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Symmetries and Sasakian Structures

Charles P. Boyer and Krzysztof Galicki

in Sasakian Geometry

Published in print:
2007
Published Online:
January 2008
ISBN:
9780198564959
eISBN:
9780191713712
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198564959.003.0009
Subject:
Mathematics, Geometry / Topology

This chapter presents known results concerning symmetries of Sasakian structures, including a detailed study of the Sasakian automorphisms and various deformations of Sasakian structures. Homogeneous ... More


Random Polytopes

Matthias Reitzner

in New Perspectives in Stochastic Geometry

Published in print:
2009
Published Online:
February 2010
ISBN:
9780199232574
eISBN:
9780191716393
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199232574.003.0002
Subject:
Mathematics, Geometry / Topology

This chapter deals with random polytopes which are the convex hulls of random points. Recent developments concern mainly distributional aspects of functionals of random polytopes: estimates for ... More


Linear Programming

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:
10.1093/0198284616.003.0026
Subject:
Economics and Finance, Microeconomics

This is the third of five chapters on optimal programming (the typical mathematics of economics) and related issues as related to choice making. It discusses linear programming, which might appear to ... More


Entanglement, Quantum Geometry, and Projective Reality

Tony Robbin

in Shadows of Reality: The Fourth Dimension in Relativity, Cubism, and Modern Thought

Published in print:
2006
Published Online:
October 2013
ISBN:
9780300110395
eISBN:
9780300129625
Item type:
chapter
Publisher:
Yale University Press
DOI:
10.12987/yale/9780300110395.003.0008
Subject:
Society and Culture, Technology and Society

This chapter discusses the presence of four-dimensional polytopes within quantum geometry, specifically within the abstract state space of quantum information theory. It reveals that this state space ... More


The Plaid Master Picture Theorem

Richard Evan Schwartz

in The Plaid Model: (AMS-198)

Published in print:
2019
Published Online:
September 2019
ISBN:
9780691181387
eISBN:
9780691188997
Item type:
chapter
Publisher:
Princeton University Press
DOI:
10.23943/princeton/9780691181387.003.0009
Subject:
Mathematics, Educational Mathematics

This chapter aims to prove Theorem 1.4 and Theorem 0.3, the Plaid Master Picture Theorem. Both of these results are deduced from Theorem 8.2, which says that the union PLA of plaid polygons is ... More


Graph Master Picture Theorem

Richard Evan Schwartz

in The Plaid Model: (AMS-198)

Published in print:
2019
Published Online:
September 2019
ISBN:
9780691181387
eISBN:
9780691188997
Item type:
chapter
Publisher:
Princeton University Press
DOI:
10.23943/princeton/9780691181387.003.0014
Subject:
Mathematics, Educational Mathematics

This chapter aims to prove Theorem 0.4, the Graph Master Picture Theorem. Theorem 0.4 is proven in two different ways, the first proof is discussed here; it deduces Theorem 0.4 from Theorem 13.2, ... More


The Orbit Equivalence Theorem

Richard Evan Schwartz

in The Plaid Model: (AMS-198)

Published in print:
2019
Published Online:
September 2019
ISBN:
9780691181387
eISBN:
9780691188997
Item type:
chapter
Publisher:
Princeton University Press
DOI:
10.23943/princeton/9780691181387.003.0018
Subject:
Mathematics, Educational Mathematics

This chapter begins Part 4 of the monograph. The goal of this part is to prove the Orbit Equivalence Theorem and the Quasi-Isomorphism Theorem. Theorem 17.1 (Orbit Equivalence) states that there is a ... More


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