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1

Kamiński, Marcin. The Stochastic Perturbation Method for Computational Mechanics. Chichester, UK: John Wiley & Sons, Ltd, 2013. http://dx.doi.org/10.1002/9781118481844.

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2

H, Miller John J., ed. Singular perturbation problems in chemical physics: Analytic and computational methods. New York: J. Wiley, 1997.

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3

Freidman, M. J. Accurate computation and continuation of homoclinic and heteroclinic orbits for singular perturbation problems. [Washington, DC]: National Aeronautics and Space Administration, Office of Management, Scientific and Technical Information Program, 1993.

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4

Friedman, M. J. Accurate computation and continuation of homoclinic and heteroclinic orbits for singular perturbation problems. Huntsvilla, Ala: George C. Marshall Space Flight Center, 1993.

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5

Celestial mechanics: A computational guide for the practitioner. New York: Wiley, 1985.

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6

Lindquist, Dana R. Computation of unsteady transonic flowfields using shock capturing and the linear perturbation Euler equations. Cambridge, Mass: Gas Turbine Laboratory, Massachusetts Institute of Technology, 1991.

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7

C, Monteiro A., and United States. National Aeronautics and Space Administration., eds. Accurate computation and continuation of homoclinic and heteroclinic orbits for singular perturbation problems: Preliminary technical report for the period February 22, 1990, through October 21, 1992. [Huntsville, Ala.]: Research Institute, University of Alabama in Huntsville, 1992.

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8

Stanley, Turner Michael, Fermi National Accelerator Laboratory, and United States. National Aeronautics and Space Administration., eds. Second-order reconstruction of the inflationary potential. Batavia, IL: Fermi National Accelerator Laboratory, 1994.

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9

Stanley, Turner Michael, Fermi National Accelerator Laboratory, and United States. National Aeronautics and Space Administration., eds. Second-order reconstruction of the inflationary potential. Batavia, IL: Fermi National Accelerator Laboratory, 1994.

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10

Stanley, Turner Michael, Fermi National Accelerator Laboratory, and United States. National Aeronautics and Space Administration., eds. Second-order reconstruction of the inflationary potential. Batavia, IL: Fermi National Accelerator Laboratory, 1994.

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11

Meelan, Choudhari, and Langley Research Center, eds. Multiple scales approach to weakly nonparallel and curvature effects: Details for the novice. Hampton, Va: National Aeronautics and Space Administration, Langley Research Center, 1995.

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12

Meelan, Choudhari, and Langley Research Center, eds. Multiple scales approach to weakly nonparallel and curvature effects: Details for the novice. Hampton, Va: National Aeronautics and Space Administration, Langley Research Center, 1995.

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13

(Markus), Quandt M., Weigel H. (Herbert), and SpringerLink (Online service), eds. Spectral methods in quantum field theory. Berlin: Springer, 2009.

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14

Max-Planck-Institut. Combinatorics and physics: Mini-Workshop on Renormalization, December 15-16, 2006, Max Planck Institut für Mathematik, Bonn, Germany : Conference on Combinatorics and Physics, March 19-23, 2007, Max Planck Institut für Mathematik, Bonn, Germany. Edited by Ebrahimi-Fard Kurusch 1973-, Marcolli Matilde, Suijlekom, Walter D. van., 1978-, Max-Planck-Institut für Mathematik, and Conference on Combinatorics and Physics (2007 : Max Planck Institut für Mathematik). Providence, R.I: American Mathematical Society, 2011.

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15

United States. National Aeronautics and Space Administration., ed. An initial investigation into methods of computing transonic aerodynamic sensitivity coefficients: Semiannual progress report, January 1991 - June 1991. College Station, Tex: Aerospace Engineering Dept., Texas A&M University, 1991.

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16

United States. National Aeronautics and Space Administration., ed. An initial investigation into methods of computing transonic aerodynamic sensitivity coefficients: Semiannual progress report, July 1990 - December 1990. College Station, Tex: Aerospace Engineering Dept., Texas A&M University, 1991.

