Un semplice modo per trattare le grandezze infinite ed infinitesime

 Access to full text

 Full (PDF)

 Full (DjVu)

1. D'ALOTTO, L.. Cellular automata using infinite computations. Applied Mathematics and Computation, 218(16):8077-8082, 2012. Zbl1252.37017MR2912730DOI10.1016/j.amc.2011.10.065
2. DE COSMIS, S. and DE LEONE, R.. The use of grossone in mathematical programming and operations research. Applied Mathematics and Computation, 218(16):8029-8038, 2012. Zbl1273.90117MR2912726DOI10.1016/j.amc.2011.07.042
3. GORDON, P., Numerical cognition without words: Evidence from Amazonia, Science, 306(15):496-499, 2004. 
4. IUDIN, D.I., SERGEYEV, YA.D., and HAYAKAWA, M.. Interpretation of percolation in terms of infinity computations. Applied Mathematics and Computation, 218(16):8099-8111, 2012. Zbl1252.82059MR2912732DOI10.1016/j.amc.2011.11.044
5. IUDIN, D.I., SERGEYEV, YA.D., and HAYAKAWA, M.. Infinity computations in cellular automaton forest-fire model. Communications in Nonlinear Science and Numerical Simulation, 20(3):861-870, 2015. 
6. KANOVEI, V. and LYUBETSKY, V.. Grossone approach to Hutton and Euler transforms. Applied Mathematics and Computation, 255:36-43, 2015. Zbl1338.68300MR3316581DOI10.1016/j.amc.2014.06.037
7. LOLLI, G., Nascita di un'idea matematica, Edizioni della Scuola Normale Superiore, Pisa, 2013. Zbl1270.03012
8. LOLLI, G.. Infinitesimals and infinites in the history of mathematics: A brief survey. Applied Mathematics and Computation, 218(16):7979-7988, 2012. Zbl1255.01001MR2912722DOI10.1016/j.amc.2011.08.092
9. LOLLI, G.. Metamathematical investigations on the theory of grossone. Applied Mathematics and Computation, 255:3-14, 2015. Zbl1338.03118MR3316578DOI10.1016/j.amc.2014.03.140
10. MARGENSTERN, M.. 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. Zbl1259.03064MR2824038DOI10.1134/S2070046611030034
11. MARGENSTERN, M.. 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. Zbl1248.68526MR2912724DOI10.1016/j.amc.2011.04.014
12. MARGENSTERN, M.. Fibonacci words, hyperbolic tilings and grossone. Communications in Nonlinear Science and Numerical Simulation, 21(1-3):3-11, 2015. Zbl1329.37012MR3278319DOI10.1016/j.cnsns.2014.07.032
13. MONTAGNA, F., SIMI, G., and SORBI, A.. Taking the Pirahã seriously. Communications in Nonlinear Science and Numerical Simulation, 21(1-3):52-69, 2015. Zbl1401.03110MR3278323DOI10.1016/j.cnsns.2014.06.052
14. PICA, P., LEMER, C., IZARD, V., DEHAENE, S.. Exact and approximate arithmetic in an amazonian indigene group, Science, 306(15):499-503, 2004. 
15. SERGEYEV, YA.D., Arithmetic of Infinity, Edizioni Orizzonti Meridionali, CS, 2003, the 2d electronic edition, 2013. MR2050876
16. SERGEYEV, YA.D.. Blinking fractals and their quantitative analysis using infinite and infinitesimal numbers. Chaos, Solitons & Fractals, 33(1):50-75, 2007. MR2671948DOI10.1016/j.na.2009.02.030
17. SERGEYEV, YA.D.. A new applied approach for executing computations with infinite and infinitesimal quantities. Informatica, 19(4):567-596, 2008. Zbl1178.68018MR2589840
18. SERGEYEV, YA.D.. 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. SERGEYEV, YA.D.. Numerical computations and mathematical modelling with infinite and infinitesimal numbers. Journal of Applied Mathematics and Computing, 29:177-195, 2009. Zbl1193.68260MR2472104DOI10.1007/s12190-008-0123-7
20. SERGEYEV, YA.D.. 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. MR2671948DOI10.1016/j.na.2009.02.030
21. SERGEYEV, YA.D.. 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. MR2671948DOI10.1016/j.na.2009.02.030
22. SERGEYEV, YA.D.. Counting systems and the First Hilbert problem. Nonlinear Analysis Series A: Theory, Methods & Applications, 72(3-4):1701-1708, 2010. MR2577570DOI10.1016/j.na.2009.09.009
23. SERGEYEV, YA.D.. 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. Zbl1211.65002MR2790165
24. SERGEYEV, YA.D.. Higher order numerical differentiation on the Infinity Computer. Optimization Letters, 5(4):575-585, 2011. Zbl1230.65028MR2836038DOI10.1007/s11590-010-0221-y
25. SERGEYEV, YA.D.. 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. Zbl1268.11114MR2802036DOI10.1134/S2070046611020051
26. SERGEYEV, YA.D.. Using blinking fractals for mathematical modelling of processes of growth in biological systems. Informatica, 22(4):559-576, 2011. Zbl1268.37092MR2885687
27. SERGEYEV, YA.D. (2013) Solving ordinary differential equations by working with infinitesimals numerically on the Infinity Computer, Applied Mathematics and Computation, 219(22), 10668-10681. Zbl1303.65061MR3064573DOI10.1016/j.amc.2013.04.019
28. SERGEYEV, YA.D. (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. MR3094327DOI10.1007/978-1-4614-7582-8_1
29. SERGEYEV, YA.D. and GARRO, A.. Observability of Turing machines: A refinement of the theory of computation. Informatica, 21(3):425-454, 2010. Zbl1209.68255MR2742193
30. SERGEYEV, YA.D. and GARRO, A.. Single-tape and Multi-tape Turing Machines through the lens of the Grossone methodology. The Journal of Supercomputing, 65(2):645-663, 2013. 
31. SERGEYEV, YA.D., GARRO, A.. 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. Zbl1327.68104MR3328558DOI10.1007/978-3-319-09039-9_7
32. VITA, M.C., DE BARTOLO, S., FALLICO, C., and VELTRI, M.. Usage of infinitesimals in the Menger's Sponge model of porosity. Applied Mathematics and Computation, 218(16):8187-8196, 2012. Zbl1245.76073MR2912739DOI10.1016/j.amc.2011.06.013
33. ZELLINI, P.. Breve storia dell'infinito, Adelphi, Milano, 2006. 
34. ZHIGLJAVSKY, A.A.. Computing sums of conditionally convergent and divergent series using the concept of grossone. Applied Mathematics and Computation, 218(16):8064- 8076, 2012. Zbl1254.03123MR2912729DOI10.1016/j.amc.2011.12.034
35. ZILINSKAS, A.. 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. Zbl1245.90094MR2912735DOI10.1016/j.amc.2011.07.051
36. http://www.theinfinitycomputer.com