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Academic literature on the topic 'Singular Perturbations'

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Published: 4 June 2021
Last updated: 25 May 2023

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Journal articles on the topic "Singular Perturbations"

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Malamud, M., and H. Neidhardt. "Perturbation determinants for singular perturbations." Russian Journal of Mathematical Physics 21, no. 1 (March 2014): 55–98. http://dx.doi.org/10.1134/s1061920814010051.

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Lasserre, Jean B. "A formula for singular perturbations of Markov chains." Journal of Applied Probability 31, no. 3 (September 1994): 829–33. http://dx.doi.org/10.2307/3215160.

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We give formulas for updating both the steady-state probability distribution and the fundamental matrices of a singularly perturbed Markov chain. This formula generalizes Schweitzer's regular perturbation formulas to the case of singular perturbations.
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Lasserre, Jean B. "A formula for singular perturbations of Markov chains." Journal of Applied Probability 31, no. 03 (September 1994): 829–33. http://dx.doi.org/10.1017/s0021900200045381.

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We give formulas for updating both the steady-state probability distribution and the fundamental matrices of a singularly perturbed Markov chain. This formula generalizes Schweitzer's regular perturbation formulas to the case of singular perturbations.
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Charafi, A. "Singular perturbation I. (Spaces and singular perturbations on manifolds without boundary)." Engineering Analysis with Boundary Elements 9, no. 2 (January 1992): 191–92. http://dx.doi.org/10.1016/0955-7997(92)90069-j.

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Snyder, Chris, and Gregory J. Hakim. "Cyclogenetic Perturbations and Analysis Errors Decomposed into Singular Vectors." Journal of the Atmospheric Sciences 62, no. 7 (July 1, 2005): 2234–47. http://dx.doi.org/10.1175/jas3458.1.

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Abstract Singular vectors (SVs) have been applied to cyclogenesis, to initializing ensemble forecasts, and in predictability studies. Ideally, the calculation of the SVs would employ the analysis error covariance norm at the initial time or, in the case of cyclogenesis, a norm based on the statistics of initial perturbations, but the energy norm is often used as a more practical substitute. To illustrate the roles of the choice of norm and the vertical structure of initial perturbations, an upper-level wave with no potential vorticity perturbation in the troposphere is considered as a typical cyclogenetic perturbation or analysis error, and this perturbation is then decomposed by its projection onto each energy SV. All calculations are made, for simplicity, in the context of the quasigeostrophic Eady model (i.e., for a background flow with constant vertical shear and horizontal temperature gradient). Viewed in terms of the energy SVs, the smooth vertical structure of the typical perturbation, as well as its evolution, results from strong cancellation between the growing and decaying SVs, most of which are highly structured and tilted in the vertical. A simpler picture, involving less cancellation, follows from decomposition of the typical perturbation into SVs using an alternative initial norm, which is based on the relation between initial norms and the statistics of initial perturbations together with the empirical assumption that the initial perturbations are not dominated by interior potential vorticity. Differences between the energy SVs and those based on the alternative initial norm can be understood by noting that the energy norm implicitly assumes initial perturbations with second-order statistics given by the covariance matrix whose inverse defines the energy norm. Unlike the “typical” perturbation, perturbations with those statistics have large variance of potential vorticity in the troposphere and fine vertical structure. Finally, a brief assessment is presented of the extent to which the upper wave, and more generally the alternative initial norm, is representative of cyclogenetic perturbations and analysis errors. There is substantial evidence supporting deep perturbations with little vertical structure as frequent precursors to cyclogenesis, but surrogates for analysis errors are less conclusive: operational midlatitude analysis differences have vertical structure similar to that of the perturbations implied by the energy norm, while short-range forecast errors and analysis errors from assimilation experiments with simulated observations are more consistent with the alternative norm.
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Biyarov, Bazarkan, Dimitry Svistunov, and Gulnara Abdrasheva. "CORRECT SINGULAR PERTURBATIONS OF THE LAPLACE OPERATOR." Eurasian Mathematical Journal 11, no. 4 (2020): 25–34. http://dx.doi.org/10.32523/2077-9879-2020-11-4-25-34.

