Random Walks in the Quarter-Plane: Algebraic Methods, Boundary Value Problems and Applications (Stochastic Modelling and Applied Probability)

Book Description

This monograph aims at promoting original mathematical methods to determine the invariant measure of two-dimensional random walks in domains with boundaries. Such processes are of interest in several areas of mathematical research and are encountered in pure probabilistic problems, as well as in applications involving queuing theory. Using Riemann surfaces and boundary value problems, the authors propose completely new approaches to solve functional equations of two complex variables. These methods can also be employed to characterize the transient behavior of random walks in the quarter plane.

The Statistical Theory of Shape (Springer Series in Statistics)

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The Statistical Theory of Shape (Springer Series in Statistics)
Christopher G. Small
Manufacturer: Springer
ProductGroup: Book
Binding: Hardcover

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ASIN: 0387947299

Book Description

The shape of a data set can be defined as the total of all information under translations, rotations, and scale changes to the data. Over the last decade, shape analysis has emerged as a promising new field of statistics with applications to morphometrics, pattern recognition, archaeology, and other disciplines. This book provides a comprehensive coverage of the statistical theory of shape. Both the Kendall and the Bookstein schools of shape analysis are described. It is written for graduate students and researchers in statistics who have some knowledge of multivariate models. An understanding of the basic concepts of differential manifolds is also helpful.

Algebraic Methods in Statistics and Probability

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Algebraic Methods in Statistics and Probability
Ams Special Session on Algebraic Methods in Statistics
Manufacturer: American Mathematical Society
ProductGroup: Book
Binding: Mass Market Paperback

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ASIN: 0821826875

Book Description

Algebraic methods and arguments in statistics and probability are well known, from Gauss's least squares principle through Fisher's method of variance decomposition. The relevance of group-theoretic arguments, for example, became evident in the 1980s. Such techniques continue to be of interest today, along with other developments, such as the use of graph theory in modelling complex stochastic systems.

This volume is based on lectures presented at the AMS Special Session on Algebraic Methods and Statistics held at the University of Notre Dame (Indiana) and on contributed articles solicited for this volume. The articles are intended to foster communication between representatives of the diverse scientific areas in which these functions are utilized and to further the trend of utilizing algebraic methods in the areas of statistics and probability.

Book Description

The combination of fractal geometry and stochastic methods can be used to create convincing models in many different areas of science such as biology, chemistry, computer science, mathematics and physics. The present book deals with the mathematical theory needed for this purpose. It contains contributions by outstanding mathematicians and is meant to highlight the principal directions of research in the field. The contributors were the main speakers at the conference Fractal Geometry and Stochastics II held at Greifswald/Koserow, Germany, in August 1998.
The book is addressed to mathematicians and scientists who are interested in any of the following topics:
· fractal dimensions
· fractal measures and multifractals
· self-similar and self-affine fractals
· random fractals
· stable processes
· ergodic theory and dynamical systems
· harmonic analysis and stochastic processes on fractals
The readers will be introduced to the most recent results and problems on these subjects and also be treated to an overview of their historical development. Both researchers and graduate students will benefit from the clear expositions.

Customer Reviews:

Pictures and math........2003-03-03

This is a very nice collection of papers: tutorials, and well written research presented to a wide audience. They cover stochastic aspects, geometry, analysis, iterated function systems, algorithms, to mention just a few. And they are written by authorities in the field. Fractals make headlines from time to time[--are they everywhere?], and and they make lovely color pictures; but they are also part of a substantial mathematical theory, one with an exciting mathematical history. This very important book presents the subject in a way that it can be taught to students. Or it can be used for selfstudy! In view of the many applications to geometric analysis, to PDE, and to statistics, it is likely that fractal geometry will soon be a standard math course taught in many (more) math departments. A recent example of this: By now it is widely recognized that the selfsimilarity aspects of the wavelet algorithms are key to their sucess. The authors have produced an attractive book on fractals. There are others, for example one by Falconer from 1985[The geometry of fractal sets] with a slightly more potential theoretic bent.

The Mysteries of the Real Prime (London Mathematical Society Monographs New Series)

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Incredible implications for physics and mathematics

The Mysteries of the Real Prime (London Mathematical Society Monographs New Series)
M.J. Shai Haran
Manufacturer: Oxford University Press, USA
ProductGroup: Book
Binding: Hardcover

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Quantum Theory | Physics | Science | Subjects | Books

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In this important and original monograph, useful for both academic and professional researchers and students of mathematics and physics, the author describes his work on the Riemann zeta function and its adelic interpretation. It provides an original point of view, bringing new, highly useful dictionaries between different fields of mathematics. It develops an arithmetical approach to the continuum of real numbers and unifies many areas of mathematics including: Markov Chains, q-series, Elliptic curves, the Heisenberg group, quantum groups, and special functions (such as the Gamma, Beta, Zeta, theta, Bessel functions, the Askey-Wilson and the classical orthagonal polynomials) The text discusses real numbers from a p-adic point of view, first mooted by Araeklov. It includes original work on coherent theory, with implications for number theory and uses ideas from probability theory including Markov chains and noncommutative geometry which unifies the p-adic theory and the real theory by constructing a theory of quantum orthagonal polynomials.

