Livres : « Linear perturbation theory »

1

Jeribi, Aref. Perturbation Theory for Linear Operators. Singapore : Springer Singapore, 2021. http://dx.doi.org/10.1007/978-981-16-2528-2.

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Kato, Tosio. Perturbation Theory for Linear Operators. Berlin, Heidelberg : Springer Berlin Heidelberg, 1995. http://dx.doi.org/10.1007/978-3-642-66282-9.

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Katō, Tosio. Perturbation theory for linear operators. Berlin : Springer, 1995.

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Analytic perturbation theory for matrices and operators. Basel : Birkhäuser Verlag, 1985.

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5

Limaye, Balmohan Vishnu. Spectral perturbation and approximation with numerical experiments. [Canberra] : Centre for Mathematical Analysis, Australian National University, 1987.

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6

Craig, Ian J. D. Linear theory of fast reconnection at an X-type neutral point. Hamilton, N.Z : University of Waikato, 1992.

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Exponentially dichotomous operators and applications. Basel : Birkhäuser, 2008.

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Operator functions and localization of spectra. Berlin : Springer, 2003.

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9

Myo-Taeg, Lim, dir. Optimal control of singularly perturbed linear systems and applications : High-accuracy techniques. New York : Marcel Dekker, 2001.

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10

United States. National Aeronautics and Space Administration., dir. Comparison of dynamical approximation schemes for non-linear gravitational clustering. [Washington, D.C : National Aeronautics and Space Administration, 1995.

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Aganović, Zijad. Linear optimal control of bilinear systems : With applications to singular perturbations and weak coupling. Berlin : Springer, 1995.

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service), SpringerLink (Online, dir. Large-Scale Perturbations of Magnetohydrodynamic Regimes : Linear and Weakly Nonlinear Stability Theory. Berlin, Heidelberg : Springer-Verlag Berlin Heidelberg, 2011.

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13

1958-, Reuter Martin, dir. Classical and quantum dynamics : From classical paths to path integrals. 2^e éd. Berlin : Springer-Verlag, 1994.

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Dittrich, Walter. Classical and quantum dynamics : From classical paths to path integrals. Berlin : Springer-Verlag, 1992.

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1958-, Reuter Martin, dir. Classical and quantum dynamics : From classical paths to path integrals. 3^e éd. Berlin : Springer, 2001.

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16

Kato, Tosio. Perturbation Theory for Linear Operators. Springer London, Limited, 2013.

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Kato, Tosio. Perturbation Theory for Linear Operators. Springer London, Limited, 2012.

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18

Jeribi, Aref. Perturbation Theory for Linear Operators : Denseness and Bases with Applications. Springer, 2022.

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Jeribi, Aref. Perturbation Theory for Linear Operators : Denseness and Bases with Applications. Springer Singapore Pte. Limited, 2021.

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Faris, W. G. Self-Adjoint Operators. Springer London, Limited, 2006.

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21

Gajic, Zoran. Optimal Control of Singularly Perturbed Linear Systems and Applications (Control Engineering, Number 7). CRC, 2001.

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Gajic, Zoran. Optimal Control of Singularly Perturbed Linear Systems and Applications. Taylor & Francis Group, 2001.

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Gajic, Zoran. Optimal Control of Singularly Perturbed Linear Systems and Applications. Taylor & Francis Group, 2001.

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Gajic, Zoran. Optimal Control of Singularly Perturbed Linear Systems and Applications. Taylor & Francis Group, 2001.

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25

Cornelis V. M. van der Mee. Exponentially Dichotomous Operators and Applications. Springer London, Limited, 2008.

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Gajic, Zoran. Optimal Control of Singularly Perturbed Linear Systems and Applications. Taylor & Francis Group, 2001.

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Gajic, Zoran. Optimal Control of Singularly Perturbed Linear Systems and Applications. Taylor & Francis Group, 2001.

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Gil', Michael I. Operator Functions and Localization of Spectra. Springer, 2004.

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29

Autschbach, Jochen. Quantum Theory for Chemical Applications. Oxford University Press, 2020. http://dx.doi.org/10.1093/oso/9780190920807.001.0001.

