This book introduces readers to theories that play a crucial role in modern mathematics, such as integration and functional analysis, employing a unifying approach that views these two subjects as being deeply intertwined. This feature is particularly evident in the broad range of problems examined, the solutions of which are often supported by generous hints. If the material is split into two …
This book is an introduction to the theory of Hilbert space, a fundamental tool for non-relativistic quantum mechanics. Linear, topological, metric, and normed spaces are all addressed in detail, in a rigorous but reader-friendly fashion. The rationale for an introduction to the theory of Hilbert space, rather than a detailed study of Hilbert space theory itself, resides in the very high mathem…
This book offers a step-by-step guide to intervention research, including the methods and techniques that researchers, higher degree research students and others can use when pursuing intervention research in schools and other settings. Guided by the Intervention Research Framework, it also provides practical information on linking a program developed using a comprehensive, evidence-based appro…
This monograph provides both an introduction to and a thorough exposition of the theory of rate-independent systems, which the authors have been working on with a lot of collaborators over 15 years. The focus is mostly on fully rate-independent systems, first on an abstract level either with or even without a linear structure, discussing various concepts of solutions with full mathematical rigo…
This book examines in detail the correlation, more precisely the weighted correlation and applications involving rankings. A general application is the evaluation of methods to predict rankings. Others involve rankings representing human preferences to infer user preferences; the use of weighted correlation with microarray data and those in the domain of time series. In this book we present new…
This graduate-level textbook is primarily aimed at graduate students of statistics, mathematics, science, and engineering who have had an undergraduate course in statistics, an upper division course in analysis, and some acquaintance with measure theoretic probability. It provides a rigorous presentation of the core of mathematical statistics. Part I of this book constitutes a one-semester c…
This book presents multivariate time series methods for the analysis and optimal control of feedback systems. Although ships’ autopilot systems are considered through the entire book, the methods set forth in this book can be applied to many other complicated, large, or noisy feedback control systems for which it is difficult to derive a model of the entire system based on theory in that subj…
This book is devoted to current advances in the field of nonlinear mathematical physics and modeling of critical phenomena that can lead to catastrophic events. Pursuing a multidisciplinary approach, it gathers the work of scientists who are developing mathematical and computational methods for the study and analysis of nonlinear phenomena and who are working actively to apply these tools and c…
This book explains modern and interesting physics in heavy-fermion (HF) compounds to graduate students and researchers in condensed matter physics. It presents a theory of heavy-fermion (HF) compounds such as HF metals, quantum spin liquids, quasicrystals and two-dimensional Fermi systems. The basic low-temperature properties and the scaling behavior of the compounds are described within the fr…
This book presents the theory of gas discharge plasmas in a didactical way. It explains the processes in gas discharge plasmas. A gas discharge plasma is an ionized gas which is supported by an external electric field. Therefore its parameters are determined by processes in it. The properties of a gas discharge plasma depend on its gas component, types of external fields, their geometry and reg…