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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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