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Auteur : Grafiati

Publié le 11 mars 2023

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1

Matveev, S. V. Algoritmicheskie i kompʹi͡u︡ternye metody v trekhmernoĭ topologii. Moskva : Izd-vo Moskovskogo universiteta, 1991.

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2

T, Fomenko A., dir. Algoritmicheskie i kompʹi͡u︡ternye metody v trekhmernoĭ topologii. 2^e éd. Moskva : Nauka, 1998.

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3

Chekhovich, E. K. Optiko-ėlektronnye metody avtomatizirovannogo kontroli͡a︡ topologii izdeliĭ mikroėlektroniki. Minsk : "Nauka i tekhnika", 1989.

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4

A topological picturebook. New York : Springer-Verlag, 1987.

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5

Novotny, Antonio André, Jan Sokołowski et Antoni Żochowski. Applications of the Topological Derivative Method. Cham : Springer International Publishing, 2019. http://dx.doi.org/10.1007/978-3-030-05432-8.

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6

I, Sobolevskiĭ P., et I͡A︡novich L. A, dir. Priblizhennye metody vychislenii͡a︡ kontinualʹnykh integralov. Minsk : "Nauka i tekhnika", 1985.

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7

Novotny, Antonio André, et Jan Sokołowski. An Introduction to the Topological Derivative Method. Cham : Springer International Publishing, 2020. http://dx.doi.org/10.1007/978-3-030-36915-6.

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8

Petrovich, Novikov Sergeĭ, et Fomenko A. T, dir. Sovremennai͡a︡ geometrii͡a︡ : Metody i prilozhenii͡a︡. 2^e éd. Moskva : "Nauka," Glav. red. fiziko-matematicheskoĭ lit-ry, 1986.

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9

Paolo, Soriani, dir. The N=2 wonderland : From Calabi-Yau manifolds to topological field-theories. Singapore : World Scientific Pub., 1995.

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10

Operational quantum theory. New York : Springer, 2006.

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11

Spinors in four-dimensional spaces. New York : Springer/Birkhäuser, 2010.

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12

Daniele, Boffi, et Centro internazionale matematico estivo. Summer School, dir. Mixed finite elements, compatibility conditions, and applications : Lectures given at the C.I.M.E. Summer School held in Cetraro, Italy, June 26 - July 1, 2006. Berlin : Springer, 2008.

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13

Sobczyk, Garret. New Foundations in Mathematics : The Geometric Concept of Number. Boston : Birkhäuser Boston, 2013.

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14

Bilinear control systems : Matrices in action. Dordrecht : Springer, 2009.

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15

Meinrenken, Eckhard. Clifford Algebras and Lie Theory. Berlin, Heidelberg : Springer Berlin Heidelberg, 2013.

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16

Block, L. S. Dynamics in one dimension. Berlin : Springer-Verlag, 1992.

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17

A, Comtet, North Atlantic Treaty Organization. Scientific Affairs Division. et NATO Advanced Study Institute (1998 : Les Houches, Haute-Savoie, France), dir. Aspects topologiques de la physique en basse dimension = : Topological aspects of low dimensional systems : Ecole de Physique des Houches - UJF & INPG - Grenoble, Les Houches, Session LXIX, 7-31 July 1998. Les Ulis, France : EDP Sciences, 1999.

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18

Rudolph, Gerd. Differential Geometry and Mathematical Physics : Part I. Manifolds, Lie Groups and Hamiltonian Systems. Dordrecht : Springer Netherlands, 2013.

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19

Arnold, Johnson L., Rosenthal Lynne et National Institute of Standards and Technology (U.S.), dir. Model for Test Method Executive Control Committee (TMECC) organization and procedures part of United States Geological Survey recognition of Spatial Data Transfer Standard (SDTS) Topological Vector Profile (TVP) certification system. Gaithersburg, MD : U.S. Dept. of Commerce, Technology Administration, National Institute of Standards and Technology, 1998.

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20

Gelʹfand, I. M. Representation theory and automorphic functions. Providence, Rhode Island : American Mathematical Society : AMS Chelsea Publishing, 2016.

