This article deals with the approximate algorithm for two dimensional multi-space fractional bioheat equations (M-SFBHE). The application of the collection method will be expanding for presenting a numerical technique for solving M-SFBHE based on “shifted Jacobi-Gauss-Labatto polynomials” (SJ-GL-Ps) in the matrix form. The Caputo formula has been utilized to approximate the fractional derivative and to demonstrate its usefulness and accuracy, the proposed methodology was applied in two examples. The numerical results revealed that the used approach is very effective and gives high accuracy and good convergence.

In this paper Heun method has been used to find numerical solution for first order nonlinear functional differential equation. Moreover, this method has been modified in order to treat system of nonlinear functional differential equations .two numerical examples are given for conciliated the results of this method.

In this paper, a new third kind Chebyshev wavelets operational matrix of derivative is presented, then the operational matrix of derivative is applied for solving optimal control problems using, third kind Chebyshev wavelets expansions. The proposed method consists of reducing the linear system of optimal control problem into a system of algebraic equations, by expanding the state variables, as a series in terms of third kind Chebyshev wavelets with unknown coefficients. Example to illustrate the effectiveness of the method has been presented.

        This paper is concerned with the solution of the nanoscale structures consisting of the   with an effective mass envelope function theory, the electronic states of the  quantum ring are studied.  In calculations, the effects due to the different effective masses of electrons in and out the rings are included. The energy levels of the electron are calculated in the different shapes of rings, i.e., that the inner radius of rings sensitively change the electronic states. The energy levels of the electron are not sensitively dependent on the outer radius for large rings. The structures of  quantum rings are studied by the one electronic band Hamiltonian effective mass approximati

The problem of Bi-level programming is to reduce or maximize the function of the target by having another target function within the constraints. This problem has received a great deal of attention in the programming community due to the proliferation of applications and the use of evolutionary algorithms in addressing this kind of problem. Two non-linear bi-level programming methods are used in this paper. The goal is to achieve the optimal solution through the simulation method using the Monte Carlo method using different small and large sample sizes. The research reached the Branch Bound algorithm was preferred in solving the problem of non-linear two-level programming this is because the results were better.

      In many areas, such as simulation, numerical analysis, computer programming, decision-making, entertainment, and coding, a random number input is required. The pseudo-random number uses its seed value. In this paper, a hybrid method for pseudo number generation is proposed using Linear Feedback Shift Registers (LFSR) and Linear Congruential Generator (LCG). The hybrid method for generating keys is proposed by merging technologies. In each method, a new large in key-space group of numbers were generated separately. Also, a higher level of secrecy is gained such that the internal numbers generated from LFSR are combined with LCG (The adoption of roots in non-linear iteration loops). LCG and LFSR are linear structures and outputs

With the great development in the field of the Internet, the talk about the new media and its implications began, And its interactive services have made the future of media material sometimes participating in it and manufacturing it at other times,
the public is seeking information and choosing the appropriate ones, as well as exchanging messages with the sender after what the role of the receiver is just receiving information only.
This study aims to demonstrate the effects of using digital media in various forms and types to construct the value system of Iraqi society through the identification of the following aims:
Identify the most popular digital media for the Iraqi public in their daily lives on the Internet.
Identify

The undertaken study includes investigating the performance and effluent characteristics of the treatment plant of Al-Doura refinery. Influent concentrations for some important contaminants, which are TDS, oil and grease, TSS, COD, BOD, and turbidity were 2595 mg/L, 13934 mg/L, 466.45 mg/L, 2538.9 mg/L, 1739.2 mg/L, and 89.18 NTU, respectively, while the effluent concentrations were 1337.8 mg/L, 0.53mg/L, 21.7mg/L, 25.45 mg/L, 17.81 mg/L, and 7.08 NTU, respectively, giving removal efficiencies of 44.47%, 99.99%, 94.4%, 98.96%, 98.96% and 92.05%, respectively. All these results indicate that Al-Doura wastewater treatment plant was efficient in removing contaminants according to Iraqi and EPA specifications. Hence, the second part of this