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Incredible implications for physics and mathematics.......2003-04-16

At first it seemed this book was [spendy] but once I bought it I had no regrets. Mastering the material, means that one gets a glimpse at the potential exquisite simplicity of the p-adics. You also get a real sense that the proof of the greatest problem of all - the Riemann Hypothesis - is not far away if Haran's philosophy is pursued just one step further....

Symbolic Algebraic Methods and Verification Methods (Springer Mathematics,)

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Symbolic Algebraic Methods and Verification Methods (Springer Mathematics,)

Manufacturer: Springer
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Binding: Paperback

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ASIN: 3211835938

Book Description

The usual "implementation” of real numbers as floating point numbers on existing computers has the well-known disadvantage that most of the real numbers are not exactly representable in floating point. Also the four basic arithmetic operations can usually not be performed exactly. During the last years research in different areas has been intensified in order to overcome these problems. (LEDA-Library by K. Mehlhorn et al., "Exact arithmetic with real numbers” by A. Edalat et al., Symbolic algebraic methods, verification methods). The latest development is the combination of symbolic-algebraic methods and verification methods to so-called hybrid methods. – This book contains a collection of worked out talks on these subjects given during a Dagstuhl seminar at the Forschungszentrum für Informatik, Schloß Dagstuhl, Germany, presenting the state of the art.

Topics in Algebraic Graph Theory (Encyclopedia of Mathematics and its Applications)

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Topics in Algebraic Graph Theory (Encyclopedia of Mathematics and its Applications)

Manufacturer: Cambridge University Press
ProductGroup: Book
Binding: Hardcover

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ASIN: 0521801974

Book Description

The rapidly expanding area of algebraic graph theory uses two different branches of algebra to explore various aspects of graph theory: linear algebra (for spectral theory) and group theory (for studying graph symmetry). These areas have links with other areas of mathematics, such as logic and harmonic analysis, and are increasingly being used in such areas as computer networks where symmetry is an important feature. Other books cover portions of this material, but this book is unusual in covering both of these aspects and there are no other books with such a wide scope. Peter J. Cameron, internationally recognized for his substantial contributions to the area, served as academic consultant for this volume, and the result is ten expository chapters written by acknowledged international experts in the field. Their well-written contributions have been carefully edited to enhance readability and to standardize the chapter structure, terminology and notation throughout the book. To help the reader, there is an extensive introductory chapter that covers the basic background material in graph theory, linear algebra and group theory. Each chapter concludes with an extensive list of references.

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The complete Frost- The road not taken .......2005-11-07

For most of us most poets live through a few poems of theirs we have read in anthologies. It may be that in the case of a poet we especially love we have gone and read most of their poetry.
This volume presents a wonderful opportunity for the devotees of Frost to have in one book the work of a lifetime.
For me Frost is "The Road Not Taken" and "Birches" and "Mending Wall" and a host of scattered lines, " Good fences make good neighbors" and " The land was ours, before we were the land's".
Frost is also however, I must admit , for me the poet whose life casts a shadow on his work. Unfortunately perhaps I long ago read parts of the Thompson biography of Frost the central theme of which was his inveterate cruelty to all those around him.
All this has left me, you will excuse this, a bit 'cool toward Frost' and I personally prefer the more musical metrics of Wallace Stevens to the canny, often pithily wise lines of Frost.

You'll Never Need Another Frost Book.......2005-05-19

I took a class last semester on Robert Frost, and it was quite an experience. Frost was truly a wonderful poet who deserves every bit of praise he gets (and who is unfairly ignored in academia it seems). His words are so often true and lifechanging and beautiful and honest. Nobody is fully educated until they have read Frost's classics: "The Death of the Hired Man," "Mending Wall," "Birches," "After Apple-Picking," "Storm Fear," "Meeting and Passing," etc. There are so many good ones.

