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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


Mise-en-scène

Gary D. Rhodes and Robert Singer

in Consuming Images: Film Art and the American Television Commercial

Published in print:
2020
Published Online:
September 2020
ISBN:
9781474460682
eISBN:
9781474481083
Item type:
chapter
Publisher:
Edinburgh University Press
DOI:
10.3366/edinburgh/9781474460682.003.0004
Subject:
Film, Television and Radio, Film

Chapter 3 covers mise-en-scène, specifically examining Sets and Settings, Blocking and Direct Address, Special Effects, and Animation: all that the frame contains within its physical and visible ... More


Potential-Energy Surfaces Using Expansion Methods and Neural Networks

Lionel Raff, Ranga Komanduri, Martin Hagan, and Satish Bukkapatnam

in Neural Networks in Chemical Reaction Dynamics

Published in print:
2012
Published Online:
November 2020
ISBN:
9780199765652
eISBN:
9780197563113
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/oso/9780199765652.003.0010
Subject:
Chemistry, Physical Chemistry

Expansion methods have been employed for some time to represent the potentialenergy surface for molecular systems. The basic concept involved with any expansion method is to write the PES ... More


Genetic Algorithm (GA) and Internal Energy Transfer Calculations Using Neural Network (NN) Methods

Lionel Raff, Ranga Komanduri, Martin Hagan, and Satish Bukkapatnam

in Neural Networks in Chemical Reaction Dynamics

Published in print:
2012
Published Online:
November 2020
ISBN:
9780199765652
eISBN:
9780197563113
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/oso/9780199765652.003.0011
Subject:
Chemistry, Physical Chemistry

Genetic algorithms (GA), like NNs, can be used to fit highly nonlinear functional forms, such as empirical interatomic potentials from a large ensemble of data. Briefly, a genetic algorithm uses a ... More


Overview of Some Non –Neural Network Methods for Fitting Ab Initio Potential-Energy Databases

Lionel Raff, Ranga Komanduri, Martin Hagan, and Satish Bukkapatnam

in Neural Networks in Chemical Reaction Dynamics

Published in print:
2012
Published Online:
November 2020
ISBN:
9780199765652
eISBN:
9780197563113
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/oso/9780199765652.003.0006
Subject:
Chemistry, Physical Chemistry

In this chapter, we describe results obtained by five methods that have been employed to fit ab initio potential-energy. These methods are (i) moving or modified Shepard interpolation (MSI), (ii) ... More


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