Titlebook: Random Matrix Theory with an External Source; Edouard Brézin,Shinobu Hikami Book 2016 The Author(s) 2016 Random matrix theory.Gaussian ran

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invert

Open Intersection Numbers,The intersection numbers are defined on the moduli space of Riemann surface with .-marked points and genus .. When Riemann surface is cut and has boundary, the open intersection numbers appear. There appear open strings which touch to the boundary.

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,Gromov–Witten Invariants, P, Model,The intersection numbers of .-spin curves is a simple example of more general Gromov–Witten invariants, where the manifold . is a point.

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2197-1757 of characteristic polynomials is essential for obtaining such topological invariants. The analysis is extended to nonorientable surfaces and to surfaces with boundaries..978-981-10-3315-5978-981-10-3316-2Series ISSN 2197-1757 Series E-ISSN 2197-1765

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text, Immigration Processes and Health in the U.S.: A Brief History, Alternative and Complementary Medicine, Culture-Specific Diagnoses, Health Determinants, Occupational and Environmental Health, Methodologica978-1-4419-5659-0

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Book 2016r characteristics, and the Gromov–Witten invariants. A remarkable duality for the average of characteristic polynomials is essential for obtaining such topological invariants. The analysis is extended to nonorientable surfaces and to surfaces with boundaries..

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Intersection Numbers of Curves,chy. Kontsevich (Commun Math Phys 147:1–23, 1992, [89]) has proved this conjecture with the use of an Airy matrix model. In addition it has been realized that matrix models of this type are examples of an exact closed/open strings duality (Gaiotto and Rastelli, JHEP 07:053, 2005, [63]).