"Studying the Characteristics of Algebraic Curve Behavior For Nonstandard Method"
This research aims to study some algebraic curve behaviors in monad (halo) of the regular and irregular points. For this, the Robinson ideas can be used for limited points. Also the geometric tangent at this limited point and the analysis of the algebraic curve around the same point will be studied. Concepts of nonstandard analysis given by Robinson and its axiomatic by Nelson have been used. In this research, we have obtained a state where the point of origin is a regular point and concave is as illustrated in (5). So the curve has connection in this equation (6). There is a second state where the point of origin is an abnormal point of the curve as illustrated in (11). Finally, it has a concave that is calculated in the equation (29).
Diener M. and Lobry C. (1995), Analyse Nonstandard of Representation to Real. CNRS. , Paris.
Diener F. and Reeb G. (1989). Analyse Nonstandard. Herman, Paris.
Diener F. and Diener M . (1995), Nonstandard Analysis in Practice, Spriger-Verleg , Berlin, Heidelberg.
Henson C. W. (1997), Foundation of Nonstandard Analysis - A Gentle Introduction to Nonstandard Analysis Extension in Nonstandard Analysis : Theory and Application. ed. by N. J. Cultand and L. Arkeryd, Kluwer Academic Publishers.
Habacek K. (1979), Nonstandard Set Theory. Amer, Math. Monthly, Vol.86, No.8, pp. 659-677
Nelson E. (1977), Internal Set theory : a New Approach to Nonstandard Analysis , Bull. of Amer. Math. Sco. Vol. 83, No. 6, pp. 1165-1198.
Robinson A. (1970), Nonstandard Analysis- 2ed . American Elsevier, New-york.
Rosinger E. E. (2004), Short Introduction to Nonstandard Analysis, [arXiv : Math. GM/0407178v1,10].
Stroyan K. D. and Luxemburg W. A. (1976), Introduction to the Theory of Infinitesimal, New-York, Academic Press.
Vath M. (2007), Nonstandard Analysis , Birkhauser - Verlag, Berlin.
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