Relevant bibliographies by topics / Linear equations

Academic literature on the topic 'Linear equations'

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Published: 4 June 2021
Last updated: 26 July 2024

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Journal articles on the topic "Linear equations"

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Rohn, Jiří. "Interval solutions of linear interval equations." Applications of Mathematics 35, no. 3 (1990): 220–24. http://dx.doi.org/10.21136/am.1990.104406.

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Kurzweil, Jaroslav, and Alena Vencovská. "Linear differential equations with quasiperiodic coefficients." Czechoslovak Mathematical Journal 37, no. 3 (1987): 424–70. http://dx.doi.org/10.21136/cmj.1987.102170.

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Patel, Roshni V., and Jignesh S. Patel. "Optimization of Linear Equations using Genetic Algorithms." Indian Journal of Applied Research 2, no. 3 (October 1, 2011): 56–58. http://dx.doi.org/10.15373/2249555x/dec2012/19.

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Fraňková, Dana. "Substitution method for generalized linear differential equations." Mathematica Bohemica 116, no. 4 (1991): 337–59. http://dx.doi.org/10.21136/mb.1991.126028.

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Schwabik, Štefan. "Linear Stieltjes integral equations in Banach spaces." Mathematica Bohemica 124, no. 4 (1999): 433–57. http://dx.doi.org/10.21136/mb.1999.125994.

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Cecchi, Mariella, Zuzana Došlá, Mauro Marini, and Ivo Vrkoč. "Asymptotic properties for half-linear difference equations." Mathematica Bohemica 131, no. 4 (2006): 347–63. http://dx.doi.org/10.21136/mb.2006.133970.

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Davies, Alan, and Rainer Kress. "Linear Integral Equations." Mathematical Gazette 74, no. 470 (December 1990): 405. http://dx.doi.org/10.2307/3618171.

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S., F., and Rainer Kress. "Linear Integral Equations." Mathematics of Computation 56, no. 193 (January 1991): 379. http://dx.doi.org/10.2307/2008551.

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STEWART, G. W. "Solving Linear Equations." Science 236, no. 4800 (April 24, 1987): 461–62. http://dx.doi.org/10.1126/science.236.4800.461.

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PAN, V., and J. H. REIF. "Response:Solving Linear Equations." Science 236, no. 4800 (April 24, 1987): 462–63. http://dx.doi.org/10.1126/science.236.4800.462.

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Dissertations / Theses on the topic "Linear equations"

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Yesilyurt, Deniz. "Solving Linear Diophantine Equations And Linear Congruential Equations." Thesis, Linnéuniversitetet, Institutionen för datavetenskap, fysik och matematik, DFM, 2012. http://urn.kb.se/resolve?urn=urn:nbn:se:lnu:diva-19247.

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This report represents GCD, euclidean algorithm, linear diophantine equation and linear congruential equation. It investigates the methods for solving linear diophantine equations and linear congruential equations in several variables. There are many examples which illustrate the methods for solving equations.
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Chen, Huyuan. "Fully linear elliptic equations and semilinear fractionnal elliptic equations." Thesis, Tours, 2014. http://www.theses.fr/2014TOUR4001/document.

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Cette thèse est divisée en six parties. La première partie est consacrée à l'étude de propriétés de Hadamard et à l'obtention de théorèmes de Liouville pour des solutions de viscosité d'équations aux dérivées partielles elliptiques complètement non-linéaires avec des termes de gradient,
This thesis is divided into six parts. The first part is devoted to prove Hadamard properties and Liouville type theorems for viscosity solutions of fully nonlinear elliptic partial differential equations with gradient term
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Goedhart, Eva Govinda. "Explicit bounds for linear difference equations /." Electronic thesis, 2005. http://etd.wfu.edu/theses/available/etd-05102005-222845/.

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Jonklass, Raymond. "Learners' strategies for solving linear equations." Thesis, Stellenbosch : Stellenbosch University, 2002. http://hdl.handle.net/10019.1/52915.

