Jump to ContentJump to Main Navigation

You are looking at 1-20 of 34 items

  • Keywords: Frobenius x
Clear All Modify Search

View:

The Diophantine Frobenius Problem

Jorge L. Ramírez Alfonsín

Published in print:
2005
Published Online:
September 2007
ISBN:
9780198568209
eISBN:
9780191718229
Item type:
book
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198568209.001.0001
Subject:
Mathematics, Algebra, Combinatorics / Graph Theory / Discrete Mathematics

During the early part of the last century, F. G. Frobenius raised, in his lectures, the following problem (called the Diophantine Frobenius Problem FP): given relatively prime positive integers a1, . ... More


Hidden Markov Processes: Theory and Applications to Biology

M. Vidyasagar

Published in print:
2014
Published Online:
October 2017
ISBN:
9780691133157
eISBN:
9781400850518
Item type:
book
Publisher:
Princeton University Press
DOI:
10.23943/princeton/9780691133157.001.0001
Subject:
Mathematics, Probability / Statistics

This book explores important aspects of Markov and hidden Markov processes and the applications of these ideas to various problems in computational biology. It starts from first principles, so that ... More


Frobenius Conjugacy Classes

Nicholas M. Katz

in Convolution and Equidistribution: Sato-Tate Theorems for Finite-Field Mellin Transforms (AM-180)

Published in print:
2012
Published Online:
October 2017
ISBN:
9780691153308
eISBN:
9781400842704
Item type:
chapter
Publisher:
Princeton University Press
DOI:
10.23943/princeton/9780691153308.003.0006
Subject:
Mathematics, Number Theory

This chapter analyzes Frobenius conjugacy classes. It shows that in either the split or nonsplit case, when χ‎ is good for N, the conjugacy class FrobE,X has unitary eigenvalues in every ... More


Frobenius Tori and Weights; Getting Elements of Garith

Nicholas M. Katz

in Convolution and Equidistribution: Sato-Tate Theorems for Finite-Field Mellin Transforms (AM-180)

Published in print:
2012
Published Online:
October 2017
ISBN:
9780691153308
eISBN:
9781400842704
Item type:
chapter
Publisher:
Princeton University Press
DOI:
10.23943/princeton/9780691153308.003.0017
Subject:
Mathematics, Number Theory

This chapter works on Gₘ/k. It considers an arithmetically semisimple object N ɛ Garith which is pure of weight zero. It assumes it is of the form G[1], with G a middle extension sheaf. Thus, for ... More


The Frobenius number for small n

J. L. Ramírez Alfonsín

in The Diophantine Frobenius Problem

Published in print:
2005
Published Online:
September 2007
ISBN:
9780198568209
eISBN:
9780191718229
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198568209.003.0002
Subject:
Mathematics, Algebra, Combinatorics / Graph Theory / Discrete Mathematics

It is easy to solve FP when n = 2. Indeed, g(a1, a2) = a1a2 - a1 - a2. However, the computation of a (simple) formula when n = 3 is much more difficult and has been the subject of numerous research ... More


The general problem

J. L. Ramírez Alfonsín

in The Diophantine Frobenius Problem

Published in print:
2005
Published Online:
September 2007
ISBN:
9780198568209
eISBN:
9780191718229
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198568209.003.0003
Subject:
Mathematics, Algebra, Combinatorics / Graph Theory / Discrete Mathematics

This chapter provides a systematic exposition of the known formulas, including upper and lower bounds for g(a1, . . . , an) for general n, and for special sequences (for instance, when a1, . . . , an ... More


Generalizations and related problems

J. L. Ramírez Alfonsín

in The Diophantine Frobenius Problem

Published in print:
2005
Published Online:
September 2007
ISBN:
9780198568209
eISBN:
9780191718229
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198568209.003.0006
Subject:
Mathematics, Algebra, Combinatorics / Graph Theory / Discrete Mathematics

Let g(n, t) and h(n, t) be the largest and smallest of three of the Frobenius numbers when a1 < · · · < an = t and t = a1 < · · · < an, respectively. This chapter reviews the results on these ... More


INTRODUCTION TO MARKOV CHAINS

D. A. Bini, G. Latouche, and B. Meini

in Numerical Methods for Structured Markov Chains

Published in print:
2005
Published Online:
September 2007
ISBN:
9780198527688
eISBN:
9780191713286
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198527688.003.0001
Subject:
Mathematics, Numerical Analysis

This chapter contains a brief introduction to the fundamental concepts of Markov chains, including classification of states, irreducible classes, first passage times, stochastic complementation and ... More


Consistent Orientation of Moduli Spaces

Daniel S. Freed, Michael J. Hopkins, and Constantin Teleman

in The Many Facets of Geometry: A Tribute to Nigel Hitchin

Published in print:
2010
Published Online:
September 2010
ISBN:
9780199534920
eISBN:
9780191716010
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199534920.003.0019
Subject:
Mathematics, Geometry / Topology

In a series of papers by Freed, Hopkins, and Teleman (2003, 2005, 2007a) the relationship between positive energy representations of the loop group of a compact Lie group G and the twisted ... More


Group-Theoretic Facts about Ggeom and Garith

Nicholas M. Katz

in Convolution and Equidistribution: Sato-Tate Theorems for Finite-Field Mellin Transforms (AM-180)

Published in print:
2012
Published Online:
October 2017
ISBN:
9780691153308
eISBN:
9781400842704
Item type:
chapter
Publisher:
Princeton University Press
DOI:
10.23943/princeton/9780691153308.003.0007
Subject:
Mathematics, Number Theory

