degree super-singular expressions) admit a rigorous treatment only in terms of the equipped spaces and their scales. The main idea of the method is to use singular perturbations to change inner products in the starting rigged space, and the construc…
In addition, whenever possible these essays take the opportunity to link foundational issues to the many exciting developments that are often linked to major experimental and technological breakthroughs in exploiting the electromagnetic field and in particular, its quantum properties and its interactions with matter, as well as to advances in solid state physics (such as new quantum Hall liquid…
This book provides a complete overview of the role of machine learning in radiation oncology and medical physics, covering basic theory, methods, and a variety of applications in medical physics and radiotherapy. An introductory section explains machine learning, reviews supervised and unsupervised learning methods, discusses performance evaluation, and summarizes potential applications in radi…
This book treats ensembles of Young diagrams originating from group-theoretical contexts and investigates what statistical properties are observed there in a large-scale limit. The focus is mainly on analyzing the interesting phenomenon that specific curves appear in the appropriate scaling limit for the profiles of Young diagrams. This problem is regarded as an important origin of recent vital…
This is the story of radio astronomy, of how radio waves are generated by stars, supernova, quasars, colliding galaxies and by the very beginnings of the universe itself. The author discusses what radio astronomers are doing in the New Mexico desert, in a remote valley in Puerto Rico, and in the green Pocahontas Valley in West Virginia, as well as dozens of other remote sites around the world. …
Marco Schröter investigates the influence of the local environment on the exciton dynamics within molecular aggregates, which build, e.g., the light-harvesting complexes of plants, bacteria or algae by means of the hierarchy equations of motion (HEOM) method. He addresses the following questions in detail: How can coherent oscillations within a system of coupled molecules be interpreted? What…
This book provides a complete overview of the role of machine learning in radiation oncology and medical physics, covering basic theory, methods, and a variety of applications in medical physics and radiotherapy. An introductory section explains machine learning, reviews supervised and unsupervised learning methods, discusses performance evaluation, and summarizes potential applications in r…