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‘Quantum Theory for Chemical Applications (QTCA): From basic concepts to advanced topics’ is an introduction to quantum theory for students and practicing researchers in chemistry, chemical engineering, or materials chemistry. The text is self-contained such that only knowledge of high school physics, college introductory calculus, and college general chemistry is required, and it features many worked-out exercises. QTCA places special emphasis on the orbital models that are central to chemical applications of quantum theory. QTCA treats the important basic topics that a quantum theory text for chemistry must cover, and less-often treated models, such as the postulates of quantum theory and the mathematical background, the particle in a box, in a cylinder, and in a sphere, the harmonic oscillator and molecular vibrations, atomic and molecular orbitals, electron correlation, perturbation theory, and the basic aspects of various spectroscopies. Additional basic and advanced topics advanced topics that are covered in QTCA are band structure theory, relativistic quantum theory and its relevance to chemistry, the interactions of atoms and molecules with electromagnetic fields, and response theory. Finally, while it is not primarily a guide to computational chemistry, QTCA provides a solid theoretical background for many of the quantum chemistry methods used in contemporary research and in undergraduate computational chemistry laboratory courses. The text includes several appendices with important mathematical background, such as linear algebra and point group symmetry.

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Sjöstrand, Johannes. Non-Self-Adjoint Differential Operators, Spectral Asymptotics and Random Perturbations. Birkhäuser, 2019.

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31

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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32

Deruelle, Nathalie, et Jean-Philippe Uzan. Cosmological perturbations. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780198786399.003.0061.

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This chapter describes the first steps toward an understanding of large structures, which are observed in the universe at all scales—galaxies, groups of galaxies, and galactic clusters. It does so by studying the evolution of perturbations at linear order in Friedmann–Lemaître spacetimes. To simplify the discussion, the chapter limits the scope to the textbook case where the spatial sections of the background space are Euclidean (K = 0), and anisotropic perturbations and entropy perturbations are absent. This basically means that the matter reduces to a single fluid. The relativistic and Newtonian theories of cosmological perturbations differ. Finally, the chapter discusses the limit in which they converge.

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Edmunds, D. E., et W. D. Evans. Unbounded Linear Operators. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780198812050.003.0003.

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This chapter is concerned with closable and closed operators in Hilbert spaces, especially with the special classes of symmetric, J-symmetric, accretive and sectorial operators. The Stone–von Neumann theory of extensions of symmetric operators is treated as a special case of results for compatible adjoint pairs of closed operators. Also discussed in detail is the stability of closedness and self-adjointness under perturbations. The abstract results are applied to operators defined by second-order differential expressions, and Sims’ generalization of the Weyl limit-point, limit-circle characterization for symmetric expressions to J-symmetric expressions is proved.

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Szeftel, Jérémie, et Sergiu Klainerman. Global Nonlinear Stability of Schwarzschild Spacetime under Polarized Perturbations. Princeton University Press, 2020. http://dx.doi.org/10.23943/princeton/9780691212425.001.0001.

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One of the major outstanding questions about black holes is whether they remain stable when subject to small perturbations. An affirmative answer to this question would provide strong theoretical support for the physical reality of black holes. This book takes an important step toward solving the fundamental black hole stability problem in general relativity by establishing the stability of nonrotating black holes — or Schwarzschild spacetimes — under so-called polarized perturbations. This restriction ensures that the final state of evolution is itself a Schwarzschild space. Building on the remarkable advances made in the past fifteen years in establishing quantitative linear stability, the book introduces a series of new ideas to deal with the strongly nonlinear, covariant features of the Einstein equations. Most preeminent among them is the general covariant modulation (GCM) procedure that allows them to determine the center of mass frame and the mass of the final black hole state. Essential reading for mathematicians and physicists alike, the book introduces a rich theoretical framework relevant to situations such as the full setting of the Kerr stability conjecture.

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Deruelle, Nathalie, et Jean-Philippe Uzan. Gravitational radiation. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780198786399.003.0054.

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This chapter attempts to calculate the radiated energy of a source in the linear approximation of general relativity to infinity in the lowest order. For this, the chapter first expands the Einstein equations to quadratic order in metric perturbations. It reveals that the radiated energy is then given by the (second) quadrupole formula, which is the gravitational analog of the dipole formula in Maxwell theory. This formula is a priori valid only if the motion of the source is due to forces other than gravity. Finally, this chapter shows that, to prove this formula for the case of self-gravitating systems, the Einstein equations to quadratic order must be solved, and the radiative field in the post-linear approximation of general relativity obtained.