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Lax, Christian, and Sebastian Walcher. "Singular perturbations and scaling." Discrete & Continuous Dynamical Systems - B 25, no. 1 (2020): 1–29. http://dx.doi.org/10.3934/dcdsb.2019170.

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Astaburuaga, M. A., V. H. Cortés, C. Fernández, and R. Del Río. "Singular rank one perturbations." Journal of Mathematical Physics 63, no. 2 (February 1, 2022): 023502. http://dx.doi.org/10.1063/5.0061250.

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Soner, H. Mete. "Singular Perturbations in Manufacturing." SIAM Journal on Control and Optimization 31, no. 1 (January 1993): 132–46. http://dx.doi.org/10.1137/0331010.

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Ikegami, Gik? "Singular perturbations in foliations." Inventiones Mathematicae 95, no. 2 (June 1989): 215–46. http://dx.doi.org/10.1007/bf01393896.

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Dissertations / Theses on the topic "Singular Perturbations"

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Dyachenko, Evgueniya, and Nikolai Tarkhanov. "Singular perturbations of elliptic operators." Universität Potsdam, 2014. http://opus.kobv.de/ubp/volltexte/2014/6950/.

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We develop a new approach to the analysis of pseudodifferential operators with small parameter 'epsilon' in (0,1] on a compact smooth manifold X. The standard approach assumes action of operators in Sobolev spaces whose norms depend on 'epsilon'. Instead we consider the cylinder [0,1] x X over X and study pseudodifferential operators on the cylinder which act, by the very nature, on functions depending on 'epsilon' as well. The action in 'epsilon' reduces to multiplication by functions of this variable and does not include any differentiation. As but one result we mention asymptotic of solutions to singular perturbation problems for small values of 'epsilon'.
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Hashemi, Seyed Naser. "Singular perturbations in coupled stochastic differential equations." Thesis, National Library of Canada = Bibliothèque nationale du Canada, 2001. http://www.collectionscanada.ca/obj/s4/f2/dsk3/ftp05/NQ65244.pdf.

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Ashino, Ryuichi. "On Nagumo's Hs-stability in singular perturbations." 京都大学 (Kyoto University), 1991. http://hdl.handle.net/2433/86434.

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Beauchamp, Gerson. "Algorithms for singular systems." Diss., Georgia Institute of Technology, 1990. http://hdl.handle.net/1853/15368.

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Neuner, Christoph. "Generalized Titchmarsh-Weyl functions and super singular perturbations." Licentiate thesis, Stockholms universitet, Matematiska institutionen, 2015. http://urn.kb.se/resolve?urn=urn:nbn:se:su:diva-113389.

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In this thesis we study certain singular Sturm-Liouville differential expressions from an operator theoretic point of view.In particular we are interested in expressions that involve strongly singular potentials as introduced by Gesztesy and Zinchenko.On the ODE side, analyzing these expressions involves the so-called $m$-functions, often generalized Nevanlinna functions, who encapsulate spectral information of the underlying problem.The aim of the two papers in this thesis is to further understanding on the operator theory side.In the first paper, we use a model for super singular perturbations to describe a family of induced self-adjoint realizations of a perturbed Schr\"o\-din\-ger operator, i.e., with a potential of the form $c/x^2 + q$ where $q$ is a perturbation.Following the unperturbed example of Kurasov and Luger, we find that the so-called $Q$-function appearing in this approach is in good agreement with the above named $m$-function.Furthermore, we show that the operator model can be chosen such that $Q \equiv m$.In the second paper, we present a negative result in this area, namely that the supersingular perturbations model cannot be used for all strongly singular potentials.For a potential with a stronger singularity at the origin, namely $1/x^4$, we discuss the asymptotic behaviour of the Weyl solution at zero.It turns out that this function cannot be regularized appropriately and the operator model breaks down.
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Elago, David. "Robust computational methods for two-parameter singular perturbation problems." Thesis, University of the Western Cape, 2010. http://etd.uwc.ac.za/index.php?module=etd&action=viewtitle&id=gen8Srv25Nme4_1693_1308039217.

