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Books on the topic 'Symmetric products of curves'

Author: Grafiati

Published: 9 March 2023

Last updated: 10 March 2023

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1

McCullough, Darryl. Symmetric automorphisms of free products. Providence, R.I: American Mathematical Society, 1996.

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2

Geometric analysis on symmetric spaces. 2nd ed. Providence, R.I: American Mathematical Society, 2008.

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3

Geometric analysis on symmetric spaces. Providence, R.I: American Mathematical Society, 1994.

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4

Mahmoud, Ibrahim Mahmoud Ibrahim. On the representations of wreath products of symmetric groups. Birmingham: University of Birmingham, 1985.

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5

Gurahick, Robert M. Symmetric and alternating groups as monodromy groups of Riemann surfaces I: Generic covers and covers with many branch points. Providence, RI: American Mathematical Society, 2007.

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6

Conference on Hopf Algebras and Tensor Categories (2011 University of Almeria). Hopf algebras and tensor categories: International conference, July 4-8, 2011, University of Almería, Almería, Spain. Edited by Andruskiewitsch Nicolás 1958-, Cuadra Juan 1975-, and Torrecillas B. (Blas) 1958-. Providence, Rhode Island: American Mathematical Society, 2013.

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7

Guichardet, Alain. Symmetric Hilbert Spaces and Related Topics: Infinitely Divisible Positive Definite Functions. Continuous Products and Tensor Products. Gaussian and Poissonian Stochastic Processes. Springer London, Limited, 2006.

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8

Kerber, A. Representations of Permutation Groups I: Representations of Wreath Products and Applications to the Representation Theory of Symmetric and Alternating Groups. Springer London, Limited, 2006.

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9

Zagier, D. B. Equivariant Pontrjagin Classes and Applications to Orbit Spaces: Applications of the G-Signature Theorem to Transformation Groups, Symmetric Products and Number Theory. Springer London, Limited, 2006.

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10

(Contributor), R. Stafford, ed. Symmetric and Alternating Groups As Monodromy Groups of Riemann Surfaces 1: Generic Covers and Covers With Many Branch Points (Memoirs of the American Mathematical Society). Amer Mathematical Society, 2007.

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11

Horing, Norman J. Morgenstern. Non-Equilibrium Green’s Functions: Variational Relations and Approximations for Particle Interactions. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780198791942.003.0009.

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Chapter 09 Nonequilibrium Green’s functions (NEGF), including coupled-correlated (C) single- and multi-particle Green’s functions, are defined as averages weighted with the time-development operator U(t0+τ,t0). Linear conductivity is exhibited as a two-particle equilibrium Green’s function (Kubo-type formulation). Admitting particle sources (S:η,η+) and non-conservation of number, the non-equilibrium multi-particle Green’s functions are constructed with numbers of creation and annihilation operators that may differ, and they may be derived as variational derivatives with respect to sources η,η+ of a generating functional eW=TrU(t0+τ,t0)CS/TrU(t0+τ,t0)C. (In the non-interacting case this yields the n-particle Green’s function as a permanent/determinant of single-particle Green’s functions.) These variational relations yield a symmetric set of multi-particle Green’s function equations. Cumulants and the Linked Cluster Theorem are discussed and the Random Phase Approximation (RPA) is derived variationally. Schwinger’s variational differential formulation of perturbation theories for the Green’s function, self-energy, vertex operator, and also shielded potential perturbation theory, are reviewed. The Langreth Algebra arises from analytic continuation of integration of products of Green’s functions in imaginary time to the real-time axis with time-ordering along the integration contour in the complex time plane. An account of the Generalized Kadanoff-Baym Ansatz is presented.

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12

Khoruzhenko, Boris, and Hans-Jurgen Sommers. Characteristic polynomials. Edited by Gernot Akemann, Jinho Baik, and Philippe Di Francesco. Oxford University Press, 2018. http://dx.doi.org/10.1093/oxfordhb/9780198744191.013.19.

