Relevant bibliographies by topics / Lagrange mean value theorem

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  1. Journal articles
  2. Dissertations / Theses
  3. Book chapters
  4. Conference papers

Academic literature on the topic 'Lagrange mean value theorem'

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Published: 24 April 2022

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Journal articles on the topic "Lagrange mean value theorem"

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Lozada-Cruz, German. "Some variants of Lagrange's mean value theorem." Selecciones Matemáticas 7, no. 1 (2020): 144–50. http://dx.doi.org/10.17268/sel.mat.2020.01.13.

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Mateljevic, Miodrag, Marek Svetlik, Miloljub Albijanic, and Nebojsa Savic. "Generalizations of the Lagrange mean value theorem and applications." Filomat 27, no. 4 (2013): 515–28. http://dx.doi.org/10.2298/fil1304515m.

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In this paper we give a generalization of the Lagrange mean value theorem via lower and upper derivative, as well as appropriate criteria of monotonicity and convexity for arbitrary function f : (a, b) ( R. Some applications to the neoclassical economic growth model are given (from mathematical point of view).
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Jiang, Yinshan. "Discussion on the application of Lagrange mean value theorem." Journal of Physics: Conference Series 1682 (November 2020): 012058. http://dx.doi.org/10.1088/1742-6596/1682/1/012058.

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王, 耀革. "Structure Analysis and Application of Lagrange Mean Value Theorem." Pure Mathematics 12, no. 02 (2022): 276–79. http://dx.doi.org/10.12677/pm.2022.122032.

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Smith, Robert S. "Rolle over Lagrange-Another Shot at the Mean Value Theorem." College Mathematics Journal 17, no. 5 (1986): 403. http://dx.doi.org/10.2307/2686248.

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Smith, Robert S. "Rolle over Lagrange—Another Shot at the Mean Value Theorem." College Mathematics Journal 17, no. 5 (1986): 403–6. http://dx.doi.org/10.1080/07468342.1986.11972987.

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邱, 崇. "A Note of the Teaching of Lagrange Mean Value Theorem." Advances in Education 10, no. 01 (2020): 47–52. http://dx.doi.org/10.12677/ae.2020.101008.

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Tong, Jingcheng. "84.60 The Mean Value Theorem of Lagrange Generalised to Involve Two Functions." Mathematical Gazette 84, no. 501 (2000): 515. http://dx.doi.org/10.2307/3620790.

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Nabil, Tamer. "Solvability of Fractional Differential Inclusion with a Generalized Caputo Derivative." Journal of Function Spaces 2020 (December 26, 2020): 1–11. http://dx.doi.org/10.1155/2020/2917306.

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This paper is devoted to the investigation of a kind of generalized Caputo semilinear fractional differential inclusions with deviated-advanced nonlocal conditions. Solvability of the problem is established by means of the Leray-Schauder’s alternative approach with the help of the Lagrange mean-value classical theorem. Finally, some examples are given to delineate the efficient of theoretical results.
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Tong, Jingcheng. "Classroom notes: The mean value theorems of Lagrange and Cauchy (II)." International Journal of Mathematical Education in Science and Technology 31, no. 3 (2000): 447–49. http://dx.doi.org/10.1080/002073900287200.

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Dissertations / Theses on the topic "Lagrange mean value theorem"

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Bel, Haj Frej Ghazi. "Estimation et commande décentralisée pour les systèmes de grandes dimensions : application aux réseaux électriques." Thesis, Université de Lorraine, 2017. http://www.theses.fr/2017LORR0139/document.