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17

United States. National Aeronautics and Space Administration., ed. An initial investigation into methods of computing transonic aerodynamic sensitivity coefficients: Semiannual progress report, January 1, 1988 - June 30, 1988. College Station, Tex: Aerospace Engineering Dept., Texas A&M University, 1988.

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18

Motives, quantum field theory, and pseudodifferential operators: Conference on Motives, Quantum Field Theory, and Pseudodifferential Operators, June 2-13, 2008, Boston University, Boston, Massachusetts. Providence, R.I: American Mathematical Society, 2010.

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19

Laine, Mikko, and Aleksi Vuorinen. Basics of Thermal Field Theory: A Tutorial on Perturbative Computations. Springer London, Limited, 2016.

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20

Laine, Mikko, and Aleksi Vuorinen. Basics of Thermal Field Theory: A Tutorial on Perturbative Computations. Springer, 2016.

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21

Kaminski, Marcin. Stochastic Perturbation Method for Computational Mechanics. Wiley & Sons, Incorporated, John, 2013.

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22

Kaminski, Marcin. Stochastic Perturbation Method for Computational Mechanics. Wiley & Sons, Limited, John, 2013.

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23

Kaminski, Marcin. Stochastic Perturbation Method for Computational Mechanics. Wiley & Sons, Incorporated, John, 2013.

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24

Kaminski, Marcin. Stochastic Perturbation Method for Computational Mechanics. Wiley & Sons, Incorporated, John, 2013.

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25

Kaminski, Marcin. Stochastic Perturbation Method for Computational Mechanics. Wiley & Sons, Incorporated, John, 2013.

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26

The Stochastic Perturbation Method For Computational Mechanics. John Wiley & Sons, 2013.

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27

Vortex perturbation dynamics. Hampton, VA: Institute for Computer Applications in Science and Engineering, NASA Langley Research Center, 1995.

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28

Konstantinov, M., D. Wei Gu, V. Mehrmann, and P. Petkov. Perturbation Theory for Matrix Equations (Studies in Computational Mathematics). JAI Press, 2003.

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29

Atallah, George Chalita. Perturbation analysis of forced nonlinear oscillations using symbolic and numerical computations. 1985.

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30

Miller, John J. H. Single Perturbation Problems in Chemical Physics: Analytic and Computational Methods. Wiley & Sons, Incorporated, John, 2007.

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31

Berman, Gennady P. Perturbation Theory for Solid-state Quantum Computation With Many Quantum Bits. Rinton Press, 2005.

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32

Martin, Richard M., Lucia Reining, and David M. Ceperley. Interacting Electrons: Theory and Computational Approaches. Cambridge University Press, 2016.

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33

Martin, Richard M., Lucia Reining, and David M. Ceperley. Interacting Electrons: Theory and Computational Approaches. Cambridge University Press, 2016.

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34

Martin, Richard M., Lucia Reining, and David M. Ceperley. Interacting Electrons: Theory and Computational Approaches. Cambridge University Press, 2016.

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35

Georgescu, A. Asymptotic Treatment of Differential Equations (Applied Mathematics and Mathematical Computation Series). Chapman & Hall/CRC, 1995.

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36

Miller, John J. H. Single Perturbation Problems in Chemical Physics Vol. 97: Analytic and Computational Methods. Wiley & Sons, Incorporated, John, 2009.

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37

Wiberg, Petter. Computation of value-at-risk: The fast convolution method, dimension reduction and perturbation theory. 2002.

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38

Random Perturbation Methods with Applications in Science and Engineering. Springer, 2012.

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39

Miller, John J. H. Single Perturbation Problems in Chemical Physics: Analytic and Computational Methods, Volume 97, Advances in Chemical Physics. Wiley-Interscience, 1997.

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40

Roos, Hans-Görg, Martin Stynes, and Lutz Tobiska. Numerical Methods for Singularly Perturbed Differential Equations: Convection-Diffusion and Flow Problems (Springer Series in Computational Mathematics). Springer, 1996.

