Citations
This website concerns the systems of non-Newtonian calculus, multiplicative calculus, and nonclassical arithmetic created by Michael Grossman and Robert Katz between 1967 and 1970. The website was last edited on 24 June 2021.
Non-Newtonian Calculus [15] is cited in the book The Rainbow of Mathematics: A History of the Mathematical Sciences by the eminent mathematics-historian Ivor Grattan-Guinness. [6]
Non-Newtonian calculus is cited in an article on atmospheric temperature by Robert G. Hohlfeld, Thomas W. Drueding, and John F. Ebersole (all from U.S. Air Force Geophysics Laboratory, Atmospheric Sciences Division) . [89]
Non-Newtonian Calculus [15] is cited in an article on means by Jane Tang. [20]
The geometric calculus is cited in a book on the phenomena of growth and structure-building by Manfred Peschel and Werner Mende(both of the German Academy of Sciences Berlin). [25]
The geometric calculus is the topic of an article and a seminar by Michael Coco of Lynchburg University. [115]
Non-Newtonian calculus is cited in a book on the energy crisis by R. Gagliardi. [26]
Non-Newtonian Calculus is cited in a 2009 doctoral dissertation on nonlinear dynamical systems by David Malkin at University College London. [36]
The geometric calculus is cited by Daniel Karrasch in his 2012 doctoral dissertation "Hyperbolicity and invariant manifolds for finite time processes" at the Technical University of Dresden in Germany. [141]
The geometric calculus is cited in the article "Investigation of the solutions of the Cauchy problem and boundary-value problems for the ordinary differential equations with continuously changing order of the derivative" by N.A. Aliyev and R.G. Ahmadov (both from Baku State University in Azerbaijan). [283]
The book Averages: A New Approach [8] is cited by Christoph von Hagke in his 2012 doctoral dissertation "Coupling between climate and tectonics?" at Freie Universität Berlin. [223]
Non-Newtonian calculus is cited in the e-book Economic Statistics. [91]
Non-Newtonian differentiation was the topic of a lecture by Karol Kosar and Ivan Kupka at a student conference at Comenius University in Slovakia. [93]
Non-Newtonian calculus is cited in the article "Topological generalization of Cauchy's mean value theorem" by Ivan Kupka (Comenius University in Slovakia). [269]
The First Nonlinear System of Differential And Integral Calculus [11] is cited in the article "L'Hopital's rule and Taylor's Theorem for product calculus" by Alex Twist and Michael Spivey. [103]
Non-Newtonian calculuswas cited in the article "Why was calculus invented", published at the Boston Commons High Tech website on 31 July 2017. [361]
Non-Newtonian Calculus is cited in an article on petroleum engineering by Raymond W. K. Tang and William E. Brigham (both of Stanford University). [37]
The First Nonlinear System of Differential and Integral Calculus was cited in a lecture presented by Bruno Ćurko at the 2011 annual international symposium "Days of Frane Petric - From Petric to Boskovic" at Cres, Croatia. [109]
Non-Newtonian calculus and Robert Katz are cited in a book on popular-culture by Paul Dickson. [28]
The geometric calculus ("multiplicative calculus") is cited by Orhan Tug (Ishik University in Iraq) and Feyzi Basar (Fatih University in Turkey) in their article "On the spaces of Norlund null and Norlund convergent sequences". [281]
Non-Newtonian calculus is cited in Science Education International: The ICASE Journal: "In mathematics, limits and diversity can be seen in the difference between the Arabic numbers and Roman numerals, Euclidean geometry and non-Euclidean geometry, Newtonian calculus and non-Newtonian calculus, and the existence of multiple ways to solve a mathematical problem." [38]
The geometric integral is cited in the article "Product integration in survival analysis" by Abdushukurov Abdurakhim Akhmedovich, Muradov Rustamjon Sobitkhonovich, and Ergashev Okiljon Tuxtasin ogli (all from National University of Uzbekistan). [292]
Multiplicative calculi are cited in the article "Construction of a numerical method for finding the zeros of both smooth and nonsmooth functions" by R. Bihun and G. Tsehelyk (both from Ivan Franko National University of Lviv, in Ukraine). [348]
Non-Newtonian Calculus is cited in Gordon Mackay's book Comparative Metamathematics. (The eighteen previous editions ofComparative Metamathematics are entitled The True Nature of Mathematics.) [139]
Non-Newtonian Calculus is cited in the journal Search. [77]
Non-Newtonian Calculus is cited in the journal Science Weekly. [64]
Non-Newtonian Calculus is cited in the journal Annals of Science. [66]
Non-Newtonian Calculus is cited in the journal Science Progress. [67]
Non-Newtonian Calculus is cited in the journal Allgemeines Statistisches Archiv. [69]
Non-Newtonian Calculus is cited in the journal Il Nuovo Cimento della Societa Italiana di Fisica: A. [70]
The First Systems of Weighted Differential and Integral Calculus [9] is cited by Mark Kelbert and Pavel Mozgunov (both from theNational Research University Higher School of Economics, Moscow, Russia) in their article "Generalization of Cramer-Rao and Bhattacharyya inequalities for the weighted covariance matrix".[296] From the article: "The concept of the discrete weighted mean can be extended to the concept of the weighted mean of continuous functions [Inequalities by Hardy, Littlewood, Polya] which, for instance, plays an important role in the systems of weighted differential and integral calculus [The First Systems of Weighted Differential and Integral Calculus]."
