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Books on the topic 'Jacobian matrix'

Author: Grafiati

Published: 4 June 2021

Last updated: 1 February 2022

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1

Reider, Igor. Nonabelian Jacobian of Projective Surfaces: Geometry and Representation Theory. Berlin, Heidelberg: Springer Berlin Heidelberg, 2013.

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2

Vinokur, Marcel. Flux Jacobian matrices and generalized Roe average for an equilibrium real gas. Washington, D. C: NASA, 1988.

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3

Jacobians of matrix transformations and functions of matrix argument. Singapore: World Scientific Pub., 1997.

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4

Engel, Andreas. Taylorentwicklung, Jacobi-Matrix, ∇, δ(x) und Co. Berlin, Heidelberg: Springer Berlin Heidelberg, 2020. http://dx.doi.org/10.1007/978-3-662-59752-1.

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5

Almazán, Vicente. Alsacia jacobea: Introducción al estudio de las peregrinaciones alsacianas a Santiago de Compostela : historia, literatura, arte. Vigo, Galicia: Nigra Arte, 1994.

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6

Litvinov, G. L. (Grigoriĭ Lazarevich), 1944- editor of compilation and Sergeev, S. N., 1981- editor of compilation, eds. Tropical and idempotent mathematics and applications: International Workshop on Tropical and Idempotent Mathematics, August 26-31, 2012, Independent University, Moscow, Russia. Providence, Rhode Island: American Mathematical Society, 2014.

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7

Center, Ames Research, ed. Flux Jacobian matrices and generalized Roe average for an equilibrium real gas. Moffett Field, Calif: National Aeronautics and Space Administration, Ames Research Center, 1989.

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8

Tanasa, Adrian. Combinatorial Physics. Oxford University Press, 2021. http://dx.doi.org/10.1093/oso/9780192895493.001.0001.

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After briefly presenting (for the physicist) some notions frequently used in combinatorics (such as graphs or combinatorial maps) and after briefly presenting (for the combinatorialist) the main concepts of quantum field theory (QFT), the book shows how algebraic combinatorics can be used to deal with perturbative renormalisation (both in commutative and non-commutative quantum field theory), how analytic combinatorics can be used for QFT issues (again, for both commutative and non-commutative QFT), how Grassmann integrals (frequently used in QFT) can be used to proCve new combinatorial identities (generalizing the Lindström–Gessel–Viennot formula), how combinatorial QFT can bring a new insight on the celebrated Jacobian conjecture (which concerns global invertibility of polynomial systems) and so on. In the second part of the book, matrix models, and tensor models are presented to the reader as QFT models. Several tensor model results (such as the implementation of the large N limit and of the double-scaling limit for various such tensor models, N being here the size of the tensor) are then exposed. These results are natural generalizations of results extensively used by theoretical physicists in the study of matrix models and they are obtained through intensive use of combinatorial techniques (this time mainly enumerative techniques). The last part of the book is dedicated to the recently discovered relation between tensor models and the holographic Sachdev–Ye–Kitaev model, model which has been extensively studied in the last years by condensed matter and by high-energy physicists.

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9

Engel, Andreas. Taylorentwicklung, Jacobi-Matrix, ∇, δ und Co.: Rechenmethoden für Studierende der Physik. Springer Spektrum, 2020.

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10

Anderson, Greg W. Spectral statistics of orthogonal and symplectic ensembles. Edited by Gernot Akemann, Jinho Baik, and Philippe Di Francesco. Oxford University Press, 2018. http://dx.doi.org/10.1093/oxfordhb/9780198744191.013.5.

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This article describes a direct approach for computing scalar and matrix kernels, respectively for the unitary ensembles on the one hand and the orthogonal and symplectic ensembles on the other hand, leading to correlation functions and gap probabilities. In the classical orthogonal polynomials (Hermite, Laguerre, and Jacobi), the matrix kernels for the orthogonal and symplectic ensemble are expressed in terms of the scalar kernel for the unitary case, using the relation between the classical orthogonal polynomials going with the unitary ensembles and the skew-orthogonal polynomials going with the orthogonal and symplectic ensembles. The article states the fundamental theorem relating the orthonormal and skew-orthonormal polynomials that enter into the Christoffel-Darboux kernels

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11

Tensor-GMRES method for large sparse systems of nonlinear equations. [Moffett Field, Calif.]: Research Institute for Advanced Computer Science, NASA Ames Research Center, 1994.

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12

H, Pulliam Thomas, and Research Institute for Advanced Computer Science (U.S.), eds. Tensor-GMRES method for large sparse systems of nonlinear equations. [Moffett Field, Calif.]: Research Institute for Advanced Computer Science, NASA Ames Research Center, 1994.

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13

Tensor-GMRES method for large sparse systems of nonlinear equations. [Moffett Field, Calif.]: Research Institute for Advanced Computer Science, NASA Ames Research Center, 1994.

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14

Rajeev, S. G. Vector Fields. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780198805021.003.0001.

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The velocity of a fluid at each point of space-time is a vector field (or flow). It is best to think of it in terms of the effect of fluid flow on some scalar field. A vector field is thus a first order partial differential operator, called the material derivative in fluid mechanics. The path of a speck of dust carried along (advected) by the fluid is the integral curve of the velocity field. Even simple vector fields can have quite complicated integral curves: a manifestation of chaos. Of special interest are incompressible (with zero divergence) and irrotational (with zero curl) flows. A fixed point of a vector field is a point at which it vanishes. The derivative of a vector field at a fixed point is a matrix (the Jacobi matrix) whose spectrum is independent of the choice of coordinates.

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15

Dyson, Freeman. Spectral statistics of unitary ensembles. Edited by Gernot Akemann, Jinho Baik, and Philippe Di Francesco. Oxford University Press, 2018. http://dx.doi.org/10.1093/oxfordhb/9780198744191.013.4.

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This article focuses on the use of the orthogonal polynomial method for computing correlation functions, cluster functions, gap probability, Janossy density, and spacing distributions for the eigenvalues of matrix ensembles with unitary-invariant probability law. It first considers the classical families of orthogonal polynomials (Hermite, Laguerre, and Jacobi) and some corresponding unitary ensembles before discussing the statistical properties of N-tuples of real numbers. It then reviews the definitions of basic statistical quantities and demonstrates how their distributions can be made explicit in terms of orthogonal polynomials. It also describes the k-point correlation function, Fredholm determinants of finite-rank kernels, and resolvent kernels.

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