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S. De Cosmis and R. De Leone. The use of grossone in mathematical programming and operations research. Applied Mathematics and Computation, 218(16):8029–8038, 2012.
D. I. Iudin, Ya. D. Sergeyev and M. Hayakawa. Interpretation of percolation in terms of infinity computations. Applied Mathematics and Computation, 218(16):8099–8111, 2012.
L. D’Alotto. Cellular automata using infinite computations. Applied Mathematics and Computation, 218(16):8077–8082, 2012.
R. Florida. Did Russia really win the Sochi medal count? The Atlantic, February 23, 2014.
P. Gordon. Numerical cognition without words: Evidence from Amazonia. Science, 306(15 October):496–499, 2004.
G. Lolli. Infinitesimals and infinites in the history of mathematics: A brief survey. Applied Mathematics and Computation, 218(16):7979– 7988, 2012.
G. Lolli. Metamathematical investigations on the theory of grossone. Applied Mathematics and Computation, to appear.
C. Fallico, M. C. Vita, S. De Bartolo and M. Veltri. Usage of infinitesimals in the Menger’s Sponge model of porosity. Applied Mathematics and Computation, 218(16):8187–8196, 2012.
M. Margenstern. Using grossone to count the number of elements of infinite sets and the connection with bijections. p-Adic Numbers, Ultrametric Analysis and Applications, 3(3):196–204, 2011.
M. Margenstern. An application of grossone to the study of a family of tilings of the hyperbolic plane. Applied Mathematics and Computation, 218(16):8005–8018, 2012.
A. Robinson. Non-standard Analysis. Princeton Univ. Press, Princeton, 1996.
Ya. D. Sergeyev. Arithmetic of Infinity. Edizioni Orizzonti Meridionali, CS, 2003, 2nd electronic edition, 2013.
D. I. Iudin, Ya. D. Sergeyev and M. Hayakawa. Infinity computations in cellular automaton forest-fire model. Communications in Nonlinear Science and Numerical Simulation, 20(3):861–870, 2015.
Ya. D. Sergeyev. A new applied approach for executing computations with infinite and infinitesimal quantities. Informatica, 19(4):567–596, 2008.
Ya. D. Sergeyev. Evaluating the exact infinitesimal values of area of Sierpinski’s carpet and volume of Menger’s sponge. Chaos, Solitons & Fractals, 42(5):3042–3046, 2009.
Ya. D. Sergeyev. Numerical computations and mathematical modelling with infinite and infinitesimal numbers. Journal of Applied Mathematics and Computing, 29:177–195, 2009.
Ya. D. Sergeyev. Numerical point of view on Calculus for functions assuming finite, infinite, and infinitesimal values over finite, infinite, and infinitesimal domains. Nonlinear Analysis Series A: Theory, Methods & Applications, 71(12):e1688–e1707, 2009.
Ya. D. Sergeyev. Computer system for storing infinite, infinitesimal, and finite quantities and executing arithmetical operations with them. USA patent 7,860,914, 2010.
Ya. D. Sergeyev. Counting systems and the First Hilbert problem. Nonlinear Analysis Series A: Theory, Methods & Applications, 72(3–4):1701–1708, 2010.
Ya. D. Sergeyev. Lagrange Lecture: Methodology of numerical computations with infinities and infinitesimals. Rendiconti del Seminario Matematico dell’Università e del Politecnico di Torino, 68(2):95–113, 2010.
Ya. D. Sergeyev. Higher order numerical differentiation on the infinity computer. Optimization Letters, 5(4):575–585, 2011.
Ya. D. Sergeyev. On accuracy of mathematical languages used to deal with the Riemann zeta function and the Dirichlet eta function. p-Adic Numbers, Ultrametric Analysis and Applications, 3(2):129– 148, 2011.
Ya. D. Sergeyev. Using blinking fractals for mathematical modelling of processes of growth in biological systems. Informatica, 22(4):559–576, 2011.
Ya. D. Sergeyev. Numerical computations with infinite and infinitesimal numbers: Theory and applications. In A. Sorokin and P. M. Pardalos, editors, Dynamics of Information Systems: Algorithmic Approaches, pages 1–66. Springer, New York, 2013.
Ya. D. Sergeyev. Solving ordinary differential equations by working with infinitesimals numerically on the infinity computer. Applied Mathematics and Computation, 219(22):10668–10681, 2013.
Ya. D. Sergeyev and A. Garro. Observability of Turing machines: A refinement of the theory of computation. Informatica, 21(3):425– 454, 2010.
Ya. D. Sergeyev and A. Garro. Single-tape and multi-tape Turing machines through the lens of the Grossone methodology. Journal of Supercomputing, 65(2):645–663, 2013.
A. A. Zhigljavsky. Computing sums of conditionally convergent and divergent series using the concept of grossone. Applied Mathematics and Computation, 218(16):8064–8076, 2012.
A. Žilinskas. On strong homogeneity of two global optimization algorithms based on statistical models of multimodal objective functions. Applied Mathematics and Computation, 218(16):8131– 8136, 2012.
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Sergeyev, Y.D. The Olympic Medals Ranks, Lexicographic Ordering, and Numerical Infinities. Math Intelligencer 37, 4–8 (2015). https://doi.org/10.1007/s00283-014-9511-z
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DOI: https://doi.org/10.1007/s00283-014-9511-z