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1

Fritts, Martin J., W. Patrick Crowley, and Harold Trease, eds. The Free-Lagrange Method. Berlin/Heidelberg: Springer-Verlag, 1985. http://dx.doi.org/10.1007/bfb0032238.

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2

Dynamic economics: Optimization by the Lagrange method. New York: Oxford University Press, 1997.

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3

Bertsekas, Dimitri P. Constrained optimization and Lagrange multiplier methods. Belmont, Mass: Athena Scientific, 1996.

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4

Huynh, Hung T. Accurate upwind methods for the Euler equations. [Washington, DC]: National Aeronautics and Space Administration, 1993.

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5

1943-, Fritts M. J., Crowley William Patrick, and Trease H. 1955-, eds. The Free-Lagrange method: Proceedings of the First International Conference on Free-Lagrange methods, held at Hilton Head Island, South Carolina, March 4-6, 1985. Berlin: Springer-Verlag, 1985.

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6

Trease, Harold E., Martin F. Fritts, and W. Patrick Crowley, eds. Advances in the Free-Lagrange Method Including Contributions on Adaptive Gridding and the Smooth Particle Hydrodynamics Method. Berlin, Heidelberg: Springer Berlin Heidelberg, 1991. http://dx.doi.org/10.1007/3-540-54960-9.

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7

INRIA Workshop on Numerical Methods for the Euler Equations of Fluid Dynamics (1983 Rocquencourt, Yvelines, France). Numerical methods for the Euler equations of fluid dynamics. Philadelphia: Society for Industrial and Applied Mathematics, 1985.

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8

Anderson, W. Kyle. Grid generation and flow solution method for Euler equations on unstructured grids. [Washington, DC]: National Aeronautics and Space Administration, Office of Management, Scientific and Technical Information Program, 1992.

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9

Toro, E. F. Some aspects of shock capturing methods for gas dynamics. Cranfield, Bedford, England: Dept. of Aerodynamics and Fluid Mechanics, College of Aeronautics, Cranfield Institute of Technology, 1991.

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10

Next Free-Lagrange Conference (1990 Moran, Wyo.). Advances in the Free-Lagrange method: Including contributions on adaptive gridding and the smooth particle hydrodynamics method : proceedings of the Next Free-Lagrange Conference held at Jackson Lake Lodge, Moran, Wyoming, USA, 3-7 June 1990. Berlin: Springer-Verlag, 1991.

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11

Quirk, James J. Godunov-type schemes applied to detonation flows. Hampton, Va: Institute for Computer Applications in Science and Engineering, 1993.

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12

Felici, Helene M. A coupled Eulerian/Lagrangian method for the solution of three-dimensional vortical flows. [Washington, DC: National Aeronautics and Space Administration, 1992.

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13

Felici, Helene M. A coupled Eulerian/Lagrangian method for the solution of three-dimensional vortical flows. Cambridge, Mass: Gas Turbine Laboratory, Massachusetts Institute of Technology, 1992.

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14

Shapiro, Richard A. Adaptive finite element solution algorithm for the Euler equations. Braunschweig: Vieweg, 1991.

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15

Francesco, Bullo, and Fujimoto Kenji 1947-, eds. Lagrangian and Hamiltonian methods for nonlinear control 2006: Proceedings from the 3rd IFAC workshop, Nagoya, Japan, July 2006. Berlin: Springer, 2007.

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16

A, Astolfi, Gordillo Francisco 1964-, Schaft, A. J. van der, and International Federation of Automatic Control, eds. Lagrangian and Hamiltonian methods for nonlinear control 2003: A proceedings volume from the 2nd IFAC Workshop, Seville, Spain, 3-5 April, 2003. Oxford: Published for the International Federation of Automatic Control by Elsevier, 2003.

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17

IFAC Workshop (2000 Princeton, N.J.). Lagrangian and Hamiltonian methods for nonlinear control: A proceedings volume from the IFAC Workshop, Princeton, New Jersey, USA, 16-18 March 2000. Oxford: Pergamon, 2000.

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18

Behrens, Jörn. Adaptive Semi-Lagrange-Finite-Elemente-Methode zur Lösung der Flachwassergleichungen: Implementierung und Parallelisierung = Adaptive semi-Lagranigian [sic] finite element method for the solution of shallow water equations : implementation and parallelization. Bremerhaven: Alfred-Wegener-Institut für Polar- und Meeresforschung, 1996.

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19

Jentink, Thomas Neil. Formulation of boundary conditions for the multigrid acceleration of the Euler and Navier Stokes equations. West Lafayette, Ind: Purdue University, School of Aeronautics and Astronautics, 1990.

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20

Diskin, Boris. New factorizable discretizations for the Euler equations. Hampton, VA: Institute for Computer Applications in Science and Engineering, NASA Langley Research Center, 2002.

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21

Arthur, Rizzi, and Hirschel Ernst-Heinrich, eds. Numerical solutions of the Euler equations for steady flow problems. Braunschweig; Wiesbaden: Vieweg, 1991.

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22

Eberle, Albrecht. Numerical solutions of the Euler equations for steady flow problems. Braunschweig: Vieweg, 1992.

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23

Diskin, Boris. Analysis of boundary conditions for factorizable discretizations of the Euler equations. Hampton, VA: Institute for Computer Applications in Science and Engineering, NASA Langley Research Center, 2002.

