Combinatorial Algebra: Syntax and Semantics provides comprehensive account of many areas of combinatorial algebra. It contains self-contained proofs of more than 20 fundamental results, both classical and modern. This includes Golod–Shafarevich and Olshanskii's solutions of Burnside problems, Shirshov's solution of Kurosh's problem for PI rings, Belov's solution of Specht's problem for varieties of rings, Grigorchuk's solution of Milnor's problem, Bass–Guivarc'h theorem about growth of nilpotent groups, Kleiman's solution of Hanna Neumann's problem for varieties of groups, Adian's solution of von Neumann-Day's problem, Trahtman's solution of the road coloring problem of Adler, Goodwyn and Weiss. The book emphasize several ``universal" tools, such as trees, subshifts, uniformly recurrent words, diagrams and automata. With over 350 exercises at various levels of difficulty and with hints for the more difficult problems, this book can be used as a textbook, and aims to reach a wide and diversified audience. No prerequisites beyond standard courses in linear and abstract algebra are required. The broad appeal of this textbook extends to a variety of student levels: from advanced high-schoolers to undergraduates and graduate students, including those in search of a Ph.D. thesis who will benefit from the “Further reading and open problems” sections at the end of Chapters 2 –5. The book can also be used for self-study, engaging those beyond t he classroom setting: researchers, instructors, students, virtually anyone who wishes to learn and better understand this important area of mathematics.
This book features the refereed proceedings of the 2nd International Symposium on Computer Science in Russia held in September 2007. The 35 papers cover theory track deals with algorithms, protocols, and data structures; complexity and cryptography; formal languages, automata and their applications to computer science; computational models and concepts; proof theory; and applications of logic to computer science. Many applications are presented.
Contemporary finance and actuarial calculations have become so mathematically complex that a rigorous exposition is required for an accurate and complete presentation. This volume delivers just that. It gives a comprehensive and up-to-date methodology for financial pricing and modelling. Also included are special cases useful for practical applications. Beyond the traditional areas of hedging and investment on complete markets (the Black-Scholes and Cox-Ross-Rubinstein models), the book includes topics that are not currently available in monograph form, such as incomplete markets, markets with constraints, imperfect forms of hedging, and the convergence of calculations in finance and insurance. The book is geared toward specialists in finance and actuarial mathematics, practitioners in the financial and insurance business, students, and post-docs in corresponding areas of study. Readers should have a foundation in probability theory, random processes, and mathematical statistics.
The five, irreverant, satirical and imaginative stories contained in Diaboliad caused an uproar upon the book's first publication in 1925. Full of invention, they display Bulgakov's breathtaking stylistic range, moving at dizzying speed from grotesque satire to science fiction, from the plainest realism to the most madcap fantasy. Diaboliad is a wonderful introduction to literature's most uncategorisable and subversive genius.
This book presents and describes a series of unusual and striking strong-field phenomena concerning atoms and free electrons. Some of these phenomena are: multiphoton stimulated bremsstrahlung, free-electron lasers, wave-packet physics, above-threshold ionization, and strong-field stabilization in Rydberg atoms. The theoretical foundations and causes of the phenomena are described in detail, with all the approximations and derivations discussed. All the known and relevant experiments are described too, and their results are compared with those of the existing theoretical models.An extensive general theoretical introduction gives a good basis for subsequent parts of the book and is an independent and self-sufficient description of the most efficient theoretical methods of the strong-field and multiphoton physics. This book can serve as a textbook for graduate students.
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