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21

R, Johnson Christopher, Rumf Martin, Scheuermann Gerik, Polthier Konrad, Hege Hans-Christian 1954-, Hoffman David et SpringerLink (Online service), dir. Topology-Based Methods in Visualization II. Berlin, Heidelberg : Springer Berlin Heidelberg, 2009.

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22

David, Goforth, dir. The topology of the 2x2 games : A new periodic table / David Robinson, David Goforth. London : Routledge, 2005.

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23

service), SpringerLink (Online, dir. Families of conformally covariant differential operators, Q-curvature and holography. Basel : Birkhäuser, 2009.

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24

Dynamical systems and group actions. Providence, R.I : American Mathematical Society, 2012.

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25

1963-, Bonifant Araceli, dir. Dynamical systems (1953-2000). Providence, Rhode Island : American Mathematical Society, 2012.

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26

Representation theory and mathematical physics : Conference in honor of Gregg Zuckerman's 60th birthday, October 24--27, 2009, Yale University. Providence, R.I : American Mathematical Society, 2011.

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27

Doran, Robert S., 1937- editor of compilation, Friedman, Greg, 1973- editor of compilation et Nollet, Scott, 1962- editor of compilation, dir. Hodge theory, complex geometry, and representation theory : NSF-CBMS Regional Conference in Mathematics, June 18, 2012, Texas Christian University, Fort Worth, Texas. Providence, Rhode Island : American Mathematical Society, 2013.

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28

service), SpringerLink (Online, dir. Nonlinear Waves and Solitons on Contours and Closed Surfaces. 2^e éd. Berlin, Heidelberg : Springer Berlin Heidelberg, 2012.

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29

Simon, Barry. Operator theory. Providence, Rhode Island : American Mathematical Society, 2015.

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30

1973-, Johnson Mark W., dir. A foundation for PROPs, algebras, and modules. Providence, Rhode Island : American Mathematical Society, 2015.

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31

1937-, Doran Robert S., Sally Paul et Spice Loren 1981-, dir. Harmonic analysis on reductive, p-adic groups : AMS Special Session on Harmonic Analysis and Representations of Reductive, p-adic Groups, January 16, 2010, San Francisco, CA. Providence, R.I : American Mathematical Society, 2011.

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32

author, Tian Gang 1958, dir. The geometrization conjecture. Providence, Rhode Island : American Mathematical Society, 2014.

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33

A Topological Picturebook. Springer, 2006.

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34

Jan Sokołowski, Antoni Żochowski et Antonio André Novotny. Applications of the Topological Derivative Method. Springer International Publishing AG, 2019.

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35

Sokolowski, Jan, et Antonio André Novotny. Introduction to the Topological Derivative Method. Springer International Publishing AG, 2020.

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36

Saitoh, E. Topological spin current. Oxford University Press, 2017. http://dx.doi.org/10.1093/oso/9780198787075.003.0004.

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This chapter discusses another type of equilibrium-spin current similar to the exchange-spin current—the topological spin current. Topological spin currents are driven by topological-band structure and classified into bulk and surface topological spin currents. The former is confined onto electron-band manifolds, sometimes affecting their motions. This confinement is addressed through the standard method of combining the equations of motion and the Boltzmann equation for semi-classical electrons in a band. The latter class, on the other hand, is a surface-spin current, which is limited near surfaces of a three-dimensional system and flows along these surfaces. This type is known to appear in topological insulators, where the bulk is insulating but the surface or edge is electrically conducting due to the surface or edge state.

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37

Saito, Masahico, et Nataša Jonoska. Discrete and Topological Models in Molecular Biology. Springer, 2013.

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38

Saito, Masahico, et Nataša Jonoska. Discrete and Topological Models in Molecular Biology. Springer, 2016.

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39

Murakami, S., et T. Yokoyama. Quantum spin Hall effect and topological insulators. Oxford University Press, 2017. http://dx.doi.org/10.1093/oso/9780198787075.003.0017.