This chapter presents proofs of following theorems. Theorem 6.1: Suppose N in Garith is geometrically semisimple. Then Ggeom,N is a normal subgroup of Garith,N. Theorem 6.2: Suppose that N in Garith ... More


The Main Theorem

Nicholas M. Katz

in Convolution and Equidistribution: Sato-Tate Theorems for Finite-Field Mellin Transforms (AM-180)

Published in print:
2012
Published Online:
October 2017
ISBN:
9780691153308
eISBN:
9781400842704
Item type:
chapter
Publisher:
Princeton University Press
DOI:
10.23943/princeton/9780691153308.003.0008
Subject:
Mathematics, Number Theory

This chapter takes up the proof of the main theorem. Theorem 7.2: Suppose N in Garithι‎-pure of weight zero and arithmetically semisimple, such that the quotient group Garith,N/Ggeom,N is ℤ / nℤ. Fix ... More


Nonnegative Matrices

M. Vidyasagar

in Hidden Markov Processes: Theory and Applications to Biology

Published in print:
2014
Published Online:
October 2017
ISBN:
9780691133157
eISBN:
9781400850518
Item type:
chapter
Publisher:
Princeton University Press
DOI:
10.23943/princeton/9780691133157.003.0003
Subject:
Mathematics, Probability / Statistics

This chapter deals with nonnegative matrices, which are relevant in the study of Markov processes because the state transition matrix of such a process is a special kind of nonnegative matrix, known ... More


Von Neumann's Economic Model

S. N. Afriat

in Logic of Choice and Economic Theory

Published in print:
1987
Published Online:
November 2003
ISBN:
9780198284611
eISBN:
9780191595844
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/0198284616.003.0023
Subject:
Economics and Finance, Microeconomics

This is the last of six chapters on the logic of price, and expands on the features of von Neumann's economic model, or activity system, which was first mentioned in Chapter IV.1. The fourteen ... More


‘The Benin Things are Fine, Fine’: The Art of Africa and the Pacific Islands in Pre-War London

Rupert Richard Arrowsmith

in Modernism and the Museum: Asian, African, and Pacific Art and the London Avant-Garde

Published in print:
2010
Published Online:
January 2011
ISBN:
9780199593699
eISBN:
9780191595684
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199593699.003.0009
Subject:
Literature, Film, Media, and Cultural Studies, 20th-century and Contemporary Literature

This chapter focuses on the shift in attention of the London avant-garde towards visual art from West Africa and the Pacific islands from late 1912 into the war years. New evidence is presented ... More


Multi-parameter Singular Integrals. (AM-189)

Brian Street

Published in print:
2014
Published Online:
October 2017
ISBN:
9780691162515
eISBN:
9781400852758
Item type:
book
Publisher:
Princeton University Press
DOI:
10.23943/princeton/9780691162515.001.0001
Subject:
Mathematics, Analysis

This book develops a new theory of multi-parameter singular integrals associated with Carnot–Carathéodory balls. The book first details the classical theory of Calderón–Zygmund singular integrals and ... More


Second Order and Gaussian Fields

Ulf Grenander and Michael I. Miller

in Pattern Theory: From representation to inference

Published in print:
2006
Published Online:
November 2020
ISBN:
9780198505709
eISBN:
9780191916564
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/oso/9780198505709.003.0010
Subject:
Computer Science, Programming Languages

This chapter studies second order and Gaussian fields on the background spaces which are the continuum limits of the finite graphs. For this random processes in ... More


Markov Processes and Random Sampling

Ulf Grenander and Michael I. Miller

in Pattern Theory: From representation to inference

Published in print:
2006
Published Online:
November 2020
ISBN:
9780198505709
eISBN:
9780191916564
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/oso/9780198505709.003.0019
Subject:
Computer Science, Programming Languages

The parameter spaces of natural patterns are so complex that inference must often proceed compositionally, successively building up more and more complex structures, ... More


Categories for Quantum Theory: An Introduction

Chris Heunen and Jamie Vicary

Published in print:
2019
Published Online:
January 2020
ISBN:
9780198739623
eISBN:
9780191802584
Item type:
book
Publisher:
Oxford University Press
DOI:
10.1093/oso/9780198739623.001.0001
Subject:
Mathematics, Mathematical Physics, Applied Mathematics

Monoidal category theory serves as a powerful framework for describing logical aspects of quantum theory, giving an abstract language for parallel and sequential composition and a conceptual way to ... More


Hamiltonian Fluid Dynamics

Rick Salmon

in Lectures on Geophysical Fluid Dynamics

Published in print:
1998
Published Online:
November 2020
ISBN:
9780195108088
eISBN:
9780197561034
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/oso/9780195108088.003.0010
Subject:
Earth Sciences and Geography, Geophysics: Earth Sciences

In this final chapter, we return to the subject of the first: the fundamental principles of fluid mechanics. In chapter 1, we derived the equations of fluid motion ... More


Numerology

Christophe Reutenauer

in From Christoffel Words to Markoff Numbers

Published in print:
2018
Published Online:
January 2019
ISBN:
9780198827542
eISBN:
9780191866418
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/oso/9780198827542.003.0011
Subject:
Mathematics, Pure Mathematics

This chapter gives several examples, which may help the reader to work in concrete terms with Markoff numbers, Christoffel words, Markoff constants, and quadratic forms. In particular the thirteen ... More


View: