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Classification of Critical Points and Caustic of the Functions of Codimensions Eight and Fifteen
تصنيف النقاط الحرجة وكاؤستيك للدوال التي أبعادها المرافقة ثمانية و خمسة عشر

Authors: Mudhir A. Abdul Hussain --- Murtada. J. Mohammed
Journal: journal of kerbala university مجلة جامعة كربلاء ISSN: 18130410 Year: 2015 Volume: 13 Issue: 1 Pages: 64-77
Publisher: Kerbala University جامعة كربلاء

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Abstract

In the present paper we classified the critical points of functions of codimensions eight and fifteen by finding the geometric description of caustic, investigate the propagation of the critical points and determine the level curves of these functions in the space of parameters.

في البحث الحالي قمنا بتصنيف النقاط الحرجة للدوال التي تكون أبعادها المرافقة ثمانية و خمسة عشر وذلك من خلال إيجاد الوصف الهندسي للكاؤستيك وكذلك إيجاد أنواع النقاط الحرجة ومنحنيات المستوى لهذة الدوال في فضاء المعلمات

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Article
BIFURCATION DIAGRAM FOR NONLINEAR SYSTEM OF ALGEBRAIC EQUATIONS WITH PARAMETERS

Authors: Safaa A. Hammed --- Murtada J. Mohammed
Journal: Journal of Kufa for Mathematics and Computer مجلة الكوفة للرياضيات والحاسوب ISSN: 11712076 Year: 2015 Volume: 2 Issue: 3 Pages: 11-25
Publisher: University of Kufa جامعة الكوفة

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Abstract

In this paper we are interested instudying of bifurcation solutions of bifurcationequation (nonlinear system of algebraicequations with four or six parameters). Also, wefound a new geometrical description of theDiscriminate set(bifurcation set) with bifurcationspreading of the number of regular solutions inevery region. In addution, we calculate thetopological indices of the solutions of theproblem.

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