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Mandelbrot on mathematics", edited by Michael F. The First Nonlinear System of Differential and Integral Calculus, ISBN 0977117006, 1979. (A detailed account of the geometric calculus.) [12] Michael Grossman. "An introduction to non-Newtonian calculus", International Journal of Mathematical Education in Science and Technology, Volume 10, Number 4, pages 525-528, Taylor and Francis, 1979. [13] Michael Grossman and Robert Katz, "Isomorphic calculi", International Journal of Mathematical Education in Science and Technology, Volume 15, Number 2, pages 253-263, Taylor and Francis, 1984. [14] Michael Grossman and Robert Katz. "A new approach to means of two positive numbers", International Journal of Mathematical Education in Science and Technology, Volume 17, Number 2, pages 205-208, Taylor and Francis, 1986. [15] Michael Grossman and Robert Katz.

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Kreidik and George Shpenkov (both from the Institute of Mathematics & Physics at the University of Technology & Agriculture in Poland). That a whole family of differential and integral calculi, parallel to but nonlinear with respect to ordinary Newtonian (or Leibnizian) calculus, should have remained undiscovered (or uninvented) for so long is astonishing -- but true. These repetition items will always match the longest possible sequence; a single character class followed by '+', which matches 1 or more repetitions of characters in the class.

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R. developed the method between 1946 and 1985.) [274] Mrinmoy Majumder. Englehardt (University of Miami). (The expression "product integral" used in the article refers to the geometric integral.) [227] From that article: "... [the geometric integral] is fundamental to developing the continuously multiplicative nature of the continuous first-order kinetic rate law, not otherwise obvious." "Application of geometric calculus in numerical analysis and difference sequence spaces" is the title of an article by Khirod Boruah and Bipan Hazarika, both from Rajiv Gandhi University in India.

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Each of the following six books is cited in the journal Industrial Mathematics. [61] 1) Non-Newtonian Calculus: Volumes 43-45, page 91, 1994. 2) The First Nonlinear System of Differential and Integral Calculus: Volumes 28-30, page 143, 1978. 3) The First Systems of Weighted Differential and Integral Calculus: Volumes 31-33, page 66, 1981. 4) Meta-Calculus: Differential and Integral: Volumes 31-33, page 83, 1981. 5) Bigeometric Calculus: A System with a Scale-Free Derivative: Volumes 33-34, page 91, 1983. 6) Averages: A New Approach: Volumes 33-34, page 91, 1983.

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The dissertation is entitled "Multiplicative calculus and its applications". [191] Non-Newtonian calculus and some of its applications are the topics of the 2011 doctoral dissertation of Ugur Kadak at Gazi University in Turkey. The Wikipedia Reference Desk covering the topic of mathematics. Hence, many nonlinear functions can be represented by well-behaved exponential functions. See the next point.) For inline formulas, enclose the formula in $...$.

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But some people objected to the article, saying that NNC was "not notable". As for strange occurrences, the one I mentioned about the United States presidential election, 2000 is one example. The following excerpt is from a review written by H. For studying the time evolution of such "rough" objects, the classical, "smooth" Newtonian calculus is not enough." - Wojbor Woyczynski, Case Western Reserve University, USA; from an abstract to his seminars (in 2011 and 2012) "Non-Newtonian calculus for the dynamics of random fractal structures". [90, 104] "Together with a small, highly focused research team, Ostoja-Starzewski is working across disciplines to unite methods from solid mechanics, advanced continuum mechanics, statistical physics and mathematics.

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Vic Dannon (Gauge Institute in USA). [196] Several specific non-Newtonian calculi are discussed in a book by H. The goal of this paper is chaos examination in multiplicative dynamical systems described with the multiplicative derivative." (The expression "multiplicative derivative" refers here to the bigeometric derivative.) - Dorota Aniszewska and Marek Rybaczuk, both from Wroclaw University of Technology in Poland; from their 2008 article "Lyapunov type stability and Lyapunov exponent for exemplary multiplicative dynamical systems". [131] " ... evolution of fractal characteristics will be examined with the help of dynamical system theory or more precisely in terms of multiplicative calculus." (The expression "multiplicative calculus" refers here to the bigeometric calculus.) - Dorota Aniszewska and Marek Rybaczuk, both from Wroclaw University of Technology in Poland; from their 2009 article "Fractal characteristics of defects evolution in parallel fibre reinforced composite in quasi-static process of fracture". [184] "We advocate the use of an alternative calculus in biomedical image analysis, known as multiplicative (a.k.a. non-Newtonian) calculus. ...

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Turn your iPad into a recordable whiteboard with Educreations Interactive Whiteboard, a free app. In the article, Professors Riza and Eminaga state: "The results show that the Bigeometric Runge-Kutta method is superior to the ordinary Runge-Kutta method for a certain family of problems." [178] The geometric and bigeometric calculi were used in the article "Bigeometric Calculus and Runge Kutta Method" by Mustafa Riza (Eastern Mediterranean University in North Cyprus) and Bugce Eminaga (Girne American University in Cyprus).

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To such intellectuals, Mandelbrot was a visibly freakish phenomenon. ... Ameen. "Continuous nowhere differentiable functions", master's thesis, Eastern Mediterranean University in North Cyprus, 2014. [220] Ali Ozyapici. "Non-Newtonian calculi", master's thesis, Eastern Mediterranean University in North Cyprus, 2005. [221] Hatice Aktore. "Multiplicative Runge-Kutta methods", master's thesis, Eastern Mediterranean University in North Cyprus, 2011. [222] Bulent Bilgehan. "Efficient approximation for linear and non-linear signal representation", IET Signal Processing, DOI: 10.1049/iet-spr.2014.0070, Online ISSN 1751-9683, Institution of Engineering and Technology (IET), Spring 2015. [223] Christoph von Hagke. "Coupling between climate and tectonics?", doctoral thesis, Freie Universität Berlin in Germany, 2012. [224] Eric Gaze.

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The First Systems of Weighted Differential and Integral Calculus, ISBN 0977117014, 1980. [9] Jane Grossman. Simply Multiplication for iPad is an app that allows the user to practice simple basic multiplication facts or extend the users ability to work out complex multiplication problems up to three digit numbers. The purpose of this article is to illustrate the basics of multiplicative calculus and its application to the regularization of positive definite matrix fields." (The expression "multiplicative calculus" refers here to the geometric calculus.) [88, 96, 199, 111] The advantage of using the geometric or bigeometric calculus in some applications was demonstrated by Nico Persch, Christopher Schroers, Simon Setzer, and Joachim Weickert (Gottfried Wilhelm Leibniz Prize winner), all from Saarland University in Germany, in their two articles on imaging science called "Introducing more physics into variational depth–from–defocus" [240], and "Physically inspired depth-from-defocus" [241].