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1

Balakrishnan, A. V. A mathematical formulation of the SCOLE control problem. National Aeronautics and Space Administration, Langley Research Center, 1989.

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2

Balakrishnan, A. V. A mathematical formulation of the SCOLE control problem. National Aeronautics and Space Administration, Langley Research Center, 1985.

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3

O, Kim Kyun, and United States. National Aeronautics and Space Administration. Scientific and Technical Information Division., eds. Mixed formulation for frictionless contact problems. National Aeronautics and Space Administration, Office of Management, Scientific and Technical Information Division, 1989.

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4

-C, Chang B., Fischl Robert, and Langley Research Center, eds. A problem formulation for glideslope tracking in wind shear using advanced robust control techniques. National Aeronautics and Space Administration, Langley Research Center, 1992.

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5

B, Mujiyadi, Kironosasi Endang, Pudjianto Bambang, and Pusat Penelitian dan Pengembangan Usaha Kesejahteraan Sosial (Indonesia), eds. The models of social problem resolving: The roles of research and development in the formulation of social welfare policies : compilation of executive summaries. 2nd ed. Center of Social Welfare Research and Development, Social Development and Training Agency, Indonesia's Ministry of Social Affairs, 2005.

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6

Diaby, Moustapha. Advances in combinatorial optimization: Linear programming formulation of the traveling salesman and other hard combinatorial optimization problems. World Scientific, 2015.

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7

Center, Langley Research, ed. On the numerical formulation of parametric linear fractional transformation (LFT) uncertainty models for multivariate matrix polynomial problems. National Aeronautics and Space Administration, Langley Research Center, 1998.

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8

Kathy, Davis. Problem (re)formulation in psychotherapy. Erasmus Universiteit, 1986.

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9

McEachern, Andrew, and Daniel Ashlock. Mathematical Problem Factories. Springer International Publishing, 2021. http://dx.doi.org/10.1007/978-3-031-02436-8.

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10

Liljedahl, Peter, and Manuel Santos-Trigo, eds. Mathematical Problem Solving. Springer International Publishing, 2019. http://dx.doi.org/10.1007/978-3-030-10472-6.

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11

Singer, Florence Mihaela, Nerida F. Ellerton, and Jinfa Cai, eds. Mathematical Problem Posing. Springer New York, 2015. http://dx.doi.org/10.1007/978-1-4614-6258-3.

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12

Baumanns, Lukas. Mathematical Problem Posing. Springer Fachmedien Wiesbaden, 2022. http://dx.doi.org/10.1007/978-3-658-39917-7.

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13

Schoenfeld, Alan H. Mathematical problem solving. Academic Press, 1985.

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14

Lyles, Marjorie A. Problem formulation and organizational decision-making: Biases and assumptions underlying alternative models of strategic problem formulation. University of Illinois at Urbana-Champaign, College of Commerce and Business Administration, 1985.

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15

Dhaene, Geert. Encompassing: Formulation, properties and testing. Springer, 1997.

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16

Fugl, Annette Wilson. Physical concept and mathematical formulation of basin modelling. Riso Library, 1989.

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17

Graglia, Roberto D., Giuseppe Pelosi, and Stefano Selleri, eds. International Workshop on Finite Elements for Microwave Engineering. Firenze University Press, 2016. http://dx.doi.org/10.36253/978-88-6655-968-9.

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When Courant prepared the text of his 1942 address to the American Mathematical Society for publication, he added a two-page Appendix to illustrate how the variational methods first described by Lord Rayleigh could be put to wider use in potential theory. Choosing piecewise-linear approximants on a set of triangles which he called elements, he dashed off a couple of two-dimensional examples and the finite element method was born. … Finite element activity in electrical engineering began in earnest about 1968-1969. A paper on waveguide analysis was published in Alta Frequenza in early 1969, giv
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18

Heymann, Michael. A formulation and analysis of combat games. National Aeronautics and Space Administration, Scientific and Technical Information Branch, 1985.

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19

Lawrence, Pfleeger Shari, ed. Collecting the dots: Problem formulation and solution elements. Rand, 2004.

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20

McLeod, Douglas B., and Verna M. Adams, eds. Affect and Mathematical Problem Solving. Springer New York, 1989. http://dx.doi.org/10.1007/978-1-4612-3614-6.

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21

H, Schoenfeld Alan, ed. Mathematical thinking and problem solving. L. Erlbaum Associates, 1994.

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22

Melfried, Olson, Olson Judith K. 1947-, and National Council of Teachers of Mathematics., eds. Children are mathematical problem solvers. National Council of Teachers of Mathematics, 2002.

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23

1943-, Flowers Joe, ed. Principles of mathematical problem solving. Prentice Hall, 1999.

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24

Murphy, D. G. Formulation of a mathematical model for kinematic froth visualisation. UMIST, 1996.

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25

Jeroslow, Robert G. Logic-based decision support: Mixed integer model formulation. North-Holland, 1989.

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26

Lakin, William D. A combined integrating and differentiating matrix formulation for boundary value problems on rectangular domains. Langley Research Center, 1986.

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27

Claus, A. An arc flow formulation for the travelling salesman problem. Sloan School of Management, Massachusetts Institute of Technology, 1987.