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Thesis (MEd)--University of Stellenbosch, 2002.
ENGLISH ABSTRACT: Algebra deals amongst others with the relationship between variables. It differs from Arithmetic amongst others as there is not always a numerical solution to the problem. An algebraic expression can even be the solution to the problem in Algebra. The variables found in Algebra are often represented by letters such as X, y, etc. Equations are an integral part of Algebra. To solve an equation, the value of an unknown must be determined so that the left hand side of the equation is equal to the right hand side. There are various ways in which the solving of equations can be taught. The purpose of this study is to determine the existence of a cognitive gap as described by Herseovies & Linchevski (1994) in relation to solving linear equations. When solving linear equations, an arithmetical approach is not always effective. A new way of structural thinking is needed when solving linear equations in their different forms. In this study, learners' intuitive, informal ways of solving linear equations were examined prior to any formal instruction and before the introduction of algebraic symbols and notation. This information could help educators to identify the difficulties learners have when moving from solving arithmetical equations to algebraic equations. The learners' errors could help educators plan effective ways of teaching strategies when solving linear equations. The research strategy for this study was both quantitative and qualitative. Forty-two Grade 8 learners were chosen to individually do assignments involving different types of linear equations. Their responses were recorded, coded and summarised. Thereafter the learners' responses were interpreted, evaluated and analysed. Then a representative sample of fourteen learners was chosen randomly from the same class and semi-structured interviews were conducted with them From these interviews the learners' ways of thinking when solving linear equations, were probed. This study concludes that a cognitive gap does exist in the context of the investigation. Moving from arithmetical thinking to algebraic thinking requires a paradigm shift. To make adequate provision for this change in thinking, careful curriculum planning is required.
AFRIKAANSE OPSOMMING: Algebra behels onder andere die verwantskap tussen veranderlikes. Algebra verskil van Rekenkunde onder andere omdat daar in Algebra nie altyd 'n numeriese oplossing vir die probleem is nie. InAlgebra kan 'n algebraïese uitdrukking somtyds die oplossing van 'n probleem wees. Die veranderlikes in Algebra word dikwels deur letters soos x, y, ens. voorgestel. Vergelykings is 'n integrale deel van Algebra. Om vergelykings op te los, moet 'n onbekende se waarde bepaal word, om die linkerkant van die vergelyking gelyk te maak aan die regterkant. Daar is verskillende maniere om die oplossing van algebraïese vergelykings te onderrig. Die doel van hierdie studie is om die bestaan van 'n sogenaamde "kognitiewe gaping" soos beskryf deur Herseovies & Linchevski (1994), met die klem op lineêre vergelykings, te ondersoek. Wanneer die oplossing van 'n linêere vergelyking bepaal word, is 'n rekenkundige benadering nie altyd effektiefnie. 'n Heel nuwe, strukturele manier van denke word benodig wanneer verskillende tipes linêere vergelykings opgelos word. In hierdie studie word leerders se intuitiewe, informele metodes ondersoek wanneer hulle lineêre vergelykings oplos, voordat hulle enige formele metodes onderrig is en voordat hulle kennis gemaak het met algebraïese simbole en notasie. Hierdie inligting kan opvoeders help om leerders se kognitiewe probleme in verband met die verskil tussen rekenkundige en algebraïese metodes te identifiseer.Die foute wat leerders maak, kan opvoeders ook help om effektiewe onderrigmetodes te beplan, wanneer hulle lineêre vergelykings onderrig. As leerders eers die skuif van rekenkundige metodes na algebrarese metodes gemaak het, kan hulle besef dat hul primitiewe metodes nie altyd effektief is nie. Die navorsingstrategie wat in hierdie studie aangewend is, is kwalitatief en kwantitatief Twee-en-veertig Graad 8 leerders is gekies om verskillende tipes lineêre vergelykings individueel op te los. Hul antwoorde is daarna geïnterpreteer, geëvalueer en geanaliseer. Daarna is veertien leerders uit hierdie groep gekies en semigestruktureerde onderhoude is met hulle gevoer. Vanuit die onderhoude kon 'n dieper studie van die leerders se informele metodes van oplossing gemaak word. Die gevolgtrekking wat in hierdie studie gemaak word, is dat daar wel 'n kognitiewe gaping bestaan in die konteks van die studie. Leerders moet 'n paradigmaskuif maak wanneer hulle van rekenkundige metodes na algebraïese metodes beweeg. Hierdie klemverskuiwing vereis deeglike kurrikulumbeplanning.
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Altassan, Alaa Abdullah. "Linear equations over free Lie algebras." Thesis, University of Manchester, 2013. https://www.research.manchester.ac.uk/portal/en/theses/linear-equations-over-free-liealgebras(6e29b286-1869-4207-b054-8baab98e70df).html.

