Sergeyev: Un semplice modo per trattare le grandezze infinite ed infinitesime

Sergeyev, Yaroslav D.:
Un semplice modo per trattare le grandezze infinite ed infinitesime
La Matematica nella Società e nella Cultura. Rivista dell'Unione Matematica Italiana Serie 1 8 (2015), fasc. n.1, p. 111-147, (Italian)
pdf (556 Kb), djvu (346 Kb). | MR 3364901

Referenze Bibliografiche

[1] L. D'ALOTTO. Cellular automata using infinite computations. Applied Mathematics and Computation, 218(16):8077-8082, 2012. | fulltext (doi) | MR 2912730 | Zbl 1252.37017

[2] 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. | fulltext (doi) | MR 2912726 | Zbl 1273.90117

[3] P. GORDON, Numerical cognition without words: Evidence from Amazonia, Science, 306(15):496-499, 2004.

[4] 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. | fulltext (doi) | MR 2912732 | Zbl 1252.82059

[5] 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.

[6] V. KANOVEI and V. LYUBETSKY. Grossone approach to Hutton and Euler transforms. Applied Mathematics and Computation, 255:36-43, 2015. | fulltext (doi) | MR 3316581 | Zbl 1338.68300

[7] G. LOLLI, Nascita di un'idea matematica, Edizioni della Scuola Normale Superiore, Pisa, 2013. | Zbl 1270.03012

[8] G. LOLLI. Infinitesimals and infinites in the history of mathematics: A brief survey. Applied Mathematics and Computation, 218(16):7979-7988, 2012. | fulltext (doi) | MR 2912722 | Zbl 1255.01001

[9] G. LOLLI. Metamathematical investigations on the theory of grossone. Applied Mathematics and Computation, 255:3-14, 2015. | fulltext (doi) | MR 3316578 | Zbl 1338.03118

[10] 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. | fulltext (doi) | MR 2824038 | Zbl 1259.03064

[11] 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. | fulltext (doi) | MR 2912724 | Zbl 1248.68526

[12] M. MARGENSTERN. Fibonacci words, hyperbolic tilings and grossone. Communications in Nonlinear Science and Numerical Simulation, 21(1-3):3-11, 2015. | fulltext (doi) | MR 3278319 | Zbl 1329.37012

[13] F. MONTAGNA, G. SIMI, and A. SORBI. Taking the Pirahã seriously. Communications in Nonlinear Science and Numerical Simulation, 21(1-3):52-69, 2015. | fulltext (doi) | MR 3278323 | Zbl 1401.03110

[14] P. PICA, C. LEMER, V. IZARD, S. DEHAENE. Exact and approximate arithmetic in an amazonian indigene group, Science, 306(15):499-503, 2004.

[15] YA.D. SERGEYEV, Arithmetic of Infinity, Edizioni Orizzonti Meridionali, CS, 2003, the 2d electronic edition, 2013. | MR 2050876

[16] YA.D. SERGEYEV. Blinking fractals and their quantitative analysis using infinite and infinitesimal numbers. Chaos, Solitons & Fractals, 33(1):50-75, 2007. | fulltext (doi) | MR 2671948

[17] YA.D. SERGEYEV. A new applied approach for executing computations with infinite and infinitesimal quantities. Informatica, 19(4):567-596, 2008. | MR 2589840 | Zbl 1178.68018

[18] 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.

[19] YA.D. SERGEYEV. Numerical computations and mathematical modelling with infinite and infinitesimal numbers. Journal of Applied Mathematics and Computing, 29:177-195, 2009. | fulltext (doi) | MR 2472104 | Zbl 1193.68260

[20] 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. | fulltext (doi) | MR 2671948

[21] YA.D. SERGEYEV. Computer system for storing infinite, infinitesimal, and finite quantities and executing arithmetical operations with them. EU patent 1728149, issued 2009; USA patent 7,860,914, issued 2010; RF Patent 2395111, issued 20.07.2010. | fulltext (doi) | MR 2671948

[22] YA.D. SERGEYEV. Counting systems and the First Hilbert problem. Nonlinear Analysis Series A: Theory, Methods & Applications, 72(3-4):1701-1708, 2010. | fulltext (doi) | MR 2577570

[23] 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. | MR 2790165 | Zbl 1211.65002

[24] YA.D. SERGEYEV. Higher order numerical differentiation on the Infinity Computer. Optimization Letters, 5(4):575-585, 2011. | fulltext (doi) | MR 2836038 | Zbl 1230.65028

[25] 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. | fulltext (doi) | MR 2802036 | Zbl 1268.11114

[26] YA.D. SERGEYEV. Using blinking fractals for mathematical modelling of processes of growth in biological systems. Informatica, 22(4):559-576, 2011. | MR 2885687 | Zbl 1268.37092

[27] YA.D. SERGEYEV (2013) Solving ordinary differential equations by working with infinitesimals numerically on the Infinity Computer, Applied Mathematics and Computation, 219(22), 10668-10681. | fulltext (doi) | MR 3064573 | Zbl 1303.65061

[28] YA.D. SERGEYEV (2013) Numerical computations with infinite and infinitesimal numbers: Theory and applications, in ``Dynamics of Information Systems: Algorithmic Approaches'' edited by Sorokin, A., Pardalos, P.M., Springer, New York, pp. 1-66. | fulltext (doi) | MR 3094327

[29] YA.D. SERGEYEV and A. GARRO. Observability of Turing machines: A refinement of the theory of computation. Informatica, 21(3):425-454, 2010. | MR 2742193 | Zbl 1209.68255

[30] YA.D. SERGEYEV and A. GARRO. Single-tape and Multi-tape Turing Machines through the lens of the Grossone methodology. The Journal of Supercomputing, 65(2):645-663, 2013.

[31] YA.D. SERGEYEV, A. GARRO. The Grossone methodology perspective on Turing machines, in ``Automata, Universality, Computation'', A. Adamatzky (ed.), Springer Series ``Emergence, Complexity and Computation'', Vol. 12: 139-169, 2015. | fulltext (doi) | MR 3328558 | Zbl 1327.68104

[32] M.C. VITA, S. DE BARTOLO, C. FALLICO, and M. VELTRI. Usage of infinitesimals in the Menger's Sponge model of porosity. Applied Mathematics and Computation, 218(16):8187-8196, 2012. | fulltext (doi) | MR 2912739 | Zbl 1245.76073

[33] P. ZELLINI. Breve storia dell'infinito, Adelphi, Milano, 2006.

[34] 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. | fulltext (doi) | MR 2912729 | Zbl 1254.03123

[35] A. ZILINSKAS. 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. | fulltext (doi) | MR 2912735 | Zbl 1245.90094

[36] http://www.theinfinitycomputer.com

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Referenze Bibliografiche