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This chapter begins with a description of quantum spin Hall systems, or topological insulators, which embody a new quantum state of matter theoretically proposed in 2005 and experimentally observed later on using various methods. Topological insulators can be realized in both two dimensions (2D) and in three dimensions (3D), and are nonmagnetic insulators in the bulk that possess gapless edge states (2D) or surface states (3D). These edge/surface states carry pure spin current and are sometimes called helical. The novel property for these edge/surface states is that they originate from bulk topological order, and are robust against nonmagnetic disorder. The following sections then explain how topological insulators are related to other spin-transport phenomena.

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40

Boudreau, Joseph F., et Eric S. Swanson. Classical spin systems. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780198708636.003.0020.

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The thermodynamic properties of spin systems are evaluated with Monte Carlo methods. A review of classical thermodynamics is followed by a discussion of critical exponents. The Monte Carlo method is then applied to the two-dimensional Ising model with the goal of determining the phase diagram for magnetization. Boundary conditions, the reweighting method, autocorrelation, and critical slowing down are all explored. Cluster algorithms for overcoming critical slowing down are developed next and shown to dramatically reduce autocorrelation. A variety of spin systems that illustrate first, second, and infinite order (topological) phase transitions are explored. Finally, applications to random systems called spin glasses and to neural networks are briefly reviewed.

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41

Topological Invariants for Projection Method Patterns (Memoirs of the American Mathematical Society, No. 758). American Mathematical Society, 2002.

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42

Lectures on Topological Fluid Mechanics Lecture Notes in Mathematics. Springer, 2009.

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43

Paycha, Sylvie, Hernan Ocampo et Andrés Vargas. Geometric and Topological Methods for Quantum Field Theory. Springer, 2010.

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44

Paycha, Sylvie, Hernan Ocampo et Eddy Pariguan. Geometric and Topological Methods for Quantum Field Theory. Cambridge University Press, 2010.

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45

Paycha, Sylvie, Hernan Ocampo et Eddy Pariguan. Geometric and Topological Methods for Quantum Field Theory. Cambridge University Press, 2010.

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46

Sikorski, Krzysztof A. Optimal Solution of Nonlinear Equations. Oxford University Press, 2001. http://dx.doi.org/10.1093/oso/9780195106909.001.0001.

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Optimal Solution of Nonlinear Equations is a text/monograph designed to provide an overview of optimal computational methods for the solution of nonlinear equations, fixed points of contractive and noncontractive mapping, and for the computation of the topological degree. It is of interest to any reader working in the area of Information-Based Complexity. The worst-case settings are analyzed here. Several classes of functions are studied with special emphasis on tight complexity bounds and methods which are close to or achieve these bounds. Each chapter ends with exercises, including companies and open-ended research based exercises.

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47

Eynard, Bertrand. Random matrices and loop equations. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780198797319.003.0007.

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This chapter is an introduction to algebraic methods in random matrix theory (RMT). In the first section, the random matrix ensembles are introduced and it is shown that going beyond the usual Wigner ensembles can be very useful, in particular by allowing eigenvalues to lie on some paths in the complex plane rather than on the real axis. As a detailed example, the Plancherel model is considered from the point of RMT. The second section is devoted to the saddle-point approximation, also called the Coulomb gas method. This leads to a system of algebraic equations, the solution of which leads to an algebraic curve called the ‘spectral curve’ which determines the large N expansion of all observables in a geometric way. Finally, the third section introduces the ‘loop equations’ (i.e., Schwinger–Dyson equations associated with matrix models), which can be solved recursively (i.e., order by order in a semi-classical expansion) by a universal recursion: the ‘topological recursion’.

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48

Bonifant, Araceli, Misha Lyubich et Scott Sutherland. Frontiers in Complex Dynamics : In Celebration of John Milnor's 80th Birthday. Princeton University Press, 2014.

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49

Bonifant, Araceli, Misha Lyubich et Scott Sutherland. Frontiers in Complex Dynamics : In Celebration of John Milnor's 80th Birthday. Princeton University Press, 2014.

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50

Fre, Pietro, et Paolo Soriani. The N=2 Wonderland : From Calabi-Yau Manifolds to Topological Field Theories. World Scientific Publishing Company, 1995.

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