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Les travaux de cette thèse portent sur l’estimation et la commande décentralisée des systèmes de grande dimension. L’objectif est de développer des capteurs logiciels pouvant produire une estimation fiable des variables nécessaires pour la stabilisation des systèmes non linéaires interconnectés. Une décomposition d’un tel système de grande dimension en un ensemble de n sous-systèmes interconnectés est primordiale. Ensuite, en tenant compte de la nature du sous-système ainsi que les fonctions d’interconnexions, des lois de commande décentralisées basées observateurs ont été synthétisées. Chaque loi de commande est associée à un sous-système qui permet de le stabiliser localement, ainsi la stabilité du système global est assurée. L’existence d’un observateur et d’un contrôleur stabilisant le système dépend de la faisabilité d’un problème d’optimisation LMI. La formulation LMI, basée sur l’approche de Lyapunov, est élaborée par l’utilisation de principe de DMVT sur la fonction d’interconnexion non linéaire supposée bornée et incertaine. Ainsi des conditions de synthèse non restrictives sont obtenues. Des méthodes de synthèse de loi de commande décentralisée basée observateur ont été proposées pour les systèmes non linéaires interconnectés dans le cas continu et dans le cas discret. Des lois de commande robuste H1 décentralisées sont élaborées pour les systèmes non linéaires interconnectés en présence de perturbations et des incertitudes paramétriques. L’efficacité et la validation des approches présentées sont testées sur un modèle de réseaux électriques composé de trois générateurs interconnectés<br>This thesis focuses on the decentralized estimation and control for large scale systems. The objective is to develop software sensors that can produce a reliable estimate of the variables necessary for the interconnected nonlinear systems stability analysis. A decomposition of a such large system into a set of n interconnected subsystems is paramount for model simplification. Then, taking into account the nature of the subsystem as well as the interconnected functions, observer-based decentralized control laws have been synthesized. Each control law is associated with a subsystem which allows it to be locally stable, thus the stability of the overall system is ensured. The existence of an observer and a controller gain matrix stabilizing the system depends on the feasibility of an LMI optimization problem. The LMI formulation, based on Lyapunov approach, is elaborated by applying the DMVT technique on the nonlinear interconnection function, assumed to be bounded and uncertain. Thus, non-restrictive synthesis conditions are obtained. Observer-based decentralized control schemes have been proposed for nonlinear interconnected systems in the continuous and discrete time. Robust Hinfini decentralized controllers are provided for interconnected nonlinear systems in the presence of perturbations and parametric uncertainties. Effectiveness of the proposed schemes are verified through simulation results on a power systems with interconnected machines
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Hassan, Lama. "Observation et commande des systèmes non linéaires à retard." Phd thesis, Université de Lorraine, 2013. http://tel.archives-ouvertes.fr/tel-00934943.

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L'objectif de cette thèse est de développer des méthodes de synthèses d'observateurs et des contrôleurs basés sur un observateur pour les systèmes à retard. Différentes classes de systèmes ont été traitées avec différents types de retard. Trois méthodes ont été développées. La première méthode traite des systèmes non linéaires avec des non-linéarités lipschitziennes et consiste à transformer le système d'origine à un système LPV grâce à une reformulation de la propriété classique de Lipschitz. Cette technique est formulée pour les cas continu et discret, respectivement. Nous avons démontré, à travers des exemples numériques, que cette technique offre des conditions de synthèse moins restrictives par rapport aux résultats existants dans la littérature. La seconde méthode est développée pour une classe de systèmes singuliers avec des perturbations. La principale difficulté résidait dans la présence des dérivées des perturbations qui entravent l'analyse de la stabilité et pour laquelle deux approches ont été proposées: une approche Hinf en utilisant une fonctionnelle de Lyapunov-Krasovskii spéciale dépendante des perturbations et une approche basée sur l'utilisation d'un critère de performance W1;2. La dernière méthode est basée sur l'utilisation des matrices de pondération libres pour résoudre le problème de contrôle des systèmes non-linéaires à retards inconnus. La solution proposée fournit une condition de synthèse LMI garantissant la stabilisation du système en boucle fermée malgré la présence du retard inconnu, au lieu d'une inégalité matricielle linéaire itérative ILMI trouvée habituellement dans la littérature.
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Lin, Yu-Siang, and 林郁翔. "Discrete Mean Value Theorem." Thesis, 2014. http://ndltd.ncl.edu.tw/handle/60305687811322887486.

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碩士<br>國立中興大學<br>應用數學系所<br>102<br>In this thesis, we derive the mean value theorems for the super-harmonic, sub-harmonic and harmonic solutions on square domains. Moreover, we consider the mesh functions on the mesh squares and establish the discrete mean value theorem by using the Green’s identities on rectangles in R2. From the discrete mean value theorem, we obtain that the value of a discrete harmonic function at a mesh point (x0, y0) is the average of any discrete square which has center at this mesh point (x0, y0) . For further research, it is interesting to extend the result here to n-dimensional space.
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Hwang, Gwo-Jwu, and 黃國祖. "Mean value Theorem for one-sided differentiable function." Thesis, 2006. http://ndltd.ncl.edu.tw/handle/46244603358603144552.