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This thesis is concerned with singularly perturbed two-parameter problems. We study a tted nite difference method as applied on two different meshes namely a piecewise mesh (of Shishkin type) and a graded mesh (of Bakhvalov type) as well as a tted operator nite di erence method. We notice that results on Bakhvalov mesh are better than those on Shishkin mesh. However, piecewise uniform meshes provide a simpler platform for analysis and computations. Fitted operator methods are even simpler in these regards due to the ease of operating on uniform meshes. Richardson extrapolation is applied on one of the tted mesh nite di erence method (those based on Shishkin mesh) as well as on the tted operator nite di erence method in order to improve the accuracy and/or the order of convergence. This is our main contribution to this eld and in fact we have achieved very good results after extrapolation on the tted operator finitete difference method. Extensive numerical computations are carried out on to confirm the theoretical results.

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Lu, Nan. "Normally elliptic singular perturbation problems: local invariant manifolds and applications." Diss., Georgia Institute of Technology, 2011. http://hdl.handle.net/1853/41090.

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In this thesis, we study the normally elliptic singular perturbation problems including both finite and infinite dimensional cases, which could also be non-autonomous. In particular, we establish the existence and smoothness of O(1) local invariant manifolds and provide various estimates which are independent of small singular parameters. We also use our results on local invariant manifolds to study the persistence of homoclinic solutions under weakly dissipative and conservative per- turbations. We apply Semi-group Theory and Lyapunov-Perron Integral Equations with some careful estimates to handle the O(1) driving force in the system so that we can approximate the full system through some simpler limiting system. In the investigation of homoclinics, a diagonalization procedure and some normal form transformation should be first carried out. Such diagonalization procedure is not trivial at all. We discuss this issue in the appendix. We use Melnikov type analysis to study the weakly dissipative case, while the conservative case is based on some energy methods. As a concrete example, we have shown rigrously the persistence of homoclinic solutions of an elastic pendulum model which may be affected by damping, external forcing and other potential fields.
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Li, Yongfeng. "Nonlinear oscillation and control in the BZ chemical reaction." Diss., Atlanta, Ga. : Georgia Institute of Technology, 2008. http://hdl.handle.net/1853/26565.

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Thesis (Ph.D)--Mathematics, Georgia Institute of Technology, 2009.
Committee Chair: Yi, Yingfei; Committee Member: Chow, Shui-Nee; Committee Member: Dieci, Luca; Committee Member: Verriest, Erik; Committee Member: Weiss, Howie. Part of the SMARTech Electronic Thesis and Dissertation Collection.
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Mason, Colin Stuart. "Boundary perturbations and ultracontractivity of singular second order elliptic operators." Thesis, King's College London (University of London), 2001. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.395943.

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Shankar, Uday J. "Singular-perturbation analysis of climb-cruise-dash optimization." Thesis, Virginia Tech, 1985. http://hdl.handle.net/10919/45736.

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The method of singular-perturbation analysis is applied to the determination of range-fuel-time optimal aircraft trajectories. The problem is shown to break down into three sub-problems which are studied separately. In particular, the inner layer containing the altitude path-angle dynamics is analyzed in detail. The outer solutions are discussed in an earlier work. As a step forward in solving the ensuing nonlinear two-point boundary-value problem, linearization of the equations is suggested. Conditions for the stability of the linearized boundary-layer equations are discussed. Also, the question of parameter selection to fit the solution to the split boundary conditions is resolved. Generation of feedback laws for the angle-of-attack from the linear analysis is discussed. Finally, the techniques discussed are applied to a numerical example of a missile. The linearized feedback solution is compared to the exact solution obtained using a multiple shooting method.
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Books on the topic "Singular Perturbations"

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Shchepakina, Elena, Vladimir Sobolev, and Michael P. Mortell. Singular Perturbations. Cham: Springer International Publishing, 2014. http://dx.doi.org/10.1007/978-3-319-09570-7.

