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Functional Integrals
Integration in infinitely dimensional spaces (continual integration) is a powerful mathematical tool which is widely used in a number of fields of modern mathematics, such as analysis, the theory of differential and integral equations, probability theory and the theory of random processes. This monograph is devoted to numerical approximation methods of continual integration. A systematic description is given of the approximate computation methods of functional integrals on a wide class of measures, including measures generated by homogeneous random processes with independent increments and Gaussian processes. Many applications to problems which originate from analysis, probability and quantum physics are presented. This book will be of interest to mathematicians and physicists, including specialists in computational mathematics, functional and statistical physics, nuclear physics and quantum optics.
The Army List
None
A grammar of Mandan
Mandan is a Siouan language of North Dakota, near the geographic center of North America. There are no longer any first-language speakers after the last fluent speaker passed away in 2016. This grammar has been built from archival recordings of Mandan speakers from the 1960s through 2010, plus field work by the author undertaken between 2014 and 2016. The data from these various sources allowed for an in-depth description of the key aspects of the grammar of Mandan with special attention to the language’s complex verbal and nominal morphology. This book also includes an overview of Mandan narrative structure, culminating with an interlinear gloss of a traditional Mandan narrative and its free translation into English. This grammar is written to be used by as general an audience as possible, including Mandan community members, scholars who wish to research Siouan languages, linguistic typologists, historical linguists, and other individuals who aim to conduct research on an indigenous language of North America.
U.S. Army Register
None
Early Islamic Legal Theory
The Risāla of al-Shāfiʿī (d. 204/820), the earliest preserved work of Islamic legal theory, has been understood in previous scholarship as either the elaboration of a hierarchy of sources of law (Qurʾān, Sunna, consensus, and analogical reasoning) or an extended defense of the Sunna. Through a careful rereading of this celebrated text, this book offers a comprehensive reinterpretation of the Risāla, in which Shāfiʿī formulated an all-encompassing hermeneutic that portrays the law as a tightly interlocking structure organized around defined interactions of the Qurʾān and the Sunna. Topics covered include Shāfiʿī’s creative account of the law’s architectonics, hermeneutical techniques, legal epistemology, relationship to kalām, and the role of consensus (ijmāʿ).
