This research includes the use of an artificial intelligence algorithm, which is one of the algorithms of biological systems which is the algorithm of genetic regulatory networks (GRNs), which is a dynamic system for a group of variables representing space within time. To construct this biological system, we use (ODEs) and to analyze the stationarity of the model we use Euler's method. And through the factors that affect the process of gene expression in terms of inhibition and activation of the transcription process on DNA, we will use TF transcription factors. The current research aims to use the latest methods of the artificial intelligence algorithm. To apply Gene Regulation Networks (GRNs), we used a progr

  Necessary and sufficient conditions for the operator equation I AXAX n  * , to have a real positive definite solution X are given. Based on these conditions, some properties of the operator A as well as relation between the solutions X andAare given.

The current research aims to provide a philosophical and knowledge framework  to explain the issue of organizations dealing with Paradox phenomena by focusing on five main aspects. The first deals with the concept of paradox, and the second aspect deals with the types of forces paradox. While the third aspect regards subject of the philosophy of paradox in organization theory and the fourth side deals with methods of   solving the paradox. Finally, the last side is exposed to the subject of the paradoxes of the three provided by the study (L

This article suggests and explores a three-species food chain model that includes fear effects, refuges depending on predators, and cannibalism at the second level. The Holling type II functional response determines food consumption between stages of the food chain. This study examined the long-term behavior and impacts of the suggested model's essential elements. The model's solution properties were studied. The existence and stability of every probable equilibrium point were examined. The persistence needs of the system have been determined. It was discovered what conditions could lead to local bifurcation at equilibrium points. Appropriate Lyapunov functions are utilized to investigate the overall dynamics of the system. To support the a

Volterra – Fredholm integral equations (VFIEs) have a massive interest from researchers recently. The current study suggests a collocation method for the mixed Volterra - Fredholm integral equations (MVFIEs)."A point interpolation collocation method is considered by combining the radial and polynomial basis functions using collocation points". The main purpose of the radial and polynomial basis functions is to overcome the singularity that could associate with the collocation methods. The obtained interpolation function passes through all Scattered Point in a domain and therefore, the Delta function property is the shape of the functions. The exact solution of selective solutions was compared with the results obtained

The aim of this paper is to investigate the theoretical approach for solvability of impulsive abstract Cauchy problem for impulsive nonlinear fractional order partial differential equations with nonlocal conditions, where the nonlinear extensible beam equation is a particular application case of this problem.

In this paper, we introduce a new type of Drazin invertible operator on Hilbert spaces, which is called D-operator. Then, some properties of the class of D-operators are studied. We prove that the D-operator preserves the scalar product, the unitary equivalent property, the product and sum of two D-operators are not D-operator in general but the direct product and tenser product is also D-operator.

In this paper, the asymptotic behavior of all solutions of impulsive neutral differential equations with positive and negative coefficients and with impulsive integral term was investigated. Some sufficient conditions were obtained to ensure that all nonoscillatory solutions converge to zero. Illustrative examples were given for the main results.

     An α-fractional integral and derivative of real function have been introduced in new definitions and then, they compared with the existing definitions. According to the properties of these definitions, the formulas demonstrate that they are most significant and suitable in fractional integrals and derivatives. The definitions of α-fractional derivative and integral coincide with the existing definitions for the polynomials for 0 ≤ α < 1. Furthermore, if α = 1, the proposed definitions and the usual definition of integer derivative and integral are identical. Some of the properties of the new definitions are discussed and proved, as well, we have introduced some applications in the α- fractional derivatives and integral