[Dottorcomp] Seminari di Matematica Applicata, 20/06/2024, Yaroslav D. Sergeyev

[Stefano Lisini]

Seminari di Matematica Applicata, Dipartimento di Matematica "F. Casorati"
e Istituto del CNR IMATI "E. Magenes" di Pavia.

Giovedì 20 giugno 2024, alle ore 11.00 precise, presso l'aula Beltrami del
dipartimento di Matematica,

Yaroslav D. Sergeyev (Università della Calabria)

terrà un seminario dal titolo:
Avoiding some classical paradoxes and solving a number of applications
using numerical infinities and infinitesimals

Abstract.

In this talk, a recent computational methodology (not related to
non-standard analysis) is described briefly (see [4, 5, 6]). The new
methodology is based on the Euclid’s Common Notion “The whole is greater
than the part” applied to all quantities (finite, infinite, and
infinitesimal) and to all sets and processes (finite and infinite). It
allows people to work (see, e.g., [1, 2]) on a computer with infinities and
infinitesimals numerically (i.e., not symbolically) in a unique framework
and in all the situations requiring these notions. The main attention in
the talk is dedicated to numerical algorithms for solving ODEs (see, e.g.,
[1]) and optimization problems (see [8]). It is also shown that the new
methodology allows one to avoid a number of classical paradoxes related to
infinity and infinitesimals (see [3, 6, 7]).

For more information see the webpage https://www.theinfinitycomputer.com

[1]  Amodio, P., Iavernaro, F., Mazzia, F., Mukhametzhanov, M.S., Sergeyev,
Y.D. (2017). A generalized Taylor method of order three for the solution of
initial value problems in standard and infinity floating-point arithmetic.
Mathematics and Computers in Simula- tion, 141, 24–39.

[2]  Falcone, A., Garro, A., Mukhametzhanov, M.S., Sergeyev, Y.D. (2020).
Representation of Grossone-based arithmetic in Simulink and applications to
scientific computing. Soft Computing, 24, 17525–17539.

[3]  Nasr L. (2023). Students’ resolutions of some paradoxes of infinity in
the lens of the grossone methodology. Informatics and Education, 38(1),
83–91.

[4]  Rizza D. (2023). Primi Passi nell’Aritmetica dell’Infinito, Bonomo
Editore, Bologna.

[5]  Sergeyev, Y.D. (2003, 2nd ed. 2013). Arithmetic of Infinity. Edizioni
Orizzonti Meridionali, CS.

[6]  Sergeyev, Y.D. (2017). Numerical infinities and infinitesimals:
Methodology, applica- tions, and repercussions on two Hilbert problems. EMS
Surveys in Mathematical Sciences, 4(2), 219–320.

[7]  Sergeyev, Y.D. (2022). Some paradoxes of infinity revisited,
Mediterranean J. of Math., 19(3), 143.

[8]  Sergeyev Y.D., De Leone R., eds. (2022). Numerical Infinities and
Infinitesimals in Optimization, Springer, Cham.
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Pagina web dei Seminari di Matematica Applicata
https://matematica.unipv.it/ricerca/cicli-di-seminari/seminari
-di-matematica-applicata/
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