This paper introduces a relation between resultant and the Jacobian determinant
by generalizing Sakkalis theorem from two polynomials in two variables to the case of (n) polynomials in (n) variables. This leads us to study the results of the type:  ,            and use this relation to attack the Jacobian problem. The last section shows our contribution to proving the conjecture.

Abstract

The current research aims to identify the effect of the proposed strategy in accordance with realistic mathematics on the achievement and mathematical Interrelation of third Intermediate students. Two samples were tested from the middle third grade in a school affiliated with the General Directorate of Baghdad- Rusafa, the first for the academic year (2022-2021). The experimental group is (30) students taught according to the proposed strategy, and the control group is (30) students based on the traditional method. To achieve the research objective, the researchers developed a test for achievement consisting of (30) items and a test of sports interconnection composed of (20) items. The results of the stu

In this paper,  a Sokol-Howell prey-predator model involving strong Allee effect is proposed and analyzed. The existence, uniqueness, and boundedness are studied. All the five possible equilibria have been are obtained and their local stability conditions are established. Using Sotomayor's theorem, the conditions of local saddle-node and transcritical and pitchfork bifurcation are derived and drawn. Numerical simulations are performed to clarify the analytical results

This study has contributed to understanding a delayed prey-predator system involving cannibalism. The system is assumed to use the Holling type II functional response to describe the consuming process and incorporates the predator’s refuge against the cannibalism process. The characteristics of the solution are discussed. All potential equilibrium points have been identified. All equilibrium points’ local stability analyses for all time delay values are investigated. The system exhibits a Hopf bifurcation at the coexistence equilibrium, which is further demonstrated. The center manifold and normal form theorems for functional differential equations are then used to establish the direction of Hopf bifurcation and the stability of the per

The study the problem emerged in the inability of local companies to enter the field of active competition with other companies operating in the same economic sector due to the high cost of their products, hence, the companies that want to apply this technique can effectively compete in order to achieve those objectives.

  So this study focused on the goal of reducing the cost of products by reducing the cost product to a minimum , as the study was based in its hypothesis on the ability of companies to application this technique which in turn leads to increased profits under conditions of normal working and the power available and their potential in improving the quality of its products, as well as the need for full coordina

This study investigates the surgical and thermal effects on oral soft tissues produced by CO2 laser emitting at 10.6 micrometers with three different fluences 490.79, 1226.99 and 1840.4 J/cm2. These effects are specifically; incision depth, incision width and the tissue damage width and depth. The results showed that increasing the fluence and /or the number of beam passes increase the average depths of ablation. Moreover, increasing the fluence and the number of beam passes increase the adjacent tissue damage in width and depth. Surgeons using CO2 laser should avoid multiple pulses of the laser beam over the same area, to avoid unintentional tissue damage.

 In this paper we introduce several estimators for Binwidth of histogram estimators' .We use simulation technique to compare these estimators .In most cases, the results proved that the rule of thumb estimator is better than other estimators.