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36

Gies, Holger, et Walter Dittrich. Probing the Quantum Vacuum : Perturbative Effective Action Approach in Quantum Electrodynamics and Its Application. Springer London, Limited, 2006.

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Gies, Holger, et Walter Dittrich. Probing the Quantum Vacuum : Perturbative Effective Action Approach in Quantum Electrodynamics and Its Application. Springer Berlin / Heidelberg, 2010.

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38

Deruelle, Nathalie, et Jean-Philippe Uzan. The two-body problem and radiative losses. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780198786399.003.0055.

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This chapter begins by finding the field created by compact objects in the post-linear approximation of general relativity. The second quadrupole formula is then completely proven. Next, the chapter finds the equations of motion of the bodies in the field which they create to second order in the perturbations, assuming that their velocities are small. It shows that, to correctly describe the radiation reaction at 2.5 PN order, it will prove necessary to iterate Einstein equations a third time. This leads the discussion to the equations of motion, which generalize to order 1/c5 the EIH equations of order 1/c⁲. Finally, the chapter studies the effect of the radiation reaction force on the sources, and shows that there is an energy balance at 2.5 PN order between the energy radiated to infinity and the mechanical energy lost by the system.

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Mann, Peter. Near-Equilibrium Oscillations. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780198822370.003.0012.

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In this chapter, the theory of near-equilibrium oscillations is developed and normal mode analysis is performed. This topic requires a little bit of linear algebra when dealing with matrices, as well as an understanding of differential equations. The chapter explores small perturbations (small nudges or tiny shifts) to a stable equilibrium point in configuration space and introduces the characteristic equation. Interdisciplinary examples are then investigated, including a surface science example in which the bond frequencies of surface adsorbates are calculated, an example in which the motion of atoms in a triatomic molecule is examined and an example in which the molecular physics of atomic force microscopy is analysed. The properties of the eigenvalue problem for small oscillations are also investigated.

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Probing the Quantum Vacuum : Perturbative Effective Action Approach in Quantum Electrodynamics and Its Applications (Springer Tracts in Modern Physics). Springer, 2000.

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41

Deruelle, Nathalie, et Jean-Philippe Uzan. Tests in the solar system. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780198786399.003.0051.

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This chapter describes observable relativistic effects in the solar system. In the solar system we can, as a first approximation, neglect the gravitational field of all the stars except the Sun. In Newtonian theory, the planet trajectories are then Keplerian ellipses. Relativistic effects are weak because the dimensionless ratio characterizing them is everywhere less than GM⊙/c² R⊙≃ 2 × 10–6, and so they can be added linearly to the Newtonian perturbations due to the other planets, the non-spherical shape of celestial bodies, and so on. The chapter first describes the gravitational field of the Sun using a Schwarzschild spacetime, before moving on to look at the geodesic equation. It also discusses the bending of light, the Shapiro effect, the perihelion, post-Keplerian geodesics, and spin in a gravitational field.

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42

De Bono, Christopher, Magali Théveniau-Ruissy et Robert G. Kelly. Cardiac fields and myocardial cell lineages. Sous la direction de José Maria Pérez-Pomares, Robert G. Kelly, Maurice van den Hoff, José Luis de la Pompa, David Sedmera, Cristina Basso et Deborah Henderson. Oxford University Press, 2018. http://dx.doi.org/10.1093/med/9780198757269.003.0004.

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We focus on the origin of myocardial cells in the first and second heart fields in splanchnic mesoderm in the early embryo. Genetic lineage tracing using Cre recombinase activated conditional reporter genes has made a major contribution to our understanding of cardiac progenitor cells and will be discussed together with other experimental approaches to analysing cell lineages at the clonal level. Interactions between myocardial, epicardial and endocardial lineages are essential for coordinated function and homeostasis of the normal heart. Perturbation of heart field development and myocardial lineage contributions to the heart through developmental or acquired pathologies results in and modulates the progression of cardiac disease. Understanding the origin of myocardial lineages during embryonic development and how they converge to generate an integrated heart is thus a major biomedical objective. Furthermore, reactivation of developmental programmes is likely to be of major importance in strategies aimed at repair of the damaged heart.

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43

Tiwari, Sandip. Semiconductor Physics. Oxford University Press, 2020. http://dx.doi.org/10.1093/oso/9780198759867.001.0001.

