[FOM] practical use of infinitesimals
Vladik Kreinovich
vladik at cs.utep.edu
Wed May 5 00:01:37 EDT 2004
Dear Friends,
In view of a recent posting on a non-standard models congress, it may be of
interest to the FOM community that infinitesimals, in the form of appropriate
power series, are used in efficient algorithms for computing the ranges of
functions and in describing dynamical systems ranging from supercolliders to
checking whether an nearby-flying asteroid hits the Earth.
For details, see webpage of Martin Berz http://bt.pa.msu.edu/berz/ and
references therein. In particular, connection to
infinitesimals is described in the following papers:
Cauchy Theory on Levi-Civita Fields
M. Berz, Contemporary Mathematics, American Mathematical Society, 319, 39-52
(2002),
Proc. Seventh Intern. Conf. Non-Archimedean Analysis
http://bt.pa.msu.edu/cgi-bin/display.pl?name=rscni02
Measure Theory and Integration on the Levi-Civita Field
K. Shamseddine and M. Berz, Contemporary Mathematics, American Mathematical
Society, 319, 369-387 (2002)
Proc. Seventh Intern. Conf. Non-Archimedean Analysis
http://bt.pa.msu.edu/cgi-bin/display.pl?name=rsmni02
Intermediate Values and Inverse Functions on Non-Archimedean Fields
K. Shamseddine and M. Berz, Int. J. Math. and Math. Sciences, 30(3), 165-176
(2002)
http://bt.pa.msu.edu/cgi-bin/display.pl?name=rsijmms01
Analytical and Computational Methods for the Levi-Civita Field
M. Berz, Lecture Notes Pure Appl. Math., Proc. Sixth Intern. Conf.
Non-Archimedean Analysis, 21-34,
Marcel Dekker (2000)
http://bt.pa.msu.edu/cgi-bin/display.pl?name=rsio00
Vladik
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