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In this thesis, we study equations of the form $[x_1,u_1]+[x_2, u_2]+\ldots+[x_k,u_k]=0$ over a free Lie algebra $L$, where $k>1$ and the coefficients $u_1, u_2, \ldots,u_k$ belong to $L$. The starting point of this research is a paper [22], in which the authors embarked on a systematic study of very concrete linear equations over free Lie algebras. They focused on the given equations in the case where $k=2$. We generalise and develop a number of the results on equations with two variables to equations with an arbitrary number of indeterminates. Most of the results refer to the case where the coefficients coincide with the free generators of $L$. Throughout our research, we study some features of the solution space of these equations such as the homogenous structure and the fine homogenous structure. The main achievement in this work is that we give a detailed description of the solution space. Then we obtain explicit bases for some specific fine homogeneous components of the solution space, in particular, we give a basis for the "multilinear'' fine homogenous component. Moreover, we generalise earlier results on commutator calculus using the "language'' of free Lie algebras and apply them to determine the radical and the coordinate algebra of the solution space of the given equations.
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Chen, Hua, Wei-Xi Li, and Chao-Jiang Xu. "Gevrey hypoellipticity for linear and non-linear Fokker-Planck equations." Universität Potsdam, 2007. http://opus.kobv.de/ubp/volltexte/2009/3028/.

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Hafez, Salah Taha. "Continued fractions and solutions of linear and non-linear lattice equations." Thesis, University of Kent, 1990. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.236725.

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Torshage, Axel. "Linear Functional Equations and Convergence of Iterates." Thesis, Umeå universitet, Institutionen för matematik och matematisk statistik, 2012. http://urn.kb.se/resolve?urn=urn:nbn:se:umu:diva-56450.

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The subject of this work is functional equations with direction towards linear functional equations. The .rst part describes function sets where iterates of the functions converge to a .xed point. In the second part the convergence property is used to provide solutions to linear functional equations by de.ning solutions as in.nite sums. Furthermore, this work contains some transforms to linear form, examples of functions that belong to di¤erent classes and corresponding linear functional equations. We use Mathematica to generate solutions and solve itera- tively equations.
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Grey, David John. "Parallel solution of power system linear equations." Thesis, Durham University, 1995. http://etheses.dur.ac.uk/5429/.

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At the heart of many power system computations lies the solution of a large sparse set of linear equations. These equations arise from the modelling of the network and are the cause of a computational bottleneck in power system analysis applications. Efficient sequential techniques have been developed to solve these equations but the solution is still too slow for applications such as real-time dynamic simulation and on-line security analysis. Parallel computing techniques have been explored in the attempt to find faster solutions but the methods developed to date have not efficiently exploited the full power of parallel processing. This thesis considers the solution of the linear network equations encountered in power system computations. Based on the insight provided by the elimination tree, it is proposed that a novel matrix structure is adopted to allow the exploitation of parallelism which exists within the cutset of a typical parallel solution. Using this matrix structure it is possible to reduce the size of the sequential part of the problem and to increase the speed and efficiency of typical LU-based parallel solution. A method for transforming the admittance matrix into the required form is presented along with network partitioning and load balancing techniques. Sequential solution techniques are considered and existing parallel methods are surveyed to determine their strengths and weaknesses. Combining the benefits of existing solutions with the new matrix structure allows an improved LU-based parallel solution to be derived. A simulation of the improved LU solution is used to show the improvements in performance over a standard LU-based solution that result from the adoption of the new techniques. The results of a multiprocessor implementation of the method are presented and the new method is shown to have a better performance than existing methods for distributed memory multiprocessors.
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Serna, Rodrigo. "Solving Linear Systems of Equations in Hardware." Thesis, KTH, Skolan för elektro- och systemteknik (EES), 2016. http://urn.kb.se/resolve?urn=urn:nbn:se:kth:diva-200610.

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Books on the topic "Linear equations"

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Kanwal, Ram P. Linear Integral Equations. New York, NY: Springer New York, 2013. http://dx.doi.org/10.1007/978-1-4614-6012-1.