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P, Mortell Michael, ed. Singular perturbations and hysteresis. Philadelphia: Society for Industrial and Applied Mathematics, 2005.

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Singular perturbations I. Spaces and singular perturbations on manifolds without boundary. Amsterdam: North-Holland, 1990.

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Jager, E. M. de. The theory of singular perturbations. Amsterdam: Elsevier, 1996.

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Gie, Gung-Min, Makram Hamouda, Chang-Yeol Jung, and Roger M. Temam. Singular Perturbations and Boundary Layers. Cham: Springer International Publishing, 2018. http://dx.doi.org/10.1007/978-3-030-00638-9.

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O'Malley, Robert E. Historical Developments in Singular Perturbations. Cham: Springer International Publishing, 2014. http://dx.doi.org/10.1007/978-3-319-11924-3.

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Singular perturbation theory. New York: Springer, 2011.

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Verhulst, Ferdinand. Methods and Applications of Singular Perturbations. New York, NY: Springer New York, 2005. http://dx.doi.org/10.1007/0-387-28313-7.

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V, Kokotović Petar, Khalil Hassan K. 1950-, and IEEE Control Systems Society, eds. Singular perturbations in systems and control. New York: IEEE Press, 1986.

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Algebraic analysis of singular perturbation. Providence, R.I: American Mathematical Society, 2005.

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Book chapters on the topic "Singular Perturbations"

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Agarwal, Ravi P., and Donal O’Regan. "Singular Perturbations." In Ordinary and Partial Differential Equations, 138–44. New York, NY: Springer New York, 2009. http://dx.doi.org/10.1007/978-0-387-79146-3_18.

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Avramidi, Ivan G. "Singular Perturbations." In Heat Kernel Method and its Applications, 169–96. Cham: Springer International Publishing, 2015. http://dx.doi.org/10.1007/978-3-319-26266-6_4.

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Koshmanenko, Volodymyr, and Mykola Dudkin. "Super-singular Perturbations." In The Method of Rigged Spaces in Singular Perturbation Theory of Self-Adjoint Operators, 169–91. Cham: Springer International Publishing, 2016. http://dx.doi.org/10.1007/978-3-319-29535-0_8.

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Barbu, Luminiţa, and Gheorghe Moroşanu. "Regular and Singular Perturbations." In International Series of Numerical Mathematics, 3–15. Basel: Birkhäuser Basel, 2007. http://dx.doi.org/10.1007/978-3-7643-8331-2_1.

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Gie, Gung-Min, Makram Hamouda, Chang-Yeol Jung, and Roger M. Temam. "Singular Perturbations in Dimension One." In Singular Perturbations and Boundary Layers, 1–29. Cham: Springer International Publishing, 2018. http://dx.doi.org/10.1007/978-3-030-00638-9_1.

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Novotny, Antonio André, and Jan Sokołowski. "Singular Perturbations of Energy Functionals." In Topological Derivatives in Shape Optimization, 91–136. Berlin, Heidelberg: Springer Berlin Heidelberg, 2013. http://dx.doi.org/10.1007/978-3-642-35245-4_4.

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Korolyuk, Vladimir S., and Anatoly F. Turbin. "Singular Perturbations of Holomorphic Semigroups." In Mathematical Foundations of the State Lumping of Large Systems, 119–30. Dordrecht: Springer Netherlands, 1993. http://dx.doi.org/10.1007/978-94-011-2072-2_4.

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Dontchev, Asen L., and Tullio Zolezzi. "Singular perturbations in optimal control." In Well-Posed Optimization Problems, 248–82. Berlin, Heidelberg: Springer Berlin Heidelberg, 1993. http://dx.doi.org/10.1007/bfb0084202.

