Dodge, Yadolah

The Concise Encyclopedia of Statistics, paper editon.

2007
ISBN: 0-387-32833-5

About this book

The Concise Encyclopedia of Statistics presents the essential information about statistical tests, concepts, and analytical methods in language that is accessible to practitioners and students of the vast community using statistics in medicine, engineering, physical science, life science, social science, and business/economics.

The reference is alphabetically arranged to provide quick access to the fundamental tools of statistical methodology and biographies of famous statisticians. The more than 500 entries include definitions, history, mathematical details, limitations, examples, references, and further readings. All entries include cross-references as well as the key citations. The back matter includes a timeline of statistical inventions. This reference will be an enduring resource for locating convenient overviews about this essential field of study.

Table of contents

A.- Acceptance Region.- Accuracy.- Algorithm.- Alternative hypothesis.- Analysis of binary data.- Analysis of categorical data.- Analysis of residuals.- Analysis of variance.- Anderson Oskar.- Anderson Theodore W.- Anderson-Darling test.- Arithmetic mean.- Arithmetic triangle.- ARMA models.- Arrangement.- Attributable risk.- Autocorrelation and partial autocorrelation.- Avoidable risk.

Baddeley, A., Barany, I., Schneider, R., Weil, W.

Stochastic Geometry
Lectures given at the C.I.M.E. Summer School held in Martina Franca, Italy, September 13-18, 2004

Series: Lecture Notes in Mathematics
Subseries: Fondazione C.I.M.E., Firenze , Vol. 1892
2006, Approx. 295 p., Softcover
ISBN: 3-540-38174-0
Due: October 18, 2006

About this book

Stochastic Geometry is the mathematical discipline which studies mathematical models for random geometric structures, as they appear frequently in almost all natural sciences or technical fields. Although its roots can be traced back to the 18th century (the Buffon needle problem), the modern theory of random sets was founded by D. Kendall and G. Matheron in the early 1970's. Its rapid development was influenced by applications in Spatial Statistics and by its close connections to Integral Geometry. The volume "Stochastic Geometry" contains the lectures given at the CIME summer school in Martina Franca in September 2004. The four main lecturers covered the areas of Spatial Statistics, Random Points, Integral Geometry and Random Sets, they are complemented by two additional contributions on Random Mosaics and Crystallization Processes. The book presents an up-to-date description of important parts of Stochastic Geometry.

Table of contents

Preface.- A. Baddeley: Spatial Point Processes and their Applications.- I. Barany: Random Polytopes, Convex Bodies, and Approximation.- W. Weil: Random Sets (in Particular Boolean Models).- D. Hug: RandomMosaics.- V. Capaso, E. Villa: On the Evolution Equations of Mean Geometric Densities for a Class of Space and Time Inhomogeneous Stochastic Birth-and-growth Processes.

Bosma, Wieb; Cannon, John (Eds.)

Discovering Mathematics with Magma
Reducing the Abstract to the Concrete

Series: Algorithms and Computation in Mathematics , Vol. 19
2007, Approx. 395 p., 8 illus., Hardcover
ISBN: 3-540-37632-1

About this book

This volume celebrates the first decade of the Computer Algebra system Magma. With a design based on the ontology and semantics of algebra, Magma enables users to rapidly formulate and perform calculations in the more abstract parts of mathematics. This book introduces the reader to the role Magma plays in advanced mathematical research through 14 case studies which, in most cases, describe computations underpinning new theoretical results. The authors of the chapters were chosen both for their expertise in the particular field and for their innovative use of Magma. Although by no means exhaustive, the topics range over much of Magma's coverage of algorithmic algebra: from number theory and algebraic geometry, via representation theory and group theory to some branches of discrete mathematics and graph theory. A basic introduction to the Magma language is given in an appendix. The book is simultaneously an invitation to learn a new programming language in the context of contemporary research problems, and an exposition of the types of problem that can be investigated using computational algebra.

Table of contents

Preface.- Magma: the project.- About this volume.- How to read the Magma code?- W.Bosma: Some computational experiments in number theory.- C.Fieker: Applications of the class field theory of global fields.- N.Bruin: Some ternary Diophantine equations of signature (n,n,2).- W.Stein: Studying the Birch and Swinnerton-Dyer conjecture for modular abelian varieties using Magma.- P.B.van Wamelen: Computing with the analytic Jacobian of a genus 2 curve.- G.Brown: Graded rings and special K3 surfaces.- D.E.Taylor: Constructing the split octonions.- J.F.Carlson: Support varieties for modules.- J.F.Carlson: When is projectivity detected on subalgebras?- D.F.Holt: Cohomology and group extensions in Magma.- C.M.Roney-Dougal, W.R.Unger: Computing the primitive permuation groups of degree less than 1000.- V.Gebhardt: Computer aided discovery of a fast algorithm for testing conjugacy in braid groups.- M.Grassl: Searching for linear codes with large minimum distance.- P.Lieby: Colouring planar graphs.- G.Bailey: Appendix: The Magma Language.- Index

Hansmann, Heinz

Local and Semi-Local Bifurcations in Hamiltonian Dynamical Systems
Results and Examples

Series: Lecture Notes in Mathematics , Vol. 1893
2007, Approx. 250 p., Softcover
ISBN: 3-540-38894-X

About this book

Once again KAM theory is commited in the context of nearly integrable Hamiltonian systems. While elliptic and hyperbolic tori determine the distribution of maximal invariant tori, they form themselves n-parameter families. Hence, without the need for untypical conditions or external parameters, onemay encounter torus bifurcations of high co-dimension in a single given Hamiltonian system. The volume moves gradually from the integrable case, in which symmetries allow for reduction to bifurcating equilibria, to non.integrability, where smooth parametrisations have to be replaced byCantor sets. An important ingredient are planar singularities and their versal unfoldings, which allow to explain the underlying dynamics in a transparent way.