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This article considers characteristic polynomials and reviews a few useful results obtained in simple Gaussian models of random Hermitian matrices in the presence of an external matrix source. It first considers the products and ratio of characteristic polynomials before discussing the duality theorems for two different characteristic polynomials of Gaussian weights with external sources. It then describes the m-point correlation functions of the eigenvalues in the Gaussian unitary ensemble and how they are deduced from their Fourier transforms U(s1, … , sm). It also analyses the relation of the correlation function of the characteristic polynomials to the standard n-point correlation function using the replica and supersymmetric methods. Finally, it shows how the topological invariants of Riemann surfaces, such as the intersection numbers of the moduli space of curves, may be derived from averaged characteristic polynomials.

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13

Mann, Peter. Linear Algebra. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780198822370.003.0037.

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This chapter is key to the understanding of classical mechanics as a geometrical theory. It builds upon earlier chapters on calculus and linear algebra and frames theoretical physics in a new and useful language. Although some degree of mathematical knowledge is required (from the previous chapters), the focus of this chapter is to explain exactly what is going on, rather than give a full working knowledge of the subject. Such an approach is rare in this field, yet is ever so welcome to newcomers who are exposed to this material for the first time! The chapter discusses topology, manifolds, forms, interior products, pullback and pushforward, as well as tangent bundles, cotangent bundles, jet bundles and principle bundles. It also discusses vector fields, integral curves, flow, exterior derivatives and fibre derivatives. In addition, Lie derivatives, Lie brackets, Lie algebra, Lie–Poisson brackets, vertical space, horizontal space, groups and algebroids are explained.

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14

Mann, Peter. Differential Geometry. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780198822370.003.0038.

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This chapter is key to the understanding of classical mechanics as a geometrical theory. It builds upon earlier chapters on calculus and linear algebra and frames theoretical physics in a new and useful language. Although some degree ofmathematical knowledge is required (from the previous chapters), the focus of this chapter is to explain exactlywhat is going on, rather than give a full working knowledge of the subject. Such an approach is rare in this field, yet is ever so welcome to newcomers who are exposed to this material for the first time! The chapter discusses topology, manifolds, forms, interior products, pullback and pushforward, as well as tangent bundles, cotangent bundles, jet bundles and principle bundles. It also discusses vector fields, integral curves, flow, exterior derivatives and fibre derivatives. In addition, Lie derivatives, Lie brackets, Lie algebra, Lie–Poisson brackets, vertical space, horizontal space, groups and algebroids are explained.

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15

Садовников, Василий. Теория гетерогенного катализа. Теория хемосорбции. Publishing House Triumph, 2021. http://dx.doi.org/10.32986/978-5-40-10-01-2001.

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This monograph is a continuation of the monograph by V.V. Sadovnikov. Lateral interaction. Moscow 2006. Publishing house "Anta-Eco", 2006. ISBN 5-9730-0017-6. In this work, the foundations of the theory of heterogeneous catalysis and the theory of chemisorption are more easily formulated. The book consists of two parts, closely related to each other. These are the theoretical foundations of heterogeneous catalysis and chemisorption. In the theory of heterogeneous catalysis, an experiment is described in detail, which must be carried out in order to isolate the stages of a catalytic reaction, to find the stoichiometry of each of the stages. This experiment is based on the need to obtain the exact value of the specific surface area of the catalyst, the number of centers at which the reaction proceeds, and the output curves of each of the reaction products. The procedures for obtaining this data are described in detail. Equations are proposed and solved that allow calculating the kinetic parameters of the nonequilibrium stage and the thermodynamic parameters of the equilibrium stage. The description of the quantitative theory of chemisorption is based on the description of the motion of an atom along a crystal face. The axioms on which this mathematics should be based are formulated, the mathematical apparatus of the theory is written and the most detailed instructions on how to use it are presented. The first axiom: an atom, moving along the surface, is present only in places with minima of potential energy. The second axiom: the face of an atom is divided into cells, and the position of the atom on the surface of the face is set by one parameter: the cell number. The third axiom: the atom interacts with the surrounding material bodies only at the points of minimum potential energy. The fourth axiom: the solution of the equations is a map of the arrangement of atoms on the surface. The fifth axiom: quantitative equations are based on the concept of a statistically independent particle. The formation energies of these particles and their concentration are calculated by the developed program. The program based on these axioms allows you to simulate and calculate the interaction energies of atoms on any crystal face. The monograph is intended for students, post-graduate students and researchers studying work and working in petrochemistry and oil refining.

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