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Kress, Rainer. Linear Integral Equations. Berlin, Heidelberg: Springer Berlin Heidelberg, 1989. http://dx.doi.org/10.1007/978-3-642-97146-4.

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Kress, Rainer. Linear Integral Equations. New York, NY: Springer New York, 1999. http://dx.doi.org/10.1007/978-1-4612-0559-3.

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Kanwal, Ram P. Linear Integral Equations. Boston, MA: Birkhäuser Boston, 1997. http://dx.doi.org/10.1007/978-1-4612-0765-8.

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Kress, Rainer. Linear Integral Equations. New York, NY: Springer New York, 2014. http://dx.doi.org/10.1007/978-1-4614-9593-2.

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Kanwal, Ram P. Linear integral equations. 2nd ed. Boston: Birkhäuser, 1997.

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Lovitt, William Vernon. Linear integral equations. Mineola, N.Y: Dover Publications, 2005.

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Kress, Rainer. Linear Integral Equations. New York, NY: Springer New York, 1999.

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Kress, Rainer. Linear Integral Equations. Berlin, Heidelberg: Springer Berlin Heidelberg, 1989.

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Woodford, Chris. Solving linear and non-linear equations. New York: Ellis Horwood, 1992.

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Book chapters on the topic "Linear equations"

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Afriat, S. N. "Linear Equations." In Linear Dependence, 67–88. Boston, MA: Springer US, 2000. http://dx.doi.org/10.1007/978-1-4615-4273-5_7.

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Miyake, Toshitsune. "Linear Equations." In Linear Algebra, 33–59. Singapore: Springer Nature Singapore, 2022. http://dx.doi.org/10.1007/978-981-16-6994-1_2.

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Müller, P. C., and W. O. Schiehlen. "Matrix equations." In Linear vibrations, 296–306. Dordrecht: Springer Netherlands, 1985. http://dx.doi.org/10.1007/978-94-009-5047-4_13.

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Stroud, K. A., and Dexter Booth. "Linear equations and simultaneous linear equations." In Foundation Mathematics, 184–202. London: Macmillan Education UK, 2009. http://dx.doi.org/10.1057/978-0-230-36672-5_5.

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Kinzel, Wolfgang, and Georg Reents. "Linear Equations." In Physics by Computer, 47–80. Berlin, Heidelberg: Springer Berlin Heidelberg, 1998. http://dx.doi.org/10.1007/978-3-642-46839-1_3.

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Holden, K., and A. W. Pearson. "Linear Equations." In Introductory Mathematics for Economics and Business, 1–42. London: Macmillan Education UK, 1992. http://dx.doi.org/10.1007/978-1-349-22357-2_1.

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Woodford, C., and C. Phillips. "Linear Equations." In Numerical Methods with Worked Examples: Matlab Edition, 17–45. Dordrecht: Springer Netherlands, 2012. http://dx.doi.org/10.1007/978-94-007-1366-6_2.

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Redfern, Darren, and Colin Campbell. "Linear Equations." In The Matlab® 5 Handbook, 21–41. New York, NY: Springer New York, 1998. http://dx.doi.org/10.1007/978-1-4612-2170-8_3.

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Rao, A. Ramachandra, and P. Bhimasankaram. "Linear equations." In Texts and Readings in Mathematics, 185–217. Gurgaon: Hindustan Book Agency, 2000. http://dx.doi.org/10.1007/978-93-86279-01-9_6.

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Verhulst, Ferdinand. "Linear Equations." In Universitext, 69–82. Berlin, Heidelberg: Springer Berlin Heidelberg, 1996. http://dx.doi.org/10.1007/978-3-642-61453-8_6.

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Conference papers on the topic "Linear equations"

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Bronstein, Manuel. "Linear ordinary differential equations." In Papers from the international symposium. New York, New York, USA: ACM Press, 1992. http://dx.doi.org/10.1145/143242.143264.

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Zadrzyńska, Ewa, and Wojciech M. Zajączkowski. "Some linear parabolic system in Besov spaces." In Parabolic and Navier–Stokes equations. Warsaw: Institute of Mathematics Polish Academy of Sciences, 2008. http://dx.doi.org/10.4064/bc81-0-36.

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FREDET, A. "ALGORITHMS AROUND LINEAR DIFFERENTIAL EQUATIONS." In Proceedings of the International Conference. WORLD SCIENTIFIC, 2007. http://dx.doi.org/10.1142/9789812770752_0018.