Table of contents

1.Introduction.- 2.Bifurcations of Equilibria.- 3.Bifurcations of Periodic Orbits.- 4. Bifurcations of Invariant Tori.- 5.Perturbations of Ramified Torus Bundles.- A.Planar Singularities.- B.Stratifications.- C.Normal Form Theory.- D.Proof of the Main KAM Theorem.- E.Proofs of the Necessary Lemmata.- Glossary.- References.- Index

Garcia, Arnaldo; Stichtenoth, Henning (Eds.)

Topics in Geometry, Coding Theory and Cryptography

Series: Algebra and Applications , Vol. 6
2006, Approx. 210 p., Hardcover
ISBN: 1-4020-5333-9

About this book

The theory of algebraic function fields over finite fields has its origins in number theory. However, after Goppa`s discovery of algebraic geometry codes around 1980, many applications of function fields were found in different areas of mathematics and information theory, such as coding theory, sphere packings and lattices, sequence design, and cryptography. The use of function fields often led to better results than those of classical approaches.

This book presents survey articles on some of these new developments. Most of the material is directly related to the interaction between function fields and their various applications; in particular the structure and the number of rational places of function fields are of great significance. The topics focus on material

which has not yet been presented in other books or survey articles. Wherever applications are pointed out, a special effort has been made to present some background concerning their use.

Written for:

Mathematicians, computer scientists and engineers interested in areas of Information Theory ( Coding Theory and Cryptography ) closely related to Number Theory and to Algebraic Geometry ( algebraic curves and function fields over finite fields and their applications).

O'Mathuna, Diarmuid

Integrable Systems in Celestial Mechanics

Series: Progress in Mathematical Physics , Preliminary entry 1400
2007, Hardcover
ISBN: 0-8176-4096-7

About this book

This work focuses on the two integrable systems of relevance to celestial mechanics, both of which date back to the18th century. Under discussion are the Kepler (two-body) problem and the Euler (two-fixed center) problem, the latter being the more complex and more instructive, as it exhibits a richer and more varied solution structure. Further, because of the interesting investigations by the 20th century mathematical physicist J.P. Vinti, the Euler problem is now recognized as being intimately linked to the earth-satellite problem; in short, the Euler problem and the earth-satellite problem are in a dual complementary relation. In contrasting the issues involved in the Kepler-Euler problems, the author raises current issues in analysis and astronomy, and places these classical problems in a modern context.

The feature of O'Mathuna's treatment is that the classical procedure for deriving the exact solution to the Kepler problem can be applied in its entirety to the Euler problem. Whereas in the Kepler case the solution is expressed in terms of trigonometric functions, in the Euler case, the natural representation is in terms of Jacobian elliptic functions. These original insights have hithertofore not appeared in book form.

Table of contents

General Introduction.-The Kepler Problem (Two-Body Problem): the central Newtonian potential.-Bernoulli solution.-Features of the central Newtonian potential.-The Non-Central Newtonian Potential.-The Euler problem: two fiexd centers of attraction.-The Vinti problem: earth-satellite theory.-Implications for perturbation theories.-Relativistic context.-Index.

Kobayashi, Toshiyuki; Schmid, Wilfried; Yang, Jae-Hyun (Eds.)

Representation Theory and Automorphic Forms

Series: Progress in Mathematics , Vol. 280
2007, Approx. 300 p., 10 illus., Hardcover
ISBN: 0-8176-4505-5

About this book

This volume uses a unified approach to representation theory and automorphic forms. The invited papers, written by leading mathematicians in related fields, track recent progress in the ever expanding fields of representation theory and automorphic forms, and their association with number theory and differential geometry. Both graduate students and researchers will find inspiration in this volume.

Table of contents

Introduction.-Huang, J.: Dirac cohomology, discrete series and dimensions of spaces of automorphic forms.-Ikeda, T.: On liftings of holomorphic modular forms.-Kobayashi, T.: Visible actions on complex manifolds and multiplicity-free theorems.-Miller, S., Schmid, W.: Automorphic distributions and functional equations.-Ramakrishnan, D.: *-selfdual representations.-Shahidi, F.: Langlands Functoriality Conjecture.-Yang, J.: Harmonic Analysis on Homogeneous Spaces.-Yoshikawa, K.: Discriminant of certain K3 surfaces.-Miller, S.: Sums of automorphic forms coefficients with applications to number theory and cryptography.-References.-Index.