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碩士<br>國立臺北大學<br>統計學系<br>94<br>In the study of the behavior of probability density function of continuous random variable, if the functions are differentiable or piecewise differentiable, usually, one can apply the method of calculus to determine the monotonically, concavity, points of inflection and asymptotes of these functions to attain some properties of the probability distributions. Most of the tools in calculus are consequences of the Mean Value Theorem for Derivatives. It is a theorem about functions continuous in bounded closed intervals and differentiable in the interior of the intervals. In general, continuous probability density functions are not necessarily differentiable everywhere, typical examples such as continuous piecewise linear distributions and double exponential distributions, but they have both left and right derivatives at the points where they are not differentiable. In this thesis, we shall consider one-sided differential functions defined on some intervals in the real number system and attain a Mean Value Theorem for One-sided Derivatives by an elementary proof. We also apply the result to discuss the monotonically and concavity of functions by examine some probability density functions.
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Xu, Yuan-Feng, and 許原豐. "An analysis of optical flow algorithms for motion estimation by mean-value theorem." Thesis, 1992. http://ndltd.ncl.edu.tw/handle/94324912031756206063.

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Romero, Christopher 1978. "They Must Be Mediocre: Representations, Cognitive Complexity, and Problem Solving in Secondary Calculus Textbooks." Thesis, 2012. http://hdl.handle.net/1969.1/148224.

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A small group of profit seeking publishers dominates the American textbook market and guides the learning of the majority of our nation’s calculus students. The College Board’s AP Calculus curriculum is a de facto national standard for this gateway course that is critically important to 21st century STEM careers. A multi-representational understanding of calculus is a central pillar of the AP curriculum. This dissertation asks whether this multi-representational vision is manifest in popular calculus textbooks. This dissertation began with a survey of all AP Calculus AB Examination free response items, 2002-2011, and found that students score worse on items characterized by numerical anchors or verbal targets. Based on previously elucidated models, a new cognitive model of five levels and six principles is developed for the purpose of calculus textbook task analysis. This model explicates complexity as a function of representational input and output. Eight popular secondary calculus textbooks were selected for study based on Amazon sales rank data. All verbally anchored mathematical tasks (n=555) from sections of those books concerning the mean value theorem and all AP Calculus AB prompts (n=226) were analyzed for cognitive complexity and representational diversity using the model. The textbook study found that calculus textbooks underrepresented the numerical anchor and verbal target. It found that the textbooks were both explicitly and implicitly less cognitively complex than the AP test. The article suggested that textbook tasks should be less dense, avoid cognitive attenuation, move away from the stand-alone item, juxtapose anchor representations, scaffold student solutions, incorporate previously considered overarching concepts and include more profound follow-up questions. To date there have been no studies of calculus textbook content based on established research on cognitive learning. Given the critical role that their calculus course plays in the lives of hundreds of thousands of students annually, it is incumbent upon the College Board to establish a textbook review process at the very least in the same vain as the teacher syllabus auditing process established in recent years.
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Reis, Valdir Delgado dos. "Teoremas do valor médio e intermédio." Master's thesis, 2020. http://hdl.handle.net/10400.2/10071.

