Journal articles: 'Maximum principle'

1

Štecha, Jan, and Jan Rathouský. "Stochastic maximum principle." IFAC Proceedings Volumes 44, no. 1 (January 2011): 4714–20. http://dx.doi.org/10.3182/20110828-6-it-1002.01501.

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2

Yazhe, Chen. "Aleksandrov maximum principle and bony maximum principle for parabolic equations." Acta Mathematicae Applicatae Sinica 2, no. 4 (December 1985): 309–20. http://dx.doi.org/10.1007/bf01665846.

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3

Ivochkina, Nina. "On the maximum principle for principal curvatures." Banach Center Publications 33, no. 1 (1996): 115–26. http://dx.doi.org/10.4064/-33-1-115-126.

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4

Dmitruk, A. V., and A. M. Kaganovich. "The Hybrid Maximum Principle is a consequence of Pontryagin Maximum Principle." Systems & Control Letters 57, no. 11 (November 2008): 964–70. http://dx.doi.org/10.1016/j.sysconle.2008.05.006.

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5

Dufour, Francois, and Boris Miller. "SINGULAR STOCHASTIC MAXIMUM PRINCIPLE." IFAC Proceedings Volumes 38, no. 1 (2005): 29–34. http://dx.doi.org/10.3182/20050703-6-cz-1902.00865.

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6

Wang, Chunjie. "On Korenblum’s maximum principle." Proceedings of the American Mathematical Society 134, no. 7 (January 5, 2006): 2061–66. http://dx.doi.org/10.1090/s0002-9939-06-08311-0.

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7

LEDZEWICZ, URSZULA, and HEINZ SCHÄTTLER. "AN EXTENDED MAXIMUM PRINCIPLE." Nonlinear Analysis: Theory, Methods & Applications 29, no. 2 (July 1997): 159–83. http://dx.doi.org/10.1016/s0362-546x(96)00038-7.

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8

Parr, Robert G., and Pratim K. Chattaraj. "Principle of maximum hardness." Journal of the American Chemical Society 113, no. 5 (February 1991): 1854–55. http://dx.doi.org/10.1021/ja00005a072.

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9

Lugovtsov, B. A. "Principle of maximum discharge." Journal of Applied Mechanics and Technical Physics 32, no. 4 (1992): 563–64. http://dx.doi.org/10.1007/bf00851561.

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10

Schwick, Wilhelm. "On Korenblum’s maximum principle." Proceedings of the American Mathematical Society 125, no. 9 (1997): 2581–87. http://dx.doi.org/10.1090/s0002-9939-97-03247-4.

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11

Eschenburg, J. H. "Maximum principle for hypersurfaces." Manuscripta Mathematica 64, no. 1 (March 1989): 55–75. http://dx.doi.org/10.1007/bf01182085.

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12

Pshenichnyi, B. N., and P. I. Ginailo. "Generalized discrete maximum principle." Ukrainian Mathematical Journal 37, no. 6 (1986): 630–33. http://dx.doi.org/10.1007/bf01057434.

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13

Dreyer, Wolfgang, and Matthias Kunik. "Maximum entropy principle revisited." Continuum Mechanics and Thermodynamics 10, no. 6 (December 1, 1998): 331–47. http://dx.doi.org/10.1007/s001610050097.

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14

Mohammed, Ahmed, and Antonio Vitolo. "On the strong maximum principle." Complex Variables and Elliptic Equations 65, no. 8 (April 4, 2019): 1299–314. http://dx.doi.org/10.1080/17476933.2019.1594207.

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15

Pinchover, Yehuda. "Book Review: The maximum principle." Bulletin of the American Mathematical Society 46, no. 3 (March 16, 2009): 499–504. http://dx.doi.org/10.1090/s0273-0979-09-01246-4.

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16

Kesavan, H. K., and J. N. Kapur. "The generalized maximum entropy principle." IEEE Transactions on Systems, Man, and Cybernetics 19, no. 5 (1989): 1042–52. http://dx.doi.org/10.1109/21.44019.

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17

Agrachev, A. A., and R. V. Gamkrelidze. "The geometry of maximum principle." Proceedings of the Steklov Institute of Mathematics 273, no. 1 (July 2011): 1–22. http://dx.doi.org/10.1134/s0081543811040018.

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18

Cellina, Arrigo. "On the strong maximum principle." Proceedings of the American Mathematical Society 130, no. 2 (May 23, 2001): 413–18. http://dx.doi.org/10.1090/s0002-9939-01-06104-4.

