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Some real applications of nonlinear exponential signals will be selected to demonstrate the applicability and efficiency of the proposed representation." Bashirov and Mustafa Riza. "On Complex Multiplicative Integration", arXiv.org, Cornell University, arXiv:1307.8293, 2013. [158] Ali Uzer. "Exact solution of conducting half plane problems in terms of a rapidly convergent series and an application of the multiplicative calculus", Turkish Journal of Electrical Engineering & Computer Sciences, DOI: 10.3906/elk-1306-163, 2013. [159] Zafer Cakir. "Spaces of continuous and bounded functions over the field of geometric complex numbers", Journal of Inequalities and Applications, Volume 2013:363, doi:10.1186/1029-242X-2013-363, ISSN 1029-242X, Springer, 2013. [160] Ugur Kadak, Feyzi Basar, and Hakan Efe. "Construction of the duals of classical sequence spaces with respect to non-Newtonian calculus on reals", Fatih University, www.fatih.edu.tr/~akaya/ABSTRACTS.pdf#page=66, 2013. [161] Ahmet Faruk Çakmak and Feyzi Basar. "Certain spaces of functions over the field of non-Newtonian complex numbers", Abstract and Applied Analysis, Volume 2014, Article ID 236124, http://dx.doi.org/10.1155/2014/236124, Hindawi Publishing Corporation, 2014. [162] Ali Ozyapici and Bulent Bilgehan. "Applications of multiplicative calculus to exponential signal processing", Algerian Turkish International Days on Mathematics, http://www.fatih.edu.tr/~akaya/ABSTRACTS.pdf#page=174, 2013. [163] Martin Ostoja-Starzewski. "The inner workings of fractal materials", Media-Upload, University of Illinois at Urbana-Champaign, http://web.mechse.illinois.edu/media/uploads/web_sites/82/files/p18_20_martin_ostoja_starzewski_hi_res.20130904.52279b9f04d249.63951844.pdf, 2013. [164] Christopher Olah.

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Combine the second and third facts and split the isosceles triangle into two equal right triangles; then basic trigonometry gives half of side BC as R sin(a⁄2). You'll also find grades 1-5 lesson modules related to Eureka Math. The First Systems of Weighted Differential and Integral Calculus, ISBN 0977117014, 1980. [9] Jane Grossman. The mere fact that there can be alternative geometries was in itself a shock." - Morris Kline, from his book Mathematics: The Loss of Certainty (1980). "Georg Cantor (1845 - 1918), the creator of transfinite set theory, is one of the most imaginative and controversial figures in the history of mathematics. ...

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The geometric calculus and the bigeometric calculus were used by Hatice Aktore (Eastern Mediterranean University in North Cyprus) in an article on multiplicative Runge-Kutta methods. [133] A lecture about a complex multiplicative Runge-Kutta method was presented by Hatice Aktore and Mustafa Riza (both of Eastern Mediterranean University in North Cyprus) at the 2012 International Conference on Applied Analysis and Algebra at Yıldız Technical University in Istanbul, Turkey. [148] The geometric calculus was used by Yusuf Gurefe (Usak University in Turkey) and Emine Misirli (Ege University in Turkey) in their lecture "New Runge-Kutta methods for numerical solutions of multiplicative initial value problems" at the 2014 International Conference on Recent Advances in Pure and Applied Mathematics at Antalta, Turkey.

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Those four professors and some of their colleagues are now pursuing applications of NNC. They provide a wide variety of mathematical tools for use in science, engineering, and mathematics. They wanted to remove the article from Wikipedia. University Course: "Analysis beyond Newton and Leibniz", Saarland University, Summer 2012. [107] Ahmet Faruk Çakmak. "Some new studies on bigeometric calculus", International Conference on Applied Analysis and Algebra, Yıldız Technical University, Istanbul, Turkey, 2011. [108] Sergey P.

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In August of 1970, they created infinitely-many other calculi, including the bigeometric calculus, the anageometric calculus, the biharmonic calculus, the anaharmonic calculus, the biquadratic calculus, and the anaquadratic calculus. With colorful shapes, smooth animations, peaceful background music, your kids will have fun to solve the 4 (36 in the full version) different Tangrams we've created. A path is a sequence of templates separated by semicolons.

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Ken, a talented musician, uses the computer to compose music and to create videos and movies. It didn’t even have a clear goal, except intellectually." - Philip Ball, from his article "There’s no space for today’s young Einsteins" in The Guardian (12 February 2016). "There seem to be two kinds of discovery. Progress is made when good scientists keep working -- and keep supporting what they believe is true -- despite the criticism." - Anne Sasso, from her article "Audacity, Part 5: Rejection and Ridicule" in the magazine Science (American Association for the Advancement of Science), 11 June 2010. "A new scientific innovation does not triumph by convincing its opponents and making them see the light, but rather because its opponents eventually die, and a new generation grows up that is familiar with it." - Max Planck, from his book The Philosophy of Physics (1936). "Human progress has always been driven by a sense of adventure and unconventional thinking.

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In addition to fractal geometry and biomedical image analysis, I've come across many other areas of NNC application, some of which we anticipated years ago: growth/decay analysis (e. g., in economics and biology), dynamical systems and chaos theory, finance (e.g., rates of return), the theory of elasticity in economics, marketing, wave theory in physics, the economics of climate change, signal processing, atmospheric temperature, information technology, pathogen counts in treated water, actuarial science, tumor therapy in medicine, materials science/engineering, demographics, differential equations (including multiplicative Lorenz systems and Runge-Kutta methods), calculus of variations, finite-difference methods, averages of functions, means of two positive numbers, weighted calculus, meta-calculus, approximation theory, least-squares methods, multivariable calculus, complex analysis, functional analysis, probability theory, utility theory, Bayesian analysis, stochastics, and decision making.

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Non-Newtonian calculus has been used to derive optimization algorithms that perform better than traditional Newton based methods for Expectation-Maximization algorithms. But much to our dismay, it turned out that various pure mathematicians said NNC was useless. (Please see Appendix 1.) Some of them were rude and arrogant. In fact, the bigeometric derivative is now used to analyze the rate of change of the roughness of a fractal over time. "Random fractals, a quintessentially 20th century idea, arise as natural models of various physical, biological (think your mother's favorite cauliflower dish), and economic (think Wall Street, or the Horseshoe Casino) phenomena, and they can be characterized in terms of the mathematical concept of fractional dimension.

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In the abstract to that lecture they state: "[Geometric] calculus, which is defined in a manner analogous to the concepts in the classical calculus, has become important in recent years." [207] The geometric calculus was used in the article "New 2-point implicit block multistep method for multiplicative initial value problems" by Yusuf Gurefe (Usak University in Turkey) and Emine Misirli (Ege University in Turkey). [291] The geometric calculus is among the topics in the mathematics textbook Mathematical Analysis: Fundamentals by Agamirza Bashirov. [179] Included is application of the geometric calculus to differential equations.

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Now, you may ask, if we have eliminated any trace of objects that a number can represent a count of, that might have generated the number, what are the properties left to this abstracted number? The Interpolation Gadget in Origin allows for easy up-or-down sampling of existing data over a selected range of X values. According to our knowledge, it has never been investigated whether ERFs and ERPs follow the additive or the multiplicative model, but this knowledge is crucial, ... ." [266] Geometric arithmetic [15] was used in two articles about "multiplicative parameters-applications in economics and finance" by Helena Jasiulewicz (Wrocław University of Environmental and Life Sciences in Poland) and Wojciech Kordecki (The Witelon State University of Applied Sciences in Poland).