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# Category: Fractals

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Excerpt: "It seems plausible that people who need to study functions from this point of view might well be able to formulate problems more clearly by using [bigeometric] calculus instead of [classical] calculus." 5) Averages: A New Approach [8]: Mathematical Reviews, 1984. The geometric calculus was used by Ali Uzer (Fatih University in Turkey) in an article on wave theory in physics: "Improvement of the diffraction coefficient of GTD by using multiplicative [the geometric] calculus". [185] In the abstract to the article he states: "The given approximation techniques [based on the geometric calculus] ... can be extended to other high frequency techniques in electromagnetics."

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The writing is clear, concise, and very readable. The prerequisites are some simple differential equations, a bit of Fourier transforms, and some knowledge of software to numerically solve the various equations. His examination of calculus led him to the invention of Hilbert space, considered one of the key concepts of functional analysis and modern mathematical physics. Discussions concerning a new multiplicative accounting system and the advantages of using the geometric calculus in economic analysis are included in an article by Diana Andrada Filip (Babes-Bolyai University of Cluj-Napoca in Romania) and Cyrille Piatecki (Orléans University in France). [149] The geometric calculus was used by Hasan Özyapıcı (Eastern Mediterranean University in Cyprus), İlhan Dalcı (Eastern Mediterranean University in Cyprus), and Ali Özyapıcı (Cyprus International University) in their article "Integrating accounting and multiplicative calculus: an effective estimation of learning curve". [290] From the Abstract: "The results of this study are also expected to help researchers, practitioners, economists, business managers, and cost and managerial accountants to understand how to construct a multiplicative based learning curve to improve such decisions as pricing, profit planning, capacity management, and budgeting." (The expression "multiplicative calculus" refers here to the geometric calculus.) The non-Newtonian approach to accounting [82, 121, 149, 181, 216] was advocated by Amelia Correa (St.

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Brigham (1982). "... all the ingenious analysis which has evolved from the hypothesis of linearity is at best a first approximation to the applicable mathematics of the future." - E. It begins on day and adds 1 for each new day. From the book: "The multiplicative calculus allows us to see a great many facts which would be impossible to find by the classical additive calculus." (The expression "multiplicative calculus" refers here to the geometric calculus.) [285] The geometric calculus was presented in the article "Additive and multiplicative judgements of dialectical logic.

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Suleiman. "Common fixed points of locally contractive mappings in multiplicative metric spaces with application", International Journal of Mathematics and Mathematical Sciences, Volume 2015 (2015), Article ID 218683, http://dx.doi.org/10.1155/2015/218683, Hindawi Publishing Corporation, 2015. [215] Mustafa Riza and Bugce Eminaga. "Bigeometric Calculus and Runge Kutta Method", arXiv.org, Cornell University, arXiv:1402.2877v2, 2015. [216] Diana Andrada Filip and Cyrille Piatecki. "In defense of a non-Newtonian economic analysis through an accounting paradigm", World Economics Association, February of 2015. [217] Ahmet Faruk Cakmak and Feyzi Basar. “Some sequence spaces and matrix transformations in multiplicative sense”, TWMS Journal of Applied and Engineering Mathematics, Volume 6, Number 1, pages 27-37, 2015. [218] R.

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INDEPENDENT PRACTICE See Example 1 Find the. v- and y-intercepts. 10. i- 2- ^ -2 O -2 11. -i — I — I — I — t*- See Example 2 Graph each equation. 12. j' = 5. Because history shows that the deeper your idea cuts into the heart of a field, the more your peers are likely to challenge you. Non-Newtonian calculus has been used to derive optimization algorithms that perform better than traditional Newton based methods for Expectation-Maximization algorithms.

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Along with Archimedes, Alberuni, Leibniz, and J. 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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Not only does he believe that NNC models many real life problems more accurately than the classical calculus, he believes it is known that NNC models many real life problems more accurately than the classical calculus. A strong argument for "a non-Newtonian economic analysis" based on a new multiplicative accounting system and non-Newtonian calculus is presented in the article "In defense of a non-Newtonian economic analysis through an accounting paradigm" by Diana Andrada Filip (Babes-Bolyai University of Cluj-Napoca in Romania) and Cyrille Piatecki (Orléans University in France). [216] In that article they state: In that article they state: "The double-entry bookkeeping promoted by Luca Pacioli in the fifteenth century could be considered a strong argument in behalf of the multiplicative calculus which can be developed from the Grossman and Katz non-Newtonian calculus concept provided that one goes from an additive bookkeeping system to a multiplicative one. ...

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Lesson W-1 Extension 593 ^o^Kcis-q 'hf Explore the Volume of Prisms and Cylinders Use with Lesson 10-2 .(y. The Wilson family is driving the Civil Rights in Education Heritage Trail. If 57"= 10 m and AABC is similar to ASTU, what ratio can you use to find SU and UT7 Show how to find SU and UT to the nearest tenth of a meter. Liu, Robust Stability Analysis of Guaranteed Cost Control for Impulsive Switched Systems, IEEE Transactions on Systems, Man, and Cybernetics - Cybernetics, Vol. 38, pp. 1419-1422, 2008.

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Ameen at Eastern Mediterranean University in North Cyprus. [219] The First Systems of Weighted Differential and Integral Calculus [9] is used by Riswan Efendi (Universiti Teknologi Malaysia), Zuhaimy Ismail (Universiti Teknologi Malaysia), Nor Haniza Sarmin (Universiti Teknologi Malaysia), and Mustafa Mat Deris (Universiti Tun Hussein Onn Malaysia) in their article "A reversal model of fuzzy time series in regional load forecasting". [245] The geometric calculus was presented in the book Alternative Picture of the World, Volume 1 by Leonid G.

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No matter how many consecutive times one side lands facing up, the probability that it will do so at the next toss is always .5 (50-50). In this book was revealed a rare 27 x 27 Magic Square with astonishing properties. Julia fractals begrensd en mandelbrot fractals convergent? This attitude persisted into the current century, when fractals had been around for at least twenty-five years and chaos for forty. The professor and Bob had met a few times when the professor was working with the company as a consultant on the famous SMSG mathematics project called "The New Math".