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O Teorema do valor médio e o Teorema do valor intermédio são importantes teoremas muito usados no Cálculo integral e diferencial e não só. Neste trabalho estamos muito interessados em perceber estes teoremas, estudá-los profundamente e perceber qual o contributo dos mesmos. Para isso, visto que estão diretamente interligados com continuidade, derivadas e integrais, tivemos necessidade de ir à origem no século XVII perceber como surgiu o Cálculo pelas mãos de Isaac Newton e Gottfried Leibniz para posteriormente compreender de forma mais integral o Teorema do valor médio e o Teorema do valor intermédio que se devem, respetivamente a Joseph Louis de Lagrange e Bernard Bolzano no século XVIII, generalizados por Michel Rolle, Augustin Cauchy e Karl Weierstrass. O contexto histórico é apresentado no Capítulo 2. No Capítulo 3 analisamos os currículos do ensino secundário em Portugal e em Cabo Verde analisando a forma como os Teoremas acima referidos são lecionados e qual o grau de profundidade do seu estudo. Para perceber os Teoremas do valor médio e intermédio é necessário ter o conhecimento de limites, continuidade e derivada. Por isso, nos capítulos 5 e 6 dedicamos os primeiros tópicos especialmente a esses temas com breves revisões sobre limites, continuidade, derivadas e integrais. O Teorema do valor intermédio (Teorema de Bolzano) nos interessa muito pelo seu corolário que garante que dada uma função f contínua e dois pontos a e b do seu domínio, se f(a).f(b) < 0 então existe c no domínio de f tal que f(c) = 0. Esse corolário não só nos diz que a equação f(x) = 0 tem pelo menos uma raíz, também nos diz que tal raíz se encontra no intervalo ]a,b[. Apresentamos também um caso particular do Teorema do valor intermédio que é o Teorema de ponto fixo. Um outro teorema com fortes ligações ao Teorema do valor intermédio é o Teorema de Weierstrass que estuda os limites máximos e mínimos numa função contínua. Este mesmo teorema é usado para provar o Teorema de Rolle. O Teorema do valor médio que diz que se f é uma função contínua em [a, b] e derivável em ]a, b[ então existe um c pertencente a ]a ,b[ tal que f '(c) é igual à taxa de variação média da função em [a, b] também é estudado neste trabalho. Enfatizamos neste trabalho a importância das premissas dos teoremas, condições essas fundamentais para que se possam aplicar os teoremas. No caso do Teorema do valor médio a função deve ser contínua no intervalo [a, b] e deve ser diferenciável/derivável em ]a, b[ conceitos estudados nos capítulos 4 e 5. Não menos importante é tratado aqui o Teorema do valor médio com aplicação para integrais. Recorremos sempre ao software Geogebra para ilustrar cada um dos teoremas estudados tentando motivar as definições e as demonstrações. Também estudaremos as generalizações dos Teoremas do valor intermédio e médio.<br>The mean value theorem and the intermediate value theorem are very important theorems used in the integral and differential Calculus and in other domains. In this work we are very interested in analysing these theorems, in studying them deeply and in analysing their applications and contributions. For that, because they are directly interlinked with continuity, derivability and integration, we had the need to go to the origins in the XVII century to notice how the calculus appeared from Isaac Newton's and Gottfried Leibniz's and understand in a more profound way the mean value and intermediate value theorems whose main authors are Bernard Bolzano and Joseph Louis of Lagrange in the XVIII century, generalized later by Michel Rolle,Augustin Cauchy and Karl Weierstrass. The historical context is given in Chapter 2. In Chapter 3 we analyze the secondary school curricula of both Portugal and Cabo Verde, paying attention to the above theorems, namely the way and extent to which they are taught and studied. To understand the mean and intermediate value theorems it is necessary to have the knowledge of limits, continuity and derivability. Therefore, in the chapters 5 and 6 we dedicated the first topics especially to those themes with brief revisions on limits, continuity, derivability and integration. The intermediate value theorem (Bolzano's theorem) interests us specially because of its corollary which states that given a continuous function f and two points a and b in its domain, if f(a).f(b)<0, then there exists c in its domain such that f(c) = 0. Such corollary not only states that the equation f(x) = 0 has a root but that such a root is in the interval ]a, b[. We also presented a particular case of the intermediate value theorem that is the fixed point theorem. Another theorem with strong connections to the intermediate value theorem is the Weierstrass Theorem that studies the maximums and minimus in a continuous function. This same theorem is used to prove the Rolle's Theorem. The mean value theorem, which states that if f is a continuous function in [a, b] and derivable in ]a, b[ then exists c in ]a, b[ such that f '(c) is the average rate of variation of the function in [a, b]. In this work we emphasize the importance of the premisses in the theorems above. Being in such conditions is fundamental to be able to apply those theorem. In the case of the mean value theorem the function should be continuous in the interval [a, b] and it should be derivable in ]a, b [concepts studied in chapters 4 and 5. No less important we also study the mean value theorem for integrals. We always rely on the software Geogebra to illustrate the teorems studied and to try to motivate definitions and proofs. We also study generalization of the intermediate and mean value theorems.
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Book chapters on the topic "Lagrange mean value theorem"

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Ben-Israel, Adi, and Robert Gilbert. "Mean value theorem." In Computer-Supported Calculus. Springer Vienna, 2002. http://dx.doi.org/10.1007/978-3-7091-6146-3_7.

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Smoryński, Craig. "The Mean Value Theorem." In MVT: A Most Valuable Theorem. Springer International Publishing, 2017. http://dx.doi.org/10.1007/978-3-319-52956-1_3.

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Lang, Serge. "The Mean Value Theorem." In Undergraduate Texts in Mathematics. Springer New York, 1986. http://dx.doi.org/10.1007/978-1-4419-8532-3_5.

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Mercer, Peter R. "The Mean Value Theorem." In More Calculus of a Single Variable. Springer New York, 2014. http://dx.doi.org/10.1007/978-1-4939-1926-0_5.

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Lang, Serge. "The Mean Value Theorem." In Undergraduate Texts in Mathematics. Springer New York, 2002. http://dx.doi.org/10.1007/978-1-4613-0077-9_5.

