Published 3rd November 2011 by A K Peters/CRC Press
174 pages
Series: Research Notes in Mathematics
Hardback: 978-1-4665019-2-8:
Lectures on NX(p) deals with the question on how NX(p), the number of solutions of mod p congruences, varies with p when the family (X) of polynomial equations is fixed. While such a general question cannot have a complete answer, it offers a good occasion for reviewing various techniques in l-adic cohomology and group representations, presented in a context that is appealing to specialists in number theory and algebraic geometry.
Along with covering open problems, the text examines the size and congruence properties of NX(p) and describes the ways in which it is computed, by closed formulae and/or using efficient computers.
The first four chapters cover the preliminaries and contain almost no proofs. After an overview of the main theorems on NX(p), the book offers simple, illustrative examples and discusses the Chebotarev density theorem, which is essential in studying frobenian functions and frobenian sets. It also reviews l-adic cohomology.
The author goes on to present results on group representations that are often difficult to find in the literature, such as the technique of computing Haar measures in a compact l-adic group by performing a similar computation in a real compact Lie group. These results are then used to discuss the possible relations between two different families of equations X and Y. The author also describes the Archimedean properties of NX(p), a topic on which much less is known than in the l-adic case. Following a chapter on the Sato-Tate conjecture and its concrete aspects, the book concludes with an account of the prime number theorem and the Chebotarev density theorem in higher dimensions.
Introduction. Examples. The Chebotarev Density Theorem for a Number Field
. Review of ?-adic Cohomology. Auxiliary Results on Group Representations.
The p-adic Properties of NX(p). The Archimedean Properties of NX(p). The
Sato-Tate Conjecture. Higher Dimension: The Prime Number Theorem and the
Chebotarev Density. Relative Schemes. References. Index of Notations. Index
of Terms.
To Be Published 19th December 2011
399 pages
Series: Chapman & Hall/CRC Monographs on Statistics & Applied Probability
Hardback: 978-1-4398357-4-6:
Extreme value theory (EVT) deals with extreme (rare) events, which are sometimes reported as outliers. Certain textbooks encourage readers to remove outliers?in other words, to correct reality if it does not fit the model. Recognizing that any model is only an approximation of reality, statisticians are eager to extract information about unknown distribution making as few assumptions as possible.
Extreme Value Methods with Applications to Finance concentrates on modern topics in EVT, such as processes of exceedances, compound Poisson approximation, Poisson cluster approximation, and nonparametric estimation methods. These topics have not been fully focused on in other books on extremes. In addition, the book covers:
*Extremes in samples of random size
*Methods of estimating extreme quantiles and tail probabilities
*Self-normalized sums of random variables
*Measures of market risk
Along with examples from finance and insurance to illustrate the methods, Extreme Value Methods with Applications to Finance includes over 200 exercises, making it useful as a reference book, self-study tool, or comprehensive course text.
A systematic background to a rapidly growing branch of modern Probability and Statistics: extreme value theory for stationary sequences of random variables.
MATHEMATICAL STUDIES: MONOGRAPH SERIES(Volume 13)
ISBN: 966-7148-14-0
Price: 75.00 USD
Pages: 258
Format: 160x240 mm
Cover: cloth.
The book is devoted to the studying of ultrafilters in topological algebra. The main object of investigations is the Stone-Cech compactification betaG of a topological group G. The set betaG is a right topological semigroup and the continuity of the operation involving the left translation is extensively studied in the book. The richness of algebraic structure, makes the semigroup betaG very useful and with plenty of applications in combinatorics as well as in functional analysis, in particular, to the left convolution algebras. In the book, the algebra in the Stone-Cech compactification is used to construct and study topologies on groups.
MATHEMATICAL STUDIES: MONOGRAPH SERIES (Vol. 14)
ISBN: 966-7148-19-1
Price: 75.00 USD
Pages: 256
Format: 160x240 mm
Cover: cloth.
In this monograph, there are presented two directions of the theory of branching processes, namely, the processes with arbitrary numbers types of particles and processes with continuous state space.