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19

Wang, Shaojun, Dale Schuurmans, and Yunxin Zhao. "The Latent Maximum Entropy Principle." ACM Transactions on Knowledge Discovery from Data 6, no. 2 (July 2012): 1–42. http://dx.doi.org/10.1145/2297456.2297460.

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20

Pearson, Ralph G. "Principle of Maximum Physical Hardness." Journal of Physical Chemistry 98, no. 7 (February 1994): 1989–92. http://dx.doi.org/10.1021/j100058a044.

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21

Pearson, Ralph G. "The principle of maximum hardness." Accounts of Chemical Research 26, no. 5 (May 1993): 250–55. http://dx.doi.org/10.1021/ar00029a004.

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22

Guiasu, Silviu, and Abe Shenitzer. "The principle of maximum entropy." Mathematical Intelligencer 7, no. 1 (March 1985): 42–48. http://dx.doi.org/10.1007/bf03023004.

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23

Barbero-Liñán, M., and M. C. Muñoz-Lecanda. "Presymplectic high order maximum principle." Revista de la Real Academia de Ciencias Exactas, Fisicas y Naturales. Serie A. Matematicas 106, no. 1 (March 22, 2011): 97–110. http://dx.doi.org/10.1007/s13398-011-0022-x.

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24

Pucci, Patrizia, and James Serrin. "The strong maximum principle revisited." Journal of Differential Equations 196, no. 1 (January 2004): 1–66. http://dx.doi.org/10.1016/j.jde.2003.05.001.

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25

Mariconda, C., and G. Treu. "Gradient Maximum Principle for Minima." Journal of Optimization Theory and Applications 112, no. 1 (January 2002): 167–86. http://dx.doi.org/10.1023/a:1013052830852.

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26

Whittle, P. "A risk-sensitive maximum principle." Systems & Control Letters 15, no. 3 (September 1990): 183–92. http://dx.doi.org/10.1016/0167-6911(90)90110-g.

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27

Da̧browski, Mariusz P., and H. Gohar. "Abolishing the maximum tension principle." Physics Letters B 748 (September 2015): 428–31. http://dx.doi.org/10.1016/j.physletb.2015.07.047.

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28

Bongini, Mattia, Massimo Fornasier, Francesco Rossi, and Francesco Solombrino. "Mean-Field Pontryagin Maximum Principle." Journal of Optimization Theory and Applications 175, no. 1 (August 10, 2017): 1–38. http://dx.doi.org/10.1007/s10957-017-1149-5.

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29

Carozza, Menita, Luca Esposito, Raffaella Giova, and Francesco Leonetti. "Polyconvex functionals and maximum principle." Mathematics in Engineering 5, no. 4 (2023): 1–10. http://dx.doi.org/10.3934/mine.2023077.

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<abstract>Let us consider continuous minimizers $ u : \bar \Omega \subset \mathbb{R}^n \to \mathbb{R}^n $ of <disp-formula> <label/> <tex-math id="FE1"> \begin{document}$ \mathcal{F}(v) = \int_{\Omega} [|Dv|^p \, + \, |{\rm det}\,Dv|^r] dx, $\end{document} </tex-math></disp-formula> with $ p > 1 $ and $ r > 0 $; then it is known that every component $ u^\alpha $ of $ u = (u^1, ..., u^n) $ enjoys maximum principle: the set of interior points $ x $, for which the value $ u^\alpha(x) $ is greater than the supremum on the boundary, has null measure, that is, $ \mathcal{L}^n(\{ x \in \Omega: u^\alpha (x) > \sup_{\partial \Omega} u^\alpha \}) = 0 $. If we change the structure of the functional, it might happen that the maximum principle fails, as in the case <disp-formula> <label/> <tex-math id="FE2"> \begin{document}$ \mathcal{F}(v) = \int_{\Omega}[\max\{(|Dv|^p - 1); 0 \} \, + \, |{\rm det}\,Dv|^r] dx, $\end{document} </tex-math></disp-formula> with $ p > 1 $ and $ r > 0 $. Indeed, for a suitable boundary value, the set of the interior points $ x $, for which the value $ u^\alpha(x) $ is greater than the supremum on the boundary, has a positive measure, that is $ \mathcal{L}^n(\{ x \in \Omega: u^\alpha (x) > \sup_{\partial \Omega} u^\alpha \}) > 0 $. In this paper we show that the measure of the image of these bad points is zero, that is $ \mathcal{L}^n(u(\{ x \in \Omega: u^\alpha (x) > \sup_{\partial \Omega} u^\alpha \})) = 0 $, provided $ p > n $. This is a particular case of a more general theorem.</abstract>

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30

Meyer, J. C., and D. J. Needham. "Extended weak maximum principles for parabolic partial differential inequalities on unbounded domains." Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 470, no. 2167 (July 8, 2014): 20140079. http://dx.doi.org/10.1098/rspa.2014.0079.