The Library of America edition is a great way to be exposed to Frost's poetry. It's true that there are a lot of pretty bad poems since everything, good and bad, is included in the volume; the uncollected poems here were meant to stay uncollected. Nevertheless, that everything is here is really a great strength to the book. It's great being able to place a single poem in Frost's entire oevre. I also liked seeing how his command of the language and the forms of poetry. Seeing everything also helped to see how his conception of his role changed. Most importantly, I loved that Frost's prose and his plays were included here. There are a number of gems to be found there. I particularly enjoyed the "'Sermon' at the Rock Avenue Temple" and Frost's children's stories. The ability to read Frost's prose alongside his poetry really enhances the reading of both.

Overall, Frost was a magnificant poet who cannot be given less than five stars, and by reading everything in this edition, one can certainly gain a greater appreciation of the poet at his finest.

Pure Frost Without Editorial Heat.......2005-05-04

Are you someone who buys for the art of the book as much for the art of the contents? If so, you can't do better than any of the stellar titles from the Library Of America series of books... This splendid collection of Frost will not dissapoint...One of the many treats of this volume as is virtually true with all of the Library Of America volumes is the ease with which you can hold it comfortably in your hand...Exclusively thin acid free paper is the secret and this volume packs in a two inch thick volume what normal paper would weigh you down with five or six inches of...

What nice unedited and thorough Frost you get here!...Speaking of editing, the true Frost afficionado will want to be sure to avoid items edited by an Edward Latham...This edition is Latham free and contains Frost's work as he originally wrote it...Unfortunately, from the late sixties on, several editions of Frost went forward with unnecessary "clean up" editing by this very punctuation weilding word meister...He added to many editions extra commas and punctuation in places Frost never originally put it...If you'd like to read a much more thorough analysis of this than I can describe here, be sure to pick up a copy of writer Donald Hall's " Breakfast Served Anytime" and read the article he wrote exposing Latham and his added cleansing of Frost's work...This Library Of America edition captures Frost unedited and at his purest and best...

The reader can choose here from a smorgasbord of outstanding selections and offerings...Poetry, prose, plays...there is quite a variety of choice fare offered here...

In the words of Mr. Frost.." I'm going up to the meadow to check the newborn calf,...I shan't be long...You come too!"

A fine edition of a great American Voice. .......2005-04-11

Robert Frost is a unique American voice that many people love. A few reject him, but the majority of those whom he was writing for still love and admire his poetry. His fans always have favorites and can quote lines and whole poems from memory. When a poet gets into people's memories and hearts it is not a sure sign of greatness, but it is a good indicator of something special.

In some ways his works have aged because they are about an America that has passed. One poem that I think catches a lot of the issues surround Frost is "The Literate Farmer and the Planet Venus". This piece is about the electrification of rural America and the strangeness of it all. It talks about the speeding up of life and wonders if the future will simply do away with beds because there won't be time to sleep. The poem is set in 1926, but was published in 1942 as part of "A Witness Tree". I don't know when it was written, but if it was written around the Second World War its nostalgia seems a bit more cynical to me (which I suspect to be the case). However, if it was written back in the late 1920s then it has more whimsy and an earnest wonder.

This poet does have a capacity for irony and bite as well as humor and whimsy. His words are more conversational than lyric and that is fine. They have less music, but a great deal of color and subtle observation. It really doesn't matter what any critic says about Frost. He will outlast all of them. What matters is what he says to you. He is certainly a more worthwhile read than most of what gets published nowadays, just expect to have to deal with some words and references to an America from a century ago.

This volume from the Library of America is terrific. The table of contents in the front refers to the whole volume. The Collected Poems is the reprint that takes up most of the book and has its own table of contents as well. There is also a chronology of Frost's life, notes on sources, and many very helpful notes that can help you understand certain references. There is an index of titles and first lines, and an index of prose titles.

I always feel grateful to the Library of America whenever I get a chance to read their volumes. Heck, they are simply great to hold and flip through!

Buy this now!.......2004-02-25

Very attractive, solid and sturdy, materials are very well organized. Not the cheapest, but well worth it -- especially at the discount Amazon provides... And then there's the content -- top notch stuff, perfect.

Robert Frost: Collected Poems, Prose, & Plays Complete Poems 1949 in the Clearing Uncollected Poems Plays Lectures, Essays, Stories, and Letters

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Robert Frost: Collected Poems, Prose, & Plays Complete Poems 1949 in the Clearing Uncollected Poems Plays Lectures, Essays, Stories, and Letters
Robert; Poirier, Richard; Richardson, Mark Frost
Manufacturer: Library of America
ProductGroup: Book
Binding: Hardcover
ASIN: B000PG2GWE

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Collected Poems, Prose, & Plays
Frost Robert
Manufacturer: Library of America
ProductGroup: Book
Binding: Hardcover
ASIN: B000UITX1O

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