The monograph consists of eight chapters. The first one contains a short historical information about branching processes and concise review of literature. The second one is devoted to the basic definition and statements of theorems. The third chapter contains the results of an article by M. Jirina gGeneral branching process with continuous time parameter''.
Further, there are presented the results of Ya. Yeleyko, the limit theorems for processes with arbitrary numbers of particles. The fifth chapter follows the fundamental article of M. Jirina gStochastic branching processes with continuous state spaceh as well as Yu. Ryshov and A. Skorohod gHomogeneous branching processes with finite number types of particles and continuously changing massh'. The final chapters include theorems on convergence of sequences of Galton-Watson processes to a process with continuous state space.
Brief review of literature
Theoretical information (Processes with one type of particles. Multitype branching processes. The processes with immigration. Renewal equation.)
General branching process ( Introduction. Processes with continuous time. The homogeneous case.)
Arbitrary number of types (Equations of renewal. Limiting theorems. Transitional phenomena. Processes with immigration. Asymptotic of mathematical expectation. Asymptotic of maximum proper value.)
Continuous state space ( Introduction. B-process with discrete time. BP with continuous state space. Cumulant of processes.)
Equitype processes (Galton-Watson processes. Near-critical Galton-Watson process. Processes with immigration. Bellman-Harris critical processes. Convergence of Bellman-Harris processes.)
Multitype processes (Convergence to multitype process. Convergence to one-dimensional process. Processes which depend on age. Multivariate processes. Processes with continuous time.)
Countable number of types.
MATHEMATICAL STUDIES: MONOGRAPH SERIES (vol. 15)
ISBN: 966-7148-22-1
Price: 75.00 USD
Pages: 212
Format: 160x240 mm
Cover: cloth.
The monograph is devoted to investigation of asymptotic properties of positive functions represented by the Laplace-Stiltjes integrals. Important role of such integrals is well-known in mathematical and complex analysis, probability theory, number theory and in other regions of mathematics. Since the Laplace-Stieltjes integrals are direct generalization of the Laplace integral and the Dirichlet series with nonnegative coefficients and exponents, the investigation of the asymptotic properties of the Laplace-Stieltjes integrals is necessary and actual. The book is intended for graduate mathematical students, post-graduates and experts in the mathematical analysis and its applications. The necessary mathematical background for reading the monograph is a university course of calculus.
Preface
1. Abscissa of convergence
2. Asymptotic behaviour of maximum of the integrand
3. Estimates of laplace-stiltjes integral by maximum of the integrand
4. Generalized order of growth
5. Logarithms of laplace-stiltjes integral and of maximum of the integrand
6. Rate of convergence
7. Asymptotical behaviour of remainders
Nankai Series in Pure, Applied Mathematics and Theoretical Physics - Vol. 9
The book aims to exemplify the recent developments in operad theory, in universal algebra and related topics in algebraic topology and theoretical physics. The conference has established a better connection between mathematicians working on operads (mainly the French team) and mathematicians working in universal algebra (primarily the Chinese team), and to exchange problems, methods and techniques from these two subject areas.
Grobner-Shirshov Bases for Categories (L A Bokut et al.)
Operads, Clones, and Distributive Laws (P-L Curien)
Leibniz Supalgebras Graded by Finite Root Systems (N-H Hu et al.)
Generalized Disjunctive Languages and Universal Algebra (Y Liu)
Koszul Duality of the Category of Trees and Bar Construction for Operads (M Livernet)
Some Problems in Operad Theory (J-L Loday)
Hom-Dendriform Algebras and Rota?Baxter Hom-Algebras (A Makhlouf)
Free Field Realizations of the Current Algebras Associated with (Super) Lie Algebras (W-L Yang)
Free TD Algebras and Rooted Trees (C-Y Zhou)
Encyclopedia of Types of Algebras 2010 (G W Zinbiel)
and other papers
Readership: Mathematicians and mathematical physicists.
300pp (approx.) Pub. date: Jan 2012
ISBN: 978-981-4365-11-6