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28

Stefano, Del Giudice, and Nonino Carlo, eds. Finite element analysis in heat transfer: Basic formulation and linear problems. Taylor & Francis, 1994.

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29

K, Maini Philip, and Othmer H. G. 1943-, eds. Mathematical models for biological pattern formulation: Frontiers in biological mathematics. Springer, 2001.

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30

Pamin, Jerzy. Gradient-enhanced continuum models: Formulation, discretization and applications. Cracow University of Technology, 2004.

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31

Collis, Kevin F. Collis-Romberg mathematical problem solving profiles. Australian Council for Educational Research, 1992.

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32

Brent, West Douglas, ed. Mathematical thinking: Problem-solving and proofs. 2nd ed. Prentice Hall, 2000.

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33

D'Angelo, John P. Mathematical thinking: Problem-solving and proofs. Prentice Hall, 1997.

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34

Paredes-Veloso, Gonzalo L. An efficient formulation and solution method of the even-aged rotation and thinning problem. 1986.

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35

The Distributor's Three-Dimensional Pallet-Packing Problem: A mathematical Formulation and Heuristic Solution Approach. Storming Media, 2000.

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36

Heidarzadeh, Mohammad, Theodosios K. Papathanasiou, Yurui Fan, and Hamid Bahai. A Practical Approach to Advanced Mathematical Modelling in Civil Engineering. Oxford University PressOxford, 2025. https://doi.org/10.1093/9780191888656.001.0001.

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Abstract This book revolutionizes the teaching of mathematical modelling in civil engineering schools by systematically addressing numerous real-world engineering challenges, accompanied by MATLAB code for the first time. Commencing with mathematical modelling (Chapter 1), it delineates seven steps essential for developing a mathematical model for real-world engineering problems: problem formulation (step 1), outlining the problem and conceptualization (step 2), assumptions (step 3), parametrization and variables (step 4), deriving the equations (step 5), simulation and analysis (step 6), and
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37

Aziz, Nazrina, Syariza Abdul-Rahman, and Norhaslina Zainal Abidin, eds. Recent Applications in Quantitative Methods and Information Technology. UUM Press, 2019. http://dx.doi.org/10.32890/9789672210269.

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This book is a guide for researchers who are involved in statistical, mathematical, information technology and decision science analyses. The purpose of the book is to allow readers to get research ideas on a wide range of topics, such as sampling plans, capital budgeting, completion time in production line, searching pattern for mobile cache replacement policy, home security system with biometric finger print and web service technology. The analyses in each chapter are explained in detail with samples of real applications in daily life to assist readers to appreciate theoretical, algorithm an
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38

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

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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.
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39

Andersen, Ib. Guide to Problem Formulation. Samfundslitteratur, 2005.

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40

Mann, Peter. Differential Equations. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780198822370.003.0035.

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This chapter presents the general formulation of the calculus of variations as applied to mechanics, relativity and field theories. The calculus of variations is a common mathematical technique used throughout classical mechanics. First developed by Euler to determine the shortest paths between fixed points along a surface, it was applied by Lagrange to mechanical problems in analytical mechanics. The variational problems in the chapter have been simplified for ease of understanding upon first introduction, in order to give a general mathematical framework. This chapter takes a relaxed approac
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41

Mercati, Flavio. Origins of the Mach–Poincaré Principle. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780198789475.003.0003.

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The problem with the definition of inertia was solved, in the simple case of free point particles, by Tait, who introduced the concept of inertial frame. Tait’s solution would have satisfied Leibniz’ request that inertia be determined dynamically, however it only works in the absence of interactions between the material bodies. Later Mach posed again the question of the origin of inertia, suggesting the idea that it should be dynamical, which was later dubbed ‘Mach’s principle’. Moreover Mach criticized also Newton’s absolute time, and introduced the basic idea of temporal relationalism, i.e.
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42

Radin, Michael A. Analyzing Mathematical Patterns — Detection & Formulation. WORLD SCIENTIFIC, 2022. http://dx.doi.org/10.1142/12986.

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43

O'Hanlon, Bill, John H. Weakland, Paul Watzlawick, Richard Fisch, and Milton H. Erickson. Change: Principles of Problem Formulation and Problem Resolution. Norton & Company, Incorporated, W. W., 2011.

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44

Mathematical Problem Solving. Elsevier, 1985. http://dx.doi.org/10.1016/c2013-0-05012-8.

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45

Kaur, Berinderjeet, Ban Har Yeap, and Manu Kapur. Mathematical Problem Solving. WORLD SCIENTIFIC, 2009. http://dx.doi.org/10.1142/7335.

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46

Mathematical Problem Papers. Creative Media Partners, LLC, 2022.

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47

Mathematical Problem Solving. Springer Nature, 2019.

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48

Radford, Ernest Marshall. Mathematical Problem Papers. Franklin Classics Trade Press, 2018.

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49

SCHOENFELD, Alan H. Mathematical Problem Solving. Elsevier Science & Technology Books, 2014.

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50

Radford, Ernest Marshall. Mathematical Problem Papers. Creative Media Partners, LLC, 2018.

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