Darboux Integrability of a Generalized 3D Chaotic Sprott ET9 System

في هذا البحث تم دراسة التكامل الاول من نوع داربوكس لتعميم النظام الفوضوي الثلاثي الابعاد Sprott ET9 . حيث وضحنا ان النظام لايمتلك متعددة حدود . دالة كسرية, تحليلية والداربوكس للتكامل الاول لاي قيمتين a و b. كما استطعنا ابجاد متعددة  حدود داربوكس لهذا النظام بقرب المفكوك الاسي. باستخدام وزن متعددة الحدود المتجانسة التي ساعدتنا في برهان الطريقة.In this paper, the first integrals of Darboux type of the generalized Sprott ET9 chaotic system will be studied. This study showed that the system has no polynomial, rational, analytic and Darboux first integrals for any value of . All the Darboux polynomials for this system were derived together with its exponential factors. Using the weight homogenous polynomials helped us prove the process

A new Mean Deviation and Advanced Mean Deviation Techniques to Solve Multi-Objective Fractional Programming Problem Via Point-Slopes Formula

In this paper, we have proposed a new technique to find an efficient solution to fractional programming problems (FPP). The multi-objective fractional programming problem (MOFPP) is converted into multi-objective linear programming (MOLPP) utilizing the point-slopes formula for a plane, which has equivalent weights to the MOFPP. The MOLPP is diminished to a single objective linear programming problem (SOLPP) through using two new techniques for the values of the objective function and suggesting an algorithm for its solution. Finally, we obtained the optimal solution for MOFPP by solving the consequent linear programming problem (LPP). The proposed practicability is confirmed with the existing approaches, with some numerical examples and we indicated comparison with other techniques.&nbsp