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Obata, Nobuaki. "The Levy Laplacian and mean value theorem." In Lecture Notes in Mathematics. Springer Berlin Heidelberg, 1989. http://dx.doi.org/10.1007/bfb0087857.

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Hui-Ru, Chen, and Shang Chan-Juan. "Generalizations of the Second Mean Value Theorem for Integrals." In Lecture Notes in Electrical Engineering. Springer Berlin Heidelberg, 2011. http://dx.doi.org/10.1007/978-3-642-21697-8_83.

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Di Crescenzo, Antonio, Barbara Martinucci, and Julio Mulero. "Applications of the Quantile-Based Probabilistic Mean Value Theorem to Distorted Distributions." In Computer Aided Systems Theory – EUROCAST 2017. Springer International Publishing, 2018. http://dx.doi.org/10.1007/978-3-319-74727-9_10.

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Indlekofer, Karl-Heinz, and Nikolai M. Timofeev. "A Mean-Value Theorem for Multiplicative Functions on the Set of Shifted Primes." In Analytic and Elementary Number Theory. Springer US, 1998. http://dx.doi.org/10.1007/978-1-4757-4507-8_9.

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Kosheleva, Olga, and Karen Villaverde. "Uncertainty-Related Example Explaining Why Calculus Is Useful: Example of the Mean Value Theorem." In How Interval and Fuzzy Techniques Can Improve Teaching. Springer Berlin Heidelberg, 2017. http://dx.doi.org/10.1007/978-3-662-55993-2_5.

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Conference papers on the topic "Lagrange mean value theorem"

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Huang, Yong. "Research on Extensions and Applications of Integral Mean Value Theorem." In 2017 4th International Conference on Machinery, Materials and Computer (MACMC 2017). Atlantis Press, 2018. http://dx.doi.org/10.2991/macmc-17.2018.2.

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Zhang, Qingling, and Huazhou Hou. "Impulse analysis for nonlinear singular system via Differential Mean Value Theorem." In 2016 Chinese Control and Decision Conference (CCDC). IEEE, 2016. http://dx.doi.org/10.1109/ccdc.2016.7531145.

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Ma, Wenting. "Study of Higher Order Differential Mean Value Theorem for Multivariate Function." In 2017 5th International Conference on Machinery, Materials and Computing Technology (ICMMCT 2017). Atlantis Press, 2017. http://dx.doi.org/10.2991/icmmct-17.2017.281.

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Pei, Hongmei, Xuanhai Li, and Jielin Shang. "Two Methods of Proving the Improved Mean Value Theorem of Integral." In International Conference on Education, Management, Computer and Society. Atlantis Press, 2016. http://dx.doi.org/10.2991/emcs-16.2016.132.

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Ichalal, Dalil, Benoit Marx, Said Mammar, Didier Maquin, and Jose Ragot. "Observer for Lipschitz nonlinear systems: Mean Value Theorem and sector nonlinearity transformation." In 2012 IEEE International Symposium on Intelligent Control (ISIC). IEEE, 2012. http://dx.doi.org/10.1109/isic.2012.6398269.

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Messaoud, Ramzi Ben. "Nonlinear Unknown Input Observer Using Mean Value Theorem and Simulated Annealing Algorithm." In 2019 International Conference on Advanced Systems and Emergent Technologies (IC_ASET). IEEE, 2019. http://dx.doi.org/10.1109/aset.2019.8871002.

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Donghui Li. "On asymptotic properties for the median point of Cauchy Mean-value Theorem." In 2011 International Conference on Multimedia Technology (ICMT). IEEE, 2011. http://dx.doi.org/10.1109/icmt.2011.6002502.

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Zhang, C., Q. Lv, and J. Yan. "Numerical Solution of Mean-Value Theorem for Downward Continuation of Potential Fields." In 80th EAGE Conference and Exhibition 2018. EAGE Publications BV, 2018. http://dx.doi.org/10.3997/2214-4609.201801462.

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Ou, Yangjing, Chenghua Wang, and Feng Hong. "A Variable Step Maximum Power Point Tracking Method Using Taylor Mean Value Theorem." In 2010 Asia-Pacific Power and Energy Engineering Conference. IEEE, 2010. http://dx.doi.org/10.1109/appeec.2010.5449521.

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Rehman, O. U., I. R. Petersen, and B. Fidan. "A mean value theorem approach to robust control design for uncertain nonlinear systems." In 2012 American Control Conference - ACC 2012. IEEE, 2012. http://dx.doi.org/10.1109/acc.2012.6314677.

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