The First Systems of Weighted Differential and Integral Calculus [9] is cited in the e-book Alimony Defense: A Complete Guide, edited by Premakh. [275] From that e-book: "The concept of weighted average can be extended to functions. Weighted averages of functions play an important role in the systems of weighted differential and integral calculus [in the classical case and in the non- Newtonian case]".
The First Systems of Weighted Differential and Integral Calculus [9] is cited by the authors indicated below in their article on the global burden of cholera: Mohammad Ali, Anna Lena Lopez, Young Ae You, Young Eun Kim, Binod Sah, Brian Maskery, and John Clemens (all of the United Nations' International Vaccine Institute, Snu Research Park, San 4-8 Nakseongdae-dong Gwanak-gu, Seoul, Korea, 151 - 919). [98]
The First Systems of Weighted Differential and Integral Calculus [9] is cited by the authors indicated below in their article on thermochemistry of ammonium based ionic liquids: Sergey P. Verevkin and Vladimir N. Emer'yanenko (both of the University of Rostock, in Germany), Ingo Krossing (University of Freiburg, in Germany), and Roland Kalb (Proionic Production of Ionic Substances GmbH, in Graz, Austria). [108]
The First Systems of Weighted Differential and Integral Calculus [9] is cited by P. Arun Raj Kumar and S. Selvakumar (both of the National Institute of Technology, Tiruchirappalli, in India) in their article "Detection of distributed denial of service attacks using an ensemble of adaptive and hybrid neuro-fuzzy systems". [147]
The First Systems of Weighted Differential and Integral Calculus [9] is cited by Riswan Efendi and Zuhaimy Ismail (both of Universiti Teknologi Malaysia) together with Mustafa Mat Deris (Universiti Tun Husein Onn Malaysia) in their article "Improved weight fuzzy time series as used in the exchange rates forecasting of US dollar to ringgit Malaysia". [142]
The First Systems of Weighted Differential and Integral Calculus [9] is cited by Riswan Efendi and Zuhaimy Ismail (both of Universiti Teknologi Malaysia) together with Mustafa Mat Deris (Universiti Tun Husein Onn Malaysia) in their article "A new linguistic out-sample approach of fuzzy time series for daily forecasting of Malaysian electricity load demand". [246]
The First Systems of Weighted Differential and Integral Calculus [9] is cited by ZHENG Xu and LI Jian-Zhong (School of Computer Science and Technology, Harbin Institute of Technology, Harbin, China) in their work on wireless sensor networks in computer science. [125]
The First Systems of Weighted Differential and Integral Calculus [9] is cited by Hong-Kyu Kim (Korea University, Seoul), Mirim Lee (Korea University, Seoul), Kwang-Ryeol Lee (Korea Institute of Science and Technology, Seoul), and Jae-Chul Lee (Korea University, Seoul) in their article "How can a minor element added to a binary amorphous alloy simultaneously improve the plasticity and glass- forming ability?". [248]
The First Systems of Weighted Differential and Integral Calculus [9] is cited by Jie Zhang, Li Li, Luying Peng, Yingxian Sun, Jue Li (the first four from Tongji University School of Medicine in Shanghai, China; and the latter from The First Hospital of China Medical University, Shenyang, China) in their article "An Efficient Weighted Graph Strategy to Identify Differentiation Associated Genes in Embryonic Stem Cells". [156]
The First Systems of Weighted Differential and Integral Calculus [9] is cited by Christoffel Wilhelmus Janse Rensburg (North-West University at Potchefstroom, in South Africa) in his master-of-science dissertation (in computer science and information systems) "The relationship between process maturity models and the use and effectiveness of systems development methodologies". [247]
The First Systems of Weighted Differential and Integral Calculus [9] is cited in the article "Ideality equation" by Alex Lyubomirskiy (GEN3 Partners). [273]
The First Systems of Weighted Differential and Integral Calculus [9] is cited in the article "Service ratio-optimal, content coherence- aware data push systems" by Christos Liaskos (Foundation of Research and Technology in Hellas, Crete, Greece) and Ageliki Tsioliaridou (Democritus University of Thrace, Xanthi, Greece). [280]
The First Systems of Weighted Differential and Integral Calculus [9] is cited in the article "Developing seismic vulnerability curves for typical Iranian buildings" by Mehdi Sadeghi (Islamic Azad University in Iran), Mohsen Ghafory-Ashtiany (International Institute of Earthquake Engineering and Seismology in Iran), and Naghmeh Pakdel-Lahiji (Islamic Azad University in Iran). [284]
The First Systems of Weighted Differential and Integral Calculus [9] is cited in the article "Long term electricity demand & peak power load forecasting variables identification & selection" by Burak Omer Saracoglu, an independent scholar from Istanbul, Turkey. [352]
The First Systems of Weighted Differential and Integral Calculus [9] is cited in the master's thesis "Valet charging: influence on load shifting, charging station utilization and prioritizing queues" by Hidde P. F. van Heijst at Erasmus University Rotterdam in the Netherlands. [306]
The First Systems of Weighted Differential and Integral Calculus [9] is cited in the master's thesis "Production quality for process capability with multiple characteristics on the chip resistor production" by Sujeong Seo from the Department of Applied Statistics at Rochester Institute of Technology. [369] From the thesis: "The concepts of weighted average and its extended functions are introduced by Grossman et al (1980) [The First Systems of Weighted Differential and Integral Calculus] where it is indicated the weighted averages of functions as they pertain to the important roles in the systems of differential and integral calculus."
