In this article, the inverse source problem is determined by the partition hyperbolic equation under the left end flux tension of the string, where the extra measurement is considered. The approximate solution is obtained in the form of splitting and applying the finite difference method (FDM). Moreover, this problem is ill-posed, dealing with instability of force after adding noise to the additional condition. To stabilize the solution, the regularization matrix is considered. Consequently, it is proved by error estimates between the regularized solution and the exact solution. The numerical results show that the method is efficient and stable.

        In this paper, the necessary optimality conditions are studied and derived for a new class of the sum of two Caputo–Katugampola fractional derivatives of orders (α, ρ) and( β,ρ) with fixed the final boundary conditions. In the second study, the approximation of the left Caputo-Katugampola fractional derivative was obtained by using the shifted Chebyshev polynomials. We also use the Clenshaw and Curtis formula to approximate the integral from -1 to 1. Further, we find the critical points using the Rayleigh–Ritz method. The obtained approximation of the left fractional Caputo-Katugampola derivatives was added to the algorithm applied to the illustrative example so that we obtained the approximate results for the stat

Theoretical and experimental investigations of the transient heat transfer parameters of constant heat flux source subjected to water flowing in the downward direction in closed channel are conducted. The power increase transient is ensured by step change increase in the heat source power. The theoretical investigation involved a mathematical modeling for axially symmetric, simultaneously developing laminar water flow in a vertical annulus. The mathematical model is based on one dimensional downward flow. The boundary conditions of the studied case are based on adiabatic outer wall, while the inner wall is subjected to a constant heat flux. The heat & mass balance equation derived for specified element of bulk water within the annulu

Praise to Allah, Lord of the Worlds. Thank you very much. Blessed. As his face should be majestic and great. His authority, and may peace and blessings be upon our master Muhammad, a perpetual blessing until the Day of Judgment

And upon the God of purity, His righteous companions, and those who follow them in righteousness until the Day of Judgment. But after:-

Anyone who looks into the history of nations, peoples, and the conditions of human beings will see that naturalization as a person’s affiliation to a particular state is something that happened only in recent centuries. In ancient times, a person’s loyalty was to the tribe to which the person belonged, and he was integrated into it and attributed to it, and in

In this research, some robust non-parametric methods were used to estimate the semi-parametric regression model, and then  these methods were compared using the MSE comparison criterion, different sample sizes, levels of variance, pollution rates, and three different models were used. These methods are S-LLS S-Estimation -local smoothing, (M-LLS)M- Estimation -local smoothing, (S-NW) S-Estimation-NadaryaWatson Smoothing, and (M-NW) M-Estimation-Nadarya-Watson Smoothing.

The results in the first model proved that the (S-LLS) method was the best in the case of large sample sizes, and small sample sizes showed that the

The influence of an aortic aneurysm on blood flow waveforms is well established, but how to exploit this link for diagnostic purposes still remains challenging. This work uses a combination of experimental and computational modelling to study how aneurysms of various size affect the waveforms. Experimental studies are carried out on fusiform-type aneurysm models, and a comparison of results with those from a one-dimensional fluid–structure interaction model shows close agreement. Further mathematical analysis of these results allows the definition of several indicators that characterize the impact of an aneurysm on waveforms. These indicators are then further studied in a computational model of a systemic blood flow network. This demonstr

    In this work, we introduce Fibonacci– Halpern iterative scheme ( FH scheme) in partial ordered Banach space (POB space) for monotone total asymptotically non-expansive mapping (, MTAN mapping) that defined on weakly compact convex subset.  We also  discuss the results of weak and strong convergence for this scheme.

 Throughout  this work, compactness condition of m-th iterate  of the mapping for some natural m is necessary to ensure strong convergence, while Opial's condition has been employed to show weak convergence. Stability of FH scheme is also  studied. A numerical comparison is provided by an example to show that FH scheme is faster than Mann and Halpern iterative

This paper investigates some exact and local search methods to solve the traveling salesman problem. The Branch and Bound technique (BABT) is proposed, as an exact method, with two models. In addition, the classical Genetic Algorithm (GA) and Simulated Annealing (SA) are discussed and applied as local search methods. To improve the performance of GA we propose two kinds of improvements for GA; the first is called improved GA (IGA) and the second is Hybrid GA (HGA).

The IGA gives best results than GA and SA, while the HGA is the best local search method for all within a reasonable time for 5 ≤ n ≤ 2000, where n is the number of visited cities. An effective method of reducing the size of the TSP matrix was proposed with