Among the simplest combinatorial designs, triple systems have diverse applications in coding theory, cryptography, computer science, and statistics. This book provides a systematic and comprehensive treatment of this rich area of mathematics.

This book is a systematic account of the impressive developments in the theory of symmetric manifolds achieved over the past 50 years. It contains detailed and friendly, but rigorous, proofs of the key results in the theory. Milestones are the study of the group of holomomorphic automorphisms of bounded domains in a complex Banach space (Vigué and Upmeier in the late 1970s), Kaup's theorem on the equivalence of the categories of symmetric Banach manifolds and that of hermitian Jordan triple systems, and the culminating point in the process: the Riemann mapping theorem for complex Banach spaces (Kaup, 1982). This led to the introduction of wide classes of Banach spaces known as JB∗-triples and JBW∗-triples whose geometry has been thoroughly studied by several outstanding mathematicians in the late 1980s. The book presents a good example of fruitful interaction between different branches of mathematics, making it attractive for mathematicians interested in various fields such as algebra, differential geometry and, of course, complex and functional analysis.

Grids are special families of tripotents in Jordan triple systems. This research monograph presents a theory of grids including their classification and coordinization of their cover. Among the applications given are - classification of simple Jordan triple systems covered by a grid, reproving and extending most of the known classification theorems for Jordan algebras and Jordan pairs - a Jordan-theoretic interpretation of the geometry of the 27 lines on a cubic surface - structure theories for Hilbert-triples and JBW*-triples, the Jordan analogues of Hilbert-triples and W*-algebras which describe certain symmetric Banach manifolds. The notes are essentially self-contained and independent of the structure theory of Jordan algebras and Jordan pairs. They can be read by anyone with a basic knowledge in algebraic geometry or functional analysis. The book is intended to serve both as a reference for researchers in Jordan theory and as an introductory textbook for newcomers to the subject.

Grids are special families of tripotents in Jordan triple systems. This research monograph presents a theory of grids including their classification and coordinization of their cover. Among the applications given are - classification of simple Jordan triple systems covered by a grid, reproving and extending most of the known classification theorems for Jordan algebras and Jordan pairs - a Jordan-theoretic interpretation of the geometry of the 27 lines on a cubic surface - structure theories for Hilbert-triples and JBW*-triples, the Jordan analogues of Hilbert-triples and W*-algebras which describe certain symmetric Banach manifolds. The notes are essentially self-contained and independent of the structure theory of Jordan algebras and Jordan pairs. They can be read by anyone with a basic knowledge in algebraic geometry or functional analysis. The book is intended to serve both as a reference for researchers in Jordan theory and as an introductory textbook for newcomers to the subject.

Fuzzy systems and data mining are indispensible aspects of the digital technology on which we now all depend. Fuzzy logic is intrinsic to applications in the electrical, chemical and engineering industries, and also in the fields of management and environmental issues. Data mining is indispensible in dealing with big data, massive data, and scalable, parallel and distributed algorithms. This book presents the proceedings of FSDM 2023, the 9th International Conference on Fuzzy Systems and Data Mining, held from 10-13 November 2023 as a hybrid event, with some participants attending in Chongqing, China, and others online. The conference focuses on four main areas: fuzzy theory, algorithms and systems; fuzzy application; data mining; and the interdisciplinary field of fuzzy logic and data mining, and provides a forum for experts, researchers, academics and representatives from industry to share the latest advances in the field of fuzzy sets and data mining. This year, topics from two special sessions on granular-ball computing and the application of generative AI, as well as machine learning and neural networks, were also covered. A total of 363 submissions were received, and after careful review by the members of the international program committee, 110 papers were accepted for presentation at the conference and publication here, representing an acceptance rate of just over 30%. Covering a comprehensive range of current research and developments in fuzzy logic and data mining, the book will be of interest to all those working in the field of data science.

Topics on Steiner Systems