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This monograph studies the topological shapes of geodesics outside a large compact set in a finitely connected, complete, and noncompact surface admitting total curvature. When the surface is homeomorphic to a plane, all such geodesics behave like those of a flat cone. In particular, the rotation numbers of the geodesics are controlled by the total curvature. Accessible to beginners in differential geometry, but also of interest to specialists, this monograph features many illustrations that enhance understanding of the main ideas.
The first part of Chapter 16 in Ramanujan's second notebook is devoted to q-series. Several of the results obtained by Ramanujan are classical, but many are new. In particular, certain elegant q-continued fraction expansions have not appeared heretofore in print. In the remainder of this chapter, Ramanujan develops the theory of the classical theta-functions in a manner different from his nineteenth century predecessors such as Jacobi. Although many of Ramanujan's discoveries about theta-functions are well-known, several new results are also to be found.
We introduce the notion of a textile system. Using this, we study the dynamical properties of endomorphisms and automorphisms of topological Markov shifts including one-sided ones. The dynamical properties of automorphisms of sofic systems are also studied.
Youth Without Family to Lean On draws together interdisciplinary, global perspectives to provide a comprehensive review of the characteristics, dynamics, and development of youth (aged 15–25) who have no family to lean on, either practically or psychologically. In this timely volume, Mozes and Israelashvili bring together leading international experts to present updated knowledge, information on existing interventions, and unanswered questions in relation to youth without family to lean on, in pursuit of fostering these youth’s positive development. The various chapters in this book include discussions on different topics such as social support, developing a sense of belonging, parental ...
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This book explores theoretical and practical implications of reflecting the fair value of liabilities for insurance companies. In addition, the contributions discuss the disclosure of these values to the financial and regulatory communities and auditing firms which are actually calculating this illusive but important variable. It combines contributions by distinguished practitioners from the insurance, accounting and finance fields, with those of prominent academics. One of the central themes of the collection is that adequate disclosure of the true economic value of insurance company liabilities is both possible and desirable. Wherever possible, the insurance valuation process is wedded with modern financial theory. For example, the use of option pricing theory is applied to insurance companies, where the true value of the firm's liabilities is a critical variable. Methods such as cash flow, earned profit and indirect discount are explored.
Probability & Statistics with Integrated Software Routines is a calculus-based treatment of probability concurrent with and integrated with statistics through interactive, tailored software applications designed to enhance the phenomena of probability and statistics. The software programs make the book unique.The book comes with a CD containing the interactive software leading to the Statistical Genie. The student can issue commands repeatedly while making parameter changes to observe the effects. Computer programming is an excellent skill for problem solvers, involving design,
Since the late 1980s, a large number of very user-friendly tools for fuzzy control, fuzzy expert systems, and fuzzy data analysis have emerged. This has changed the character of this area and started the area of `fuzzy technology'. The next large step in the development occurred in 1992 when almost independently in Europe, Japan and the USA, the three areas of fuzzy technology, artificial neural nets and genetic algorithms joined forces under the title of `computational intelligence' or `soft computing'. The synergies which were possible between these three areas have been exploited very successfully. Practical Applications of Fuzzy Sets focuses on model and real applications of fuzzy sets, and is structured into four major parts: engineering and natural sciences; medicine; management; and behavioral, cognitive and social sciences. This book will be useful for practitioners of fuzzy technology, scientists and students who are looking for applications of their models and methods, for topics of their theses, and even for venture capitalists who look for attractive possibilities for investments.
This broad text provides a complete overview of most standard statistical methods, including multiple regression, analysis of variance, experimental design, and sampling techniques. Assuming a background of only two years of high school algebra, this book teaches intelligent data analysis and covers the principles of good data collection. * Provides a complete discussion of analysis of data including estimation, diagnostics, and remedial actions * Examples contain graphical illustration for ease of interpretation * Intended for use with almost any statistical software * Examples are worked to a logical conclusion, including interpretation of results * A complete Instructor's Manual is available to adopters
Mathematical Interest Theory provides an introduction to how investments grow over time. This is done in a mathematically precise manner. The emphasis is on practical applications that give the reader a concrete understanding of why the various relationships should be true. Among the modern financial topics introduced are: arbitrage, options, futures, and swaps. Mathematical Interest Theory is written for anyone who has a strong high-school algebra background and is interested in being an informed borrower or investor. The book is suitable for a mid-level or upper-level undergraduate course or a beginning graduate course. The content of the book, along with an understanding of probability, w...