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In this paper, we establish extended maximum principles for solutions to linear parabolic partial differential inequalities on unbounded domains, where the solutions satisfy a variety of growth/decay conditions on the unbounded domain. We establish a conditional maximum principle, which states that a solution u to a linear parabolic partial differential inequality satisfies a maximum principle whenever a suitable weight function can be exhibited. Our extended maximum principles are then established by exhibiting suitable weight functions and applying the conditional maximum principle. In addition, we include several specific examples, to highlight the importance of certain generic conditions, which are required in the statements of maximum principles of this type. Furthermore, we demonstrate how to obtain associated comparison theorems from our extended maximum principles.

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31

NEDOSHOVENKO, Andrii. "Synthesis of maximum economy, efficiency and proportionality as principles of public procurement execution." Economics. Finances. Law 5/3, no. - (May 30, 2022): 25–30. http://dx.doi.org/10.37634/efp.2022.5(3).6.

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The principles of maximum economy, efficiency and proportionality belong to the institutional principles, as they determine the guiding ideas and principles of public procurement. Certain issues related to the principle of maximum economy, efficiency and proportionality were researched in the publications of N. Zdyrko, K. Chuchalina, T.O. Mulik, V.O. Psota et al. Nevertheless, existing publications are mostly devoted to the disclosure of the concept of maximum economy, efficiency and proportionality principles without coverage relationship among these principles. The purpose of this study is to reveal the problematic issues of maximum economy, efficiency and proportionality correlation as requirements which are set out in a separate principle of public procurement. The content and importance of maximum economy, efficiency and proportionality as principles of public procurement are analyzed within the article. The importance of this principle and its superiority among other principles of public procurement are substantiated. The contradictory aspects of the relationship between maximum economy and efficiency are highlighted in the paper, and the feasibility and possibility of their harmonization and comparison are justified. Practical aspects of maximum economy and efficiency execution in public procurement are revealed. The functional significance and place of proportionality in relation to the maximum economy and efficiency are covered. The author reaches a conclusion that principle of economy should not be opposed to the principle of efficiency because these principles do not contradict each other. Differences in subjects, objects and other conditions of procurement contracts demands a differentiated approach to the analysis of efficiency and maximum economy in public procurement.

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32

Berestycki, Henri, Italo Capuzzo Dolcetta, Alessio Porretta, and Luca Rossi. "Maximum Principle and generalized principal eigenvalue for degenerate elliptic operators." Journal de Mathématiques Pures et Appliquées 103, no. 5 (May 2015): 1276–93. http://dx.doi.org/10.1016/j.matpur.2014.10.012.

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33

Antón, I., and J. López-Gómez. "Principal eigenvalue and maximum principle for cooperative periodic–parabolic systems." Nonlinear Analysis 178 (January 2019): 152–89. http://dx.doi.org/10.1016/j.na.2018.07.014.

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34

Stehlík, Petr, and Jonáš Volek. "Maximum Principles for Discrete and Semidiscrete Reaction-Diffusion Equation." Discrete Dynamics in Nature and Society 2015 (2015): 1–13. http://dx.doi.org/10.1155/2015/791304.

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We study reaction-diffusion equations with a general reaction functionfon one-dimensional lattices with continuous or discrete timeux′ (or Δtux)=k(ux-1-2ux+ux+1)+f(ux),x∈Z. We prove weak and strong maximum and minimum principles for corresponding initial-boundary value problems. Whereas the maximum principles in the semidiscrete case (continuous time) exhibit similar features to those of fully continuous reaction-diffusion model, in the discrete case the weak maximum principle holds for a smaller class of functions and the strong maximum principle is valid in a weaker sense. We describe in detail how the validity of maximum principles depends on the nonlinearity and the time step. We illustrate our results on the Nagumo equation with the bistable nonlinearity.

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35

Zemliak, Alexander. "Circuit Optimization Study According to the Maximum Principle." WSEAS TRANSACTIONS ON COMPUTERS 20 (December 9, 2021): 362–71. http://dx.doi.org/10.37394/23205.2021.20.38.

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The minimization of the processor time of designing can be formulated as a problem of time minimization for transitional process of dynamic system. A special control vector that changes the internal structure of the equations of optimization procedure serves as a principal tool for searching the best strategies with the minimal CPU time. In this case a well-known maximum principle of Pontryagin is the best theoretical approach for finding of the optimum structure of control vector. Practical approach for realization of the maximum principle is based on the analysis of behavior of a Hamiltonian for various strategies of optimization. The possibility of applying the maximum principle to the problem of optimization of electronic circuits is analyzed. It is shown that in spite of the fact that the problem of optimization is formulated as a nonlinear task, and the maximum principle in this case isn't a sufficient condition for obtaining a minimum of the functional, it is possible to obtain the decision in the form of local minima. The relative acceleration of the CPU time for the best strategy found by means of maximum principle compared with the traditional approach is equal two to three orders of magnitude.