The First Systems of Weighted Differential and Integral Calculus [9] is cited in the master's thesis, in computer science and engineering, called "Training strategies for the time series classification problem" by Guan-Cheng Guo at National Sun Yat-sen University in Taiwan. [351]
The First Systems of Weighted Differential and Integral Calculus [9] is cited in the journal Praxis der Mathematik. [79]
Meta-Calculus: Differential and Integral [7] is cited in the journal Indian Journal of Theoretical Physics. [80]
Each of the following two books is cited in the journal Publicationes Mathematicae. [56]
1) Non-Newtonian Calculus: Volume 19, page 351, 1972.
2) Bigeometric Calculus: A System with a Scale-Free Derivative: Volume 32, page 282, 1985.
Each of the following two books is cited in the journal Acta Scientiarum Mathematicarum. [60]
1) Non-Newtonian Calculus: Volume 33, page 361, 1972.
2) The First Nonlinear System of Differential and Integral Calculus: Volumes 42-43, page 225, 1980.
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.
Each of the following two books is cited in the journal Economic Books: Current Selections. [81]
1) The First Systems of Weighted Differential and Integral Calculus: Volume 9, page 29, 1982.
2) Meta-Calculus: Differential and Integral: Volume 9, page 29, 1982.
Non-Newtonian calculus is cited in the journal Ciência e cultura. [39]
Non-Newtonian calculus is cited in the journal American Statistical Association: 1997 Proceedings of the Section on Bayesian Statistical Science. [40]
Non-Newtonian Calculus is cited in the Australian Journal of Statistics. [73]
Non-Newtonian Calculus is cited in the journal Physique au Canada. [83]
Non-Newtonian Calculus is cited in the journal Synthese. [74]
Non-Newtonian Calculus is cited in the journal Mathematical Education. [75]
Non-Newtonian Calculus is cited in the the journal Institute of Mathematical Statistics Bulletin. [76]
NOTE. Non-Newtonian calculus was recommended as a featured topic for the 21st-century college-mathematics-curriculum, in the keynote speech at the 27th International Conference on Technology in Collegiate Mathematics (ICTCM) on 13 March 2015. The keynote speaker was the mathematics-educator Eric Gaze. His speech is entitled "Complexity, Computation, and Quantitative Reasoning: A Mathematics Curriculum for the 21st Century". (The conference was sponsored by Pearson PLC, the largest education company and the largest book publisher in the world; and the Electronic Proceedings of the conference were hosted by Math Archives (archives.math.utk.edu) with partial support provided by the National Science Foundation.) [224]
NOTE. A special-session (mini-symposium) called "Non-Newtonian Calculus" was held at the 17th International Conference on Computational and Mathematical Methods in Science and Engineering (CMMSE), 4-8 July 2017, at Rota, Cadiz - Spain. The 2017 CMMSE Scientific Committee included over 50 distinguished scholars in a variety of fields, and CMMSE conferences are attended by numerous scholars worldwide. The special-session on non-Newtonian calculus was organized by Fernando Córdova-Lepe and Marco Mora, both from Universidad Católica del Maule in Chile. Included among the papers delivered at the special session on non- Newtonian calculus: "Introductory elements for the development of a multiplicative statistic" by Carol Pavez Rojas, Fernando Córdova-Lepe, and Karina Vilches Ponce (all from Universidad Católica del Maule in Chile); "Linearity and its algebra in the bi- geometrical context" (i.e., multiplicative linear-algebra) by Fernando Córdova-Lepe, Rodrigo del Valle, and Karina Vilches Ponce (all from Universidad Católica del Maule in Chile); and "Bigeometric Complex Calculus" by Agamirza E. Bashirov and Sajedeh Norozpour (both from Eastern Mediterranean University in North Cyprus). "Bigeometric Complex Calculus" was also presented at the special- session "Mathematical Modeling and Computational PDE". [324, 383, 384, 385] From a translation (from Spanish) of the conference-announcement:
"Non-Newtonian Calculus (NNC) ... has been increasing its development through the recoding of the multiplicative world (from the point of view of the standard calculation) as an essentially linear domain, and therein lies the nucleus of importance. Many advances and applications in science, engineering and mathematics are appearing more frequently.
"This mini symposium will be one of the first international meetings of a dispersed scientific community that has worked or is working on this topic and annoting a mark in the history of the NNC. Taking into account the novelty of the subject, all topics related to NNC (theory and applications) are welcome."
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