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A graduate-level text, Semiconductor physics: Principles, theory and nanoscale covers the central topics of the field, together with advanced topics related to the nanoscale and to quantum confinement, and integrates the understanding of important attributes that go beyond the conventional solid-state and statistical expositions. Topics include the behavior of electrons, phonons and photons; the energy and entropic foundations; bandstructures and their calculation; the behavior at surfaces and interfaces, including those of heterostructures and their heterojunctions; deep and shallow point perturbations; scattering and transport, including mesoscale behavior, using the evolution and dynamics of classical and quantum ensembles from a probabilistic viewpoint; energy transformations; light-matter interactions; the role of causality; the connections between the quantum and the macroscale that lead to linear responses and Onsager relationships; fluctuations and their connections to dissipation, noise and other attributes; stress and strain effects in semiconductors; properties of high permittivity dielectrics; and remote interaction processes. The final chapter discusses the special consequences of the principles to the variety of properties (consequences of selection rules, for example) under quantum-confined conditions and in monolayer semiconductor systems. The text also bring together short appendices discussing transform theorems integral to this study, the nature of random processes, oscillator strength, A and B coefficients and other topics important for understanding semiconductor behavior. The text brings the study of semiconductor physics to the same level as that of the advanced texts of solid state by focusing exclusively on the equilibrium and off-equilibrium behaviors important in semiconductors.

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Ross, John, Igor Schreiber et Marcel O. Vlad. Determination of Complex Reaction Mechanisms. Oxford University Press, 2006. http://dx.doi.org/10.1093/oso/9780195178685.001.0001.

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In a chemical system with many chemical species several questions can be asked: what species react with other species: in what temporal order: and with what results? These questions have been asked for over one hundred years about simple and complex chemical systems, and the answers constitute the macroscopic reaction mechanism. In Determination of Complex Reaction Mechanisms authors John Ross, Igor Schreiber, and Marcel Vlad present several systematic approaches for obtaining information on the causal connectivity of chemical species, on correlations of chemical species, on the reaction pathway, and on the reaction mechanism. Basic pulse theory is demonstrated and tested in an experiment on glycolysis. In a second approach, measurements on time series of concentrations are used to construct correlation functions and a theory is developed which shows that from these functions information may be inferred on the reaction pathway, the reaction mechanism, and the centers of control in that mechanism. A third approach is based on application of genetic algorithm methods to the study of the evolutionary development of a reaction mechanism, to the attainment given goals in a mechanism, and to the determination of a reaction mechanism and rate coefficients by comparison with experiment. Responses of non-linear systems to pulses or other perturbations are analyzed, and mechanisms of oscillatory reactions are presented in detail. The concluding chapters give an introduction to bioinformatics and statistical methods for determining reaction mechanisms.

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Convection Diffusion Problems : An Introduction to Their Analysis and Numerical Solution. American Mathematical Society, 2018.

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Corsi, Ilaria, et Luis Fernando Marques-Santos, dir. Ecotoxicology in Marine Environments : The Protective Role of ABC Transporters in Sea Urchin Embryos and Larvae. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780198786962.003.0018.

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Anthropogenic contaminants with the potential to disrupt biological functions enter aquatic ecosystems from a variety of sources, and pose a potential risk to the long-term sustainability of these ecosystems. Sea urchin embryos and larvae, largely used in developmental biology, have great sensitivity toward environmental perturbations, including several anthropogenic stressors. Much attention has recently been devoted to the sea urchin “chemical defensome,” or genes predicted to be involved in chemical defense to confer resilience and survival to developing embryos, with special attention to the ATP-binding cassette (ABC) transporter genes. The present chapter discusses the role of ABC transporters as the first line of cell defense against both natural and anthropogenic toxicants and their relevance to ecotoxicological studies, including the identification of substrates or inhibitors among natural and anthropogenic toxins and contaminants as well as the circumvention of the multixenobiotic resistance phenotype in realistic exposure scenarios.

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47

Dittrich, Walter, et Martin Reuter. Classical and Quantum Dynamics : From Classical Paths to Path Integrals. Springer, 2020.

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Dittrich, Walter, et Martin Reuter. Classical and Quantum Dynamics : From Classical Paths to Path Integrals. Springer, 2015.

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Dittrich, Walter, et Martin Reuter. Classical and Quantum Dynamics : From Classical Paths to Path Integrals. Springer, 2011.

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Classical and Quantum Dynamics : From Classical Paths to Path Integrals. Springer, 2012.

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