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36

Fattorini, H. "The maximum principle in infinite dimension." Discrete and Continuous Dynamical Systems 6, no. 3 (April 2000): 557–74. http://dx.doi.org/10.3934/dcds.2000.6.557.

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37

Darooneh, Amir. "Utility Function from Maximum Entropy Principle." Entropy 8, no. 1 (January 31, 2006): 18–24. http://dx.doi.org/10.3390/e8010018.

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38

Golubkin, Valerii Nikolaevich, and Grigorii Borisovich Sizykh. "MAXIMUM PRINCIPLE FOR THE BERNOULLI FUNCTION." TsAGI Science Journal 46, no. 5 (2015): 485–90. http://dx.doi.org/10.1615/tsagiscij.v46.i5.50.

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39

Artstein, Zvi. "Pontryagin Maximum Principle Revisited with Feedbacks." European Journal of Control 17, no. 1 (January 2011): 46–54. http://dx.doi.org/10.3166/ejc.17.46-54.

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40

Avakov, E., and G. Magaril-Ilyayev. "Generalized Maximum Principle in Optimal Control." Доклады академии наук 483, no. 3 (November 2018): 237–40. http://dx.doi.org/10.31857/s086956520003235-1.

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41

Ganguly, Siddhartha, Souvik Das, Debasish Chatterjee, and Ravi Banavar. "Rate Constrained Discrete-time Maximum Principle." IFAC-PapersOnLine 54, no. 19 (2021): 346–51. http://dx.doi.org/10.1016/j.ifacol.2021.11.101.

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42

PETROVICI, M. A., C. DAMIAN, and D. COLTUC. "Maximum Entropy Principle in Image Restoration." Advances in Electrical and Computer Engineering 18, no. 2 (2018): 77–84. http://dx.doi.org/10.4316/aece.2018.02010.

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43

Kipka, Robert, and Rohit Gupta. "The Discrete-Time Geometric Maximum Principle." SIAM Journal on Control and Optimization 57, no. 4 (January 2019): 2939–61. http://dx.doi.org/10.1137/16m1101489.

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44

Roupas, Zacharias. "Gravitational potential from maximum entropy principle." Classical and Quantum Gravity 37, no. 9 (April 14, 2020): 097001. http://dx.doi.org/10.1088/1361-6382/ab8144.

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45

Lim, A. E. B., and Xun Yu Zhou. "A new risk-sensitive maximum principle." IEEE Transactions on Automatic Control 50, no. 7 (July 2005): 958–66. http://dx.doi.org/10.1109/tac.2005.851441.

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46

Gedalin, M. "Maximum entropy principle for anisotropic plasma." Physics of Fluids B: Plasma Physics 3, no. 8 (August 1991): 2149. http://dx.doi.org/10.1063/1.859627.

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47

LI, XIANG, and BAODING LIU. "MAXIMUM ENTROPY PRINCIPLE FOR FUZZY VARIABLES." International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems 15, supp02 (April 2007): 43–52. http://dx.doi.org/10.1142/s0218488507004595.

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The concept of fuzzy entropy is used to provide a quantitative measure of the uncertainty associated with every fuzzy variable. This paper proposes the maximum entropy principle for fuzzy variables, that is, out of all the membership functions satisfying given constraints, choose the one that has maximum entropy. The problem is what is the specific formulation of the maximum entropy membership function. The purpose of this paper is to solve this problem by Euler–Lagrange equation.

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48

Avakov, E. R., and G. G. Magaril-Il’yaev. "Pontryagin maximum principle, relaxation, and controllability." Doklady Mathematics 93, no. 2 (March 2016): 193–96. http://dx.doi.org/10.1134/s1064562416020216.

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49

Avakov, E. R., and G. G. Magaril-Il’yaev. "Generalized Maximum Principle in Optimal Control." Doklady Mathematics 98, no. 3 (November 2018): 575–78. http://dx.doi.org/10.1134/s1064562418070116.

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50

Canuto, Claudio. "Spectral methods and a maximum principle." Mathematics of Computation 51, no. 184 (1988): 615. http://dx.doi.org/10.1090/s0025-5718-1988-0930226-2.

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Journal articles on the topic 'Maximum principle'

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