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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


Numerical semigroups

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/9780198568209.003.0007
Subject:
Mathematics, Algebra, Combinatorics / Graph Theory / Discrete Mathematics

This chapter introduces the concept of numerical semigroups. Several properties of the gaps and nongaps of a semigroup are investigated, and the importance of the role played by the Frobenius number ... More


Stochastic Dynamics In Hilbert Space

Heinz-Peter Breuer and Francesco Petruccione

in The Theory of Open Quantum Systems

Published in print:
2007
Published Online:
January 2010
ISBN:
9780199213900
eISBN:
9780191706349
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199213900.003.06
Subject:
Physics, Theoretical, Computational, and Statistical Physics

This chapter contains the foundations of the stochastic formulation of continuous measurements carried out on an open quantum system. It shows that the time evolution of the state vector, conditioned ... More


Symmetric Markovian Semigroups and Dirichlet Forms

Zhen-Qing Chen and Masatoshi Fukushima

in Symmetric Markov Processes, Time Change, and Boundary Theory (LMS-35)

Published in print:
2011
Published Online:
October 2017
ISBN:
9780691136059
eISBN:
9781400840564
Item type:
chapter
Publisher:
Princeton University Press
DOI:
10.23943/princeton/9780691136059.003.0001
Subject:
Mathematics, Probability / Statistics

This chapter studies the concepts of Dirichlet form and Dirichlet space by first working with a σ‎-finite measure space (E,B(E),m) without any topological assumption on E and establish the ... More


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