Geodesic
Observer's mathematics applications to number theory, geometry, analysis, classical and quantum mechanics
Učënye zapiski Kazanskogo universiteta. Seriâ Fiziko-matematičeskie nauki, Uchenye Zapiski Kazanskogo Universiteta. Seriya Fiziko-Matematicheskie Nauki, Tome 153 (2011) no. 3, pp. 196-203 Cet article a éte moissonné depuis la source Math-Net.Ru

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When we consider and analyze physical events with the purpose of creating corresponding models, we often assume that the mathematical apparatus used in modeling is infallible. In particular, this relates to the use of infinity in various aspects and the use of Newton's definition of a limit in analysis. We believe that is where the main problem lies in contemporary study of nature. This work considers mathematical and physical aspects in a setting of arithmetic, algebra, geometry, and topology provided by Observer's Mathematics, see www.mathrelativity.com.
Keywords: Hilbert, wave, Schrödinger, Lorentz, Schwartz
Mots-clés : soliton, observer. 
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B. Khots; D. Khots. Observer's mathematics applications to number theory, geometry, analysis, classical and quantum mechanics. Učënye zapiski Kazanskogo universiteta. Seriâ Fiziko-matematičeskie nauki, Uchenye Zapiski Kazanskogo Universiteta. Seriya Fiziko-Matematicheskie Nauki, Tome 153 (2011) no. 3, pp. 196-203. http://geodesic.mathdoc.fr/item/UZKU_2011_153_3_a17/

[1] Khots B., Khots D., Mathematics of Relativity, URL: , 2004 http://www.mathrelativity.com

[2] Khots B., Khots D., “An Introduction to Mathematics of Relativity”, Lecture Notes in Theoretical and Mathematical Physics, v. 7, ed. A. V. Aminova, Kazan State University, Kazan, 2006, 269–306

[3] Khots B., Khots D., “Observer's Mathematics – Mathematics of Relativity”, Appl. Math. Comput., 187:1 (2007), 228–238 | DOI | MR | Zbl

[4] Khots D., Khots B., “Quantum Theory and Observer's Mathematics”, AIP Conf. Proc., 962 (2007), 261–264 | DOI | MR | Zbl

[5] Khots B., Khots D., “Analogy of Fermat's last problem in Observer's Mathematics – Mathematics of Relativity”, Talk at the International Congress of Mathematicians, Madrid, Spain, 2006 URL: http://icm2006.org/v_f/AbsDef/Shorts/abs_0358.pdf

[6] Khots B., Khots D., “Analogy of Hilbert's tenth problem in Observer's Mathematics”, Talk at the International Congress of Mathematicians, Hyderabad, India, 2010 URL: http://www.icm2010.in/wp-content/icmfiles/abstracts/Contributed-Abstracts-5July2010.pdf

[7] Khots B., Khots D., “Non-Euclidean Geometry in Observer's Mathematics”, Acta Physica Debrecina, 42 (2008), 112–119

[8] Khots B., Khots D., “Quantum Theory from Observer's Mathematics point of view”, AIP Conf. Proc., 1232 (2010), 294–298 | DOI

[9] Khots B., Khots D., “Solitary Waves and Dispersive Equations from Observer's Mathematics point of view”, Geometry “in large”, topology and applications, Kharkov, Ukraine, 2010, 86–95