The integral transformations is a complicated function from a function space into a simple function in transformed space. Where the function being characterized easily and manipulated through integration in transformed function space. The two parametric form of SEE transformation and its basic characteristics have been demonstrated in this study. The transformed function of a few fundamental functions along with its time derivative rule is shown. It has been demonstrated how two parametric SEE transformations can be used to solve linear differential equations. This research provides a solution to population growth rate equation. One can contrast these outcomes with different Laplace type transformations

In this article four samples of HgBa₂Ca₂Cu_2.4Ag_0.6O_8+δ were prepared and irradiated with different doses of gamma radiation 6, 8 and 10 Mrad. The effects of gamma irradiation on structure of HgBa₂Ca₂Cu_2.4Ag_0.6O_8+δ samples were characterized using X-ray diffraction. It was concluded that there effect on structure by gamma irradiation. Scherrer, crystallization, and Williamson equations were applied based on the X-ray diffraction diagram and for all gamma doses, to calculate crystal size, strain, and degree of crystallinity. I

       In this paper, we focus on designing feed forward neural network (FFNN) for solving Mixed Volterra – Fredholm Integral Equations (MVFIEs) of second kind in 2–dimensions. in our method, we present a multi – layers model consisting of a hidden layer which has five hidden units (neurons) and one linear output unit. Transfer function (Log – sigmoid) and training algorithm (Levenberg – Marquardt) are used as a sigmoid activation of each unit. A comparison between the results of numerical experiment and the analytic solution of some examples has been carried out in order to justify the efficiency and the accuracy of our method.

This paper deals with the continuous classical optimal control problem for triple partial differential equations of parabolic type with initial and boundary conditions; the Galerkin method is used to prove the existence and uniqueness theorem of the state vector solution for given continuous classical control vector. The proof of the existence theorem of a continuous classical optimal control vector associated with the triple linear partial differential equations of parabolic type is given. The derivation of the Fréchet derivative for the cost function is obtained. At the end, the theorem of the necessary conditions for optimality of this problem is stated and is proved.

    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