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41

Juillard, Michel. Dynamic Stochastic General Equilibrium Models. Edited by Shu-Heng Chen, Mak Kaboudan, and Ye-Rong Du. Oxford University Press, 2018. http://dx.doi.org/10.1093/oxfordhb/9780199844371.013.4.

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Dynamic Stochastic General Equilibrium (DSGE) models have become popular in macroeconomics, but the combination of nonlinear microeconomic behavior of the agents and model-consistent expectations raise intricate computational issues; this chapter reviews solution methods and estimation of DSGE models. Perfect foresight deterministic models can easily be solved with a great degree of accuracy. In practice, medium-sized stochastic models can only be solved by local approximation or the perturbation approach. The Bayesian approach to estimation is privileged. It provides a convenient way to communicate both the prior information available to the econo-metrician and new information revealed by the data. This chapter focuses on methods frequently used in applied work rather than aiming at being exhaustive.
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42

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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43

Banasiak, Jacek, and Luisa Arlotti. Perturbations of Positive Semigroups with Applications (Springer Monographs in Mathematics). Springer, 2005.

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44

Perturbations of Positive Semigroups with Applications. Springer, 2006.

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45

Numerical Methods for Singularly Perturbed Differential Equations: Convection-Diffusion and Flow Problems (Springer Series in Computational Mathematics). 2nd ed. Springer, 2007.

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46

Dyall, Kenneth G., and Knut Faegri. Introduction to Relativistic Quantum Chemistry. Oxford University Press, 2007. http://dx.doi.org/10.1093/oso/9780195140866.001.0001.

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This book provides an introduction to the essentials of relativistic effects in quantum chemistry, and a reference work that collects all the major developments in this field. It is designed for the graduate student and the computational chemist with a good background in nonrelativistic theory. In addition to explaining the necessary theory in detail, at a level that the non-expert and the student should readily be able to follow, the book discusses the implementation of the theory and practicalities of its use in calculations. After a brief introduction to classical relativity and electromagnetism, the Dirac equation is presented, and its symmetry, atomic solutions, and interpretation are explored. Four-component molecular methods are then developed: self-consistent field theory and the use of basis sets, double-group and time-reversal symmetry, correlation methods, molecular properties, and an overview of relativistic density functional theory. The emphases in this section are on the basics of relativistic theory and how relativistic theory differs from nonrelativistic theory. Approximate methods are treated next, starting with spin separation in the Dirac equation, and proceeding to the Foldy-Wouthuysen, Douglas-Kroll, and related transformations, Breit-Pauli and direct perturbation theory, regular approximations, matrix approximations, and pseudopotential and model potential methods. For each of these approximations, one-electron operators and many-electron methods are developed, spin-free and spin-orbit operators are presented, and the calculation of electric and magnetic properties is discussed. The treatment of spin-orbit effects with correlation rounds off the presentation of approximate methods. The book concludes with a discussion of the qualitative changes in the picture of structure and bonding that arise from the inclusion of relativity.
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47

An initial investigation into methods of computing transonic aerodynamic sensitivity coefficients: Final report. College Station, Tex: Aerospace Engineering Dept., Texas A&M University, Texas Engineering Experiment Station, 1994.

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48

An initial investigation into methods of computing transonic aerodynamic sensitivity coefficients: Semiannual progress report, January 1991 - June 1991. College Station, Tex: Aerospace Engineering Dept., Texas A&M University, 1991.

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49

An initial investigation into methods of computing transonic aerodynamic sensitivity coefficients: Semiannual progress report, July 1991- December 1991. College Station, Tex: Aerospace Engineering Dept., Texas A&M University, 1992.

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50

An initial investigation into methods of computing transonic aerodynamic sensitivity coefficients: Semiannual progress report, July 1, 1987-December 31, 1987. College Station, Tex: Aerospace Engineering Dept., Texas A&M University, Texas Engineering Experiment Station, 1988.

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