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Berkenbosch, Maint. "Moduli spaces for linear differential equations." In The Conference on Differential Equations and the Stokes Phenomenon. WORLD SCIENTIFIC, 2002. http://dx.doi.org/10.1142/9789812776549_0002.

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MIGUEL, JOSÉ J., ANDREI SHINDIAPIN, and ARCADY PONOSOV. "STABILITY AND LINEAR CHAIN TRICK." In Proceedings of the International Conference on Differential Equations. WORLD SCIENTIFIC, 2005. http://dx.doi.org/10.1142/9789812702067_0194.

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Guihong Wang, Haiyan Liu, and Xiangfeng Liu. "The application of excel in solving linear equations and nonlinear equation." In 2011 International Conference on Computer Science and Service System (CSSS). IEEE, 2011. http://dx.doi.org/10.1109/csss.2011.5974400.

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Čermák, Jan A. N. "The Schröder equation and asymptotic properties of linear delay differential equations." In The 7'th Colloquium on the Qualitative Theory of Differential Equations. Szeged: Bolyai Institute, SZTE, 2003. http://dx.doi.org/10.14232/ejqtde.2003.6.6.

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Chochiev, T. Z. "On non-linear equation, generalizing the equations of the Riccati class." In General question of world science. "Л-Журнал", 2018. http://dx.doi.org/10.18411/gq-31-03-2018-01.

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Stevens, B. L. "Derivation of aircraft, linear state equations from implicit nonlinear equations." In 29th IEEE Conference on Decision and Control. IEEE, 1990. http://dx.doi.org/10.1109/cdc.1990.203642.

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LASSAS, MATTI. "INVERSE PROBLEMS FOR LINEAR AND NON-LINEAR HYPERBOLIC EQUATIONS." In International Congress of Mathematicians 2018. WORLD SCIENTIFIC, 2019. http://dx.doi.org/10.1142/9789813272880_0199.

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Reports on the topic "Linear equations"

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Jain, Himanshu, Edmund M. Clarke, and Orna Grumberg. Efficient Craig Interpolation for Linear Diophantine (Dis)Equations and Linear Modular Equations. Fort Belvoir, VA: Defense Technical Information Center, February 2008. http://dx.doi.org/10.21236/ada476801.

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Cohen, Herbert E. The Instability of Linear Heterogeneous Lanchester Equations. Fort Belvoir, VA: Defense Technical Information Center, November 1991. http://dx.doi.org/10.21236/ada243519.

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Nirenberg, Louis. Techniques in Linear and Nonlinear Partial Differential Equations. Fort Belvoir, VA: Defense Technical Information Center, September 1987. http://dx.doi.org/10.21236/ada187109.

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Rundell, William, and Michael S. Pilant. Undetermined Coefficient Problems for Quasi-Linear Parabolic Equations. Fort Belvoir, VA: Defense Technical Information Center, September 1992. http://dx.doi.org/10.21236/ada256012.

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Pilant, Michael S., and William Rundell. Undetermined Coefficient Problems for Quasi-Linear Parabolic Equations. Fort Belvoir, VA: Defense Technical Information Center, December 1989. http://dx.doi.org/10.21236/ada218462.

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Subasi, Yigit. Quantum algorithms for linear systems of equations [Slides]. Office of Scientific and Technical Information (OSTI), December 2017. http://dx.doi.org/10.2172/1774402.

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Mathia, Karl. Solutions of linear equations and a class of nonlinear equations using recurrent neural networks. Portland State University Library, January 2000. http://dx.doi.org/10.15760/etd.1354.

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Parzen, George. Linear Orbits Parameters for the Exact Equations of Motion. Office of Scientific and Technical Information (OSTI), February 1994. http://dx.doi.org/10.2172/1119381.

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Chen, Goong, and Han-Kun Wang. Pointwise Stabilization for Coupled Quasilinear and Linear Wave Equations. Fort Belvoir, VA: Defense Technical Information Center, January 1988. http://dx.doi.org/10.21236/ada190031.

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Herzog, K. J., M. D. Morris, and T. J. Mitchell. Bayesian approximation of solutions to linear ordinary differential equations. Office of Scientific and Technical Information (OSTI), November 1990. http://dx.doi.org/10.2172/6242347.

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