"Studying the Characteristics of Algebraic Curve Behavior For Nonstandard Method"
DOI:
https://doi.org/10.25007/ajnu.v7n3a203Keywords:
Monad, Infinitesimal, Limited, Shadow, Regular and Irregular pointsAbstract
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).
Downloads
References
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.
Downloads
Published
How to Cite
Issue
Section
License
Authors retain copyright
The use of a Creative Commons License enables authors/editors to retain copyright to their work. Publications can be reused and redistributed as long as the original author is correctly attributed.
- Copyright
- The researcher(s), whether a single or joint research paper, must sell and transfer to the publisher (the Academic Journal of Nawroz University) through all the duration of the publication which starts from the date of entering this Agreement into force, the exclusive rights of the research paper/article. These rights include the translation, reuse of papers/articles, transmit or distribute, or use the material or parts(s) contained therein to be published in scientific, academic, technical, professional journals or any other periodicals including any other works derived from them, all over the world, in English and Arabic, whether in print or in electronic edition of such journals and periodicals in all types of media or formats now or that may exist in the future. Rights also include giving license (or granting permission) to a third party to use the materials and any other works derived from them and publish them in such journals and periodicals all over the world. Transfer right under this Agreement includes the right to modify such materials to be used with computer systems and software, or to reproduce or publish it in e-formats and also to incorporate them into retrieval systems.
- Reproduction, reference, transmission, distribution or any other use of the content, or any parts of the subjects included in that content in any manner permitted by this Agreement, must be accompanied by mentioning the source which is (the Academic Journal of Nawroz University) and the publisher in addition to the title of the article, the name of the author (or co-authors), journal’s name, volume or issue, publisher's copyright, and publication year.
- The Academic Journal of Nawroz University reserves all rights to publish research papers/articles issued under a “Creative Commons License (CC BY-NC-ND 4.0) which permits unrestricted use, distribution, and reproduction of the paper/article by any means, provided that the original work is correctly cited.
- Reservation of Rights
The researcher(s) preserves all intellectual property rights (except for the one transferred to the publisher under this Agreement).
- Researcher’s guarantee
The researcher(s) hereby guarantees that the content of the paper/article is original. It has been submitted only to the Academic Journal of Nawroz University and has not been previously published by any other party.
In the event that the paper/article is written jointly with other researchers, the researcher guarantees that he/she has informed the other co-authors about the terms of this agreement, as well as obtaining their signature or written permission to sign on their behalf.
The author further guarantees:
- The research paper/article does not contain any defamatory statements or illegal comments.
- The research paper/article does not violate other's rights (including but not limited to copyright, patent, and trademark rights).
This research paper/article does not contain any facts or instructions that could cause damages or harm to others, and publishing it does not lead to disclosure of any confidential information.