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24

Frink, Neal T. Tetrahedral finite-volume solutions to the Navier-Stokes equations on complex configurations. Hampton, Va: National Aeronautics and Space Administration, Langley Research Center, 1998.

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25

A new Lagrangian method for three-dimensional steady supersonic flows. [Washington, DC: National Aeronautics and Space Administration, 1993.

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26

Fritts, Martin J., Patrick W. Crowley, and Harold Trease. The Free-Lagrange Method: Proceedings of the First International Conference on Free-Lagrange Methods, Held at Hilton Head Island, South Carolina, March 4-6, 1985. Springer, 2014.

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27

The Free-Lagrange Method: Proceedings of the First International Conference on Free-Lagrange Methods, Held at Hilton Head Island, South Carolina, March 4–6, 1985. Springer, 1985.

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28

Review of preconditioning methods for fluid dynamics. Hampton, Va: National Aeronautics and Space Administration, Langley Research Center, 1992.

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29

Modified interior distance functions (theory and methods). Fairfax, Va: Dept. of Operations Research, School of Information Technology and Engineering, George Mason University, 1995.

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30

Canonical-variables multigrid method for steady-state Euler equation. Hampton, Va: National Aeronautics and Space Administration, Langley Research Center, 1994.

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31

Center, Langley Research, ed. Canonical-variables multigrid method for steady-state Euler equation. Hampton, Va: National Aeronautics and Space Administration, Langley Research Center, 1994.

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32

Canonical-variables multigrid method for steady-state Euler equation. Hampton, Va: National Aeronautics and Space Administration, Langley Research Center, 1994.

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33

United States. National Aeronautics and Space Administration., ed. An extended Lagrangian method. [Washington, D.C: National Aeronautics and Space Administration, 1995.

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34

United States. National Aeronautics and Space Administration., ed. An extended Lagrangian method. [Washington, D.C: National Aeronautics and Space Administration, 1995.

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35

United States. National Aeronautics and Space Administration., ed. An extended Lagrangian method. [Washington, DC: National Aeronautics and Space Administration, 1992.

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36

United States. National Aeronautics and Space Administration., ed. An extended Lagrangian method. [Washington, DC: National Aeronautics and Space Administration, 1992.

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37

United States. National Aeronautics and Space Administration., ed. Structural optimization of large structural systems by optimality criteria methods. [Washington, DC: National Aeronautics and Space Administration, 1992.

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38

A highly parallel multigrid-like method for the solution of the Euler equations. [Moffett Field, Calif.]: Research Institute for Advanced Computer Science, NASA Ames Research Center, 1989.

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39

Atomization simulations using an Eulerian-VOF-Lagrangian method. [Washington, DC: National Aeronautics and Space Administration, 1994.

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40

A second-order accurate kinetic-theory-based method for inviscid compressible flows. [Washington, D.C.]: National Aeronautics and Space Administration, Scientific and Technical Information Branch, 1987.

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41

United States. National Aeronautics and Space Administration. Scientific and Technical Information Branch., ed. A second-order accurate kinetic-theory-based method for inviscid compressible flows. [Washington, D.C.]: National Aeronautics and Space Administration, Scientific and Technical Information Branch, 1987.

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42

United States. National Aeronautics and Space Administration. Scientific and Technical Information Branch., ed. A second-order accurate kinetic-theory-based method for inviscid compressible flows. [Washington, D.C.]: National Aeronautics and Space Administration, Scientific and Technical Information Branch, 1987.

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43

Hagelberg, Carl R. Existence of a solution to a variational data assimilation method in two-dimensional hydrodynamics. 1992.

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44

J, Mavriplis D., and Langley Research Center, eds. Agglomeration multigrid for the three-dimensional Euler equations. Hampton, Va: National Aeronautics and Space Administration, Langley Research Center, 1994.

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45

Center, Langley Research, ed. Three dimensional unstructured multigrid for the Euler equations. Hampton, Va: National Aeronautics and Space Administration, Langley Research Center, 1991.

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46

Golan, Amos. Entropy Maximization. Oxford University Press, 2017. http://dx.doi.org/10.1093/oso/9780199349524.003.0004.

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Abstract:
In this chapter I develop the essential maximum entropy procedure, which is an inversion procedure for inferring an unknown probability distribution function from incomplete information. The formulation here is the root of info-metrics and is grounded in the motivations provided in Chapter 2 and the metrics defined in Chapter 3. Once the basic maximum entropy problem is defined and the solution is derived via the method of Lagrange multipliers, I derive and discuss its dual formulation. I then define and discuss the concept of conjugate variables, which is related to the Lagrange multipliers. Throughout, the mathematical derivations are supported by graphical illustrations and supplemented with heuristic arguments and with numerous examples in ideal settings.
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47

Leonard, N. E., and R. Ortega. Lagrangian and Hamiltonian Methods for Nonlinear Control 2000 (IFAC Proceedings Volumes). Pergamon, 2000.

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48

Leonard, N. E., and R. Ortega. Lagrangian and Hamiltonian Methods for Nonlinear Control 2000 (IFAC Proceedings Volumes). Pergamon, 2000.

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49

(Editor), A. Astolfi, A J Van Der Schaft (Editor), and Francisco Gordillo (Editor), eds. Lagrangian and Hamiltonian Methods in Nonlinear Control 2003: Workshop (IFAC Proceedings Volumes). Pergamon, 2003.

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50

Lagrangian and Hamiltonian Methods in Nonlinear Control 2003: Workshop (IFAC Proceedings Volumes). Pergamon, 2003.

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