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The Cohomology of Commutative Semigroups
This book provides an organized exposition of the current state of the theory of commutative semigroup cohomology, a theory which was originated by the author and has matured in the past few years. The work contains a fundamental scientific study of questions in the theory. The various approaches to commutative semigroup cohomology are compared. The problems arising from definitions in higher dimensions are addressed. Computational methods are reviewed. The main application is the computation of extensions of commutative semigroups and their classification. Previously the components of the theory were scattered among a number of research articles. This work combines all parts conveniently in one volume. It will be a valuable resource for future students of and researchers in commutative semigroup cohomology and related areas.
Encyclopedia of the Canonical Ḥadīth
An encyclopedic work on Islam with English translations. This book presents a sourcebook of the development of Islam in its various facets during the first three centuries since its foundation. It concludes with an index and glossary of names and concepts, which functions at the same time as a concordance.
The Biography of Muhammad
This book considers the Arabic biographies of Prophet Muhammad, the earliest of which dates from two centuries after his life. These biographies, prized by Muslims, have been approached in the Western study of Islam from a range of positions. Some scholars reject them entirely, seeing in them products of the Muslim community’s idealisation of its history, while others accept them at face value, reasoning that, if not exact versions of events, the events could not have differed too much from their descriptions. The author revisits the debate and reconsiders several key incidents in the life of the Prophet. By compiling an extensive corpus of materials and comparing them closely, this book a...
Commutative Semigroups
This is the first book about commutative semigroups in general. Emphasis is on structure but the other parts of the theory are at least surveyed and a full set of about 850 references is included. The book is intended for mathematicians who do research on semigroups or who encounter commutative semigroups in their research.
Jaina Epistemology in Historical and Comparative Perspective
The Nyayavatara, erroneously ascribed by tradition to Siddhasena Divakara, was either the first or one of the first serious Jaina treatises on epistemology. Its author enters polemics with other - mostly Buddhist - epistemological schools and endeavours to establish a Jaina epistemological tradition of its own. Despite its importance, the work is rather secondary in the sense that it relies, for the most part, on the Buddhist logical legacy. The first extant commentary is the Nyayavatara-vivrti of Siddharsigani. Its significance is often underestimated, for its author was responsible for the subsequent development of Jaina epistemological thought to a much larger degree than it has so far been recognised. He refers to major philosophical schools of his times, e.g. to Sautrantika, Yogacara, Sunya-vada, Samkhya, Mimamsa, Nyaya, Vaisesika, Advaita-vedanta, the materialists, etc. The gloss (Tippana) of Devabhadra is in addition a useful source of quotations. (Franz Steiner 2001)
Symmetries and Semi-invariants in the Analysis of Nonlinear Systems
This book details the analysis of continuous- and discrete-time dynamical systems described by differential and difference equations respectively. Differential geometry provides the tools for this, such as first-integrals or orbital symmetries, together with normal forms of vector fields and of maps. A crucial point of the analysis is linearization by state immersion. The theory is developed for general nonlinear systems and specialized for the class of Hamiltonian systems. By using the strong geometric structure of Hamiltonian systems, the results proposed are stated in a different, less complex and more easily comprehensible manner. They are applied to physically motivated systems, to demonstrate how much insight into known properties is gained using these techniques. Various control systems applications of the techniques are characterized including: computation of the flow of nonlinear systems; computation of semi-invariants; computation of Lyapunov functions for stability analysis and observer design.