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Holcman, David, and Zeev Schuss. "Singular Perturbations in Higher Dimensions." In Applied Mathematical Sciences, 49–113. Cham: Springer International Publishing, 2018. http://dx.doi.org/10.1007/978-3-319-76895-3_3.

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Lions, J. L. "Exact Controllability and Singular Perturbations." In Mathematical Sciences Research Institute Publications, 217–47. New York, NY: Springer US, 1987. http://dx.doi.org/10.1007/978-1-4613-9583-6_8.

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Conference papers on the topic "Singular Perturbations"

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Abed, Eyad. "New results in multiparameter singular perturbations." In 1986 25th IEEE Conference on Decision and Control. IEEE, 1986. http://dx.doi.org/10.1109/cdc.1986.267612.

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Pedersen, M. "Singular boundary perturbations of distributed systems." In 29th IEEE Conference on Decision and Control. IEEE, 1990. http://dx.doi.org/10.1109/cdc.1990.203625.

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Abed, Eyad. "A new parameter estimate in singular perturbations." In 1985 24th IEEE Conference on Decision and Control. IEEE, 1985. http://dx.doi.org/10.1109/cdc.1985.268900.

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FRIDMAN, LEONID. "PERIODIC MOTIONS IN VSS AND SINGULAR PERTURBATIONS." In Proceedings of the 6th IEEE International Workshop on Variable Structure Systems. WORLD SCIENTIFIC, 2000. http://dx.doi.org/10.1142/9789812792082_0034.

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Dabney, J. B., F. H. Ghorbel, and Zhiyong Wang. "Modeling closed kinematic chains via singular perturbations." In Proceedings of 2002 American Control Conference. IEEE, 2002. http://dx.doi.org/10.1109/acc.2002.1024573.

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Oseledets, Ivan, and Valentin Khrulkov. "Art of Singular Vectors and Universal Adversarial Perturbations." In 2018 IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR). IEEE, 2018. http://dx.doi.org/10.1109/cvpr.2018.00893.

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Dontchev, A., and V. Veliov. "Singular perturbations in linear control systems with constraints." In 1986 25th IEEE Conference on Decision and Control. IEEE, 1986. http://dx.doi.org/10.1109/cdc.1986.267266.

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Dmitriev, Mikhail, and Dmitry Makarov. "Stabilization of Quasilinear Systems with Multiparameter Singular Perturbations." In 2020 13th International Conference Management of large-scale system development (MLSD). IEEE, 2020. http://dx.doi.org/10.1109/mlsd49919.2020.9247844.

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Nipp, Kaspar, Daniel Stoffer, Peter Szmolyan, Theodore E. Simos, George Psihoyios, and Ch Tsitouras. "Graph Transform and Blow-up in Singular Perturbations." In NUMERICAL ANALYSIS AND APPLIED MATHEMATICS: International Conference on Numerical Analysis and Applied Mathematics 2009: Volume 1 and Volume 2. AIP, 2009. http://dx.doi.org/10.1063/1.3241616.

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Wang, Liming, and Eduardo D. Sontag. "A Remark on Singular Perturbations of Strongly Monotone Systems." In Proceedings of the 45th IEEE Conference on Decision and Control. IEEE, 2006. http://dx.doi.org/10.1109/cdc.2006.376929.

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Reports on the topic "Singular Perturbations"

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Losey, D. C., and J. C. Lee. Singular perturbation analysis of the neutron transport equation. Office of Scientific and Technical Information (OSTI), July 1996. http://dx.doi.org/10.2172/393304.

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Stephen B. Margolis and Melvin R. Baer. A Singular-Perturbation Analysis of the Burning-Rate Eigenvalue for a Two-Temperature Model of Deflagrations in Confined Porous Energetic Materials. Office of Scientific and Technical Information (OSTI), November 2000. http://dx.doi.org/10.2172/768286.

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