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Exercises in Functional Analysis
This book of exercises in Functional Analysis contains almost 450 exercises (all with complete solutions), providing supplementary examples, counter-examples and applications for the basic notions usually presented in an introductory course in Functional Analysis. It contains three parts. The first one contains exercises on the general properties for sets in normed spaces, linear bounded operators on normed spaces, reflexivity, compactness in normed spaces, and on the basic principles in Functional Analysis: the Hahn-Banach theorem, the Uniform Boundedness Principle, the Open Mapping and the Closed Graph theorems. The second one contains exercises on the general theory of Hilbert spaces, the Riesz representation theorem, orthogonality in Hilbert spaces, the projection theorem and linear bounded operators on Hilbert spaces. The third one deals with linear topological spaces, and includes a large number of exercises on the weak topologies.
Strongly Irreducible Operators on Hilbert Space
This volume provides a comprehensive treatment of strongly irreducible operators acting on a complex separable infinite dimensional Hilbert space, and to expose and reflect the internal structure of operators by analyzing and studying irreducibility of operators. Much of the material presented here appears in book form for the first time.
Concurrency, Specification and Programming
This book presents novel approaches to the formal specification of concurrent and parallel systems, mathematical models for describing such systems, and programming and verification concepts for their implementation. A special emphasis is on methods based on artificial intelligence and machine learning techniques. Chapters are revised selected papers from the 29th International Workshop on Concurrency, Specification, and Programming (CS&P 2021), Berlin, Germany. Nine independent chapters cover formal approaches to topics such as requirements formalization, parsing, or granular computing, as well as their applications in recommender systems, decision making, security, optimization, and other areas. The book thus addresses both researchers and practitioners in its field.
Hymenoptera: Evolution, Biodiversity and Biological Control
The Hymenoptera is one of the largest orders of terrestrial arthropods and comprises the sawflies, wasps, ants, bees and parasitic wasps. Hymenoptera: Evolution, Biodiversity and Biological Control examines the current state of all major areas of research for this important group of insects, including systematics, biological control, behaviour, ecology, and physiological interactions between parasitoids and hosts. The material in this volume originates from papers presented at the Fourth International Hymenoptera Conference held in Canberra, Australia in early 1999. This material has been extensively rewritten, refereed and edited; culminating in this authoritative and comprehensive collection of review and research papers on the Hymenoptera. The authors include many world-leading researchers in their respective fields, and this synthesis of their work will be a valuable resource for researchers and students of Hymenoptera, molecular systematics and insect ecology.
