In this article, a numerical method integrated with statistical data simulation technique is introduced to solve a nonlinear system of ordinary differential equations with multiple random variable coefficients. The utilization of Monte Carlo simulation with central divided difference formula of finite difference (FD) method is repeated n times to simulate values of the variable coefficients as random sampling instead being limited as real values with respect to time. The mean of the n final solutions via this integrated technique, named in short as mean Monte Carlo finite difference (MMCFD) method, represents the final solution of the system. This method is proposed for the first time to calculate the numerical solution obtained fo

In this paper, we present new algorithm for the solution of the nonlinear high order multi-point boundary value problem with suitable multi boundary conditions. The algorithm is based on the semi-analytic technique and the solutions are calculated in the form of a rapid convergent series. It is observed that the method gives more realistic series solution that converges very rapidly in physical problems. Illustrative examples are provided to demonstrate the efficiency and simplicity of the proposed method in solving this type of multi- point boundary value problems.

     A partial temporary immunity SIR epidemic model involv nonlinear treatment rate is proposed and studied. The basic reproduction number  is determined. The local and global stability of all equilibria of the model are analyzed. The conditions for occurrence of local bifurcation in the proposed epidemic model are established. Finally, numerical simulation is used to confirm our obtained analytical results and specify the control set of parameters that affect the dynamics of the model.

Average per capita GDP income is an important economic indicator. Economists use this term to determine the amount of progress or decline in the country's economy. It is also used to determine the order of countries and compare them with each other. Average per capita GDP income was first studied using the Time Series (Box Jenkins method), and the second is linear and non-linear regression; these methods are the most important and most commonly used statistical methods for forecasting because they are flexible and accurate in practice. The comparison is made to determine the best method between the two methods mentioned above using specific statistical criteria. The research found that the best approach is to build a model for predi

Estimation of the unknown parameters in 2-D sinusoidal signal model can be considered as important and difficult problem. Due to the difficulty to find estimate of all the parameters of this type of models at the same time, we propose sequential non-liner least squares method and sequential robust  M method after their development through the use of sequential  approach in the estimate suggested by Prasad et al to estimate unknown frequencies and amplitudes for the 2-D sinusoidal compounds but depending on Downhill Simplex Algorithm in solving non-linear equations for the purpose of obtaining non-linear parameters estimation which represents frequencies and then use of least squares formula to estimate

In this work, the linear properties of Vitamin D₃-5000IU soft gel were investigated by measuring its absorption and fluorescence spectra. It was observed that there was a shift towards longer wavelength within limits (75 nm), with quantitative efficiency equal to (33.58%). The values of absorbance were used to calculate the extinction coefficient, optical refractive index, optical conductivity and optical dielectric constant values.

The non-linear properties of Vitamin D₃-5000IU soft gel was also studied using the Z-Scan technique by using Neodymium-doped Yttrium Garnet (Nd: YAG) continuous laser (CW) emitting in       &n

Positron annihilation lifetime (PAL) technique has been employed to
study the microstructural changes of polyurethane (PU), EUXIT 101
and epoxy risen (EP), EUXIT 60 by Gamma-ray irradiation with the
dose range (95.76 - 957.6) kGy. The size of the free volume hole and
their fraction in PU and EP were determined from ortho-positronium
lifetime component and its intensity in the measured lifetime spectra.
The results show that the irradiation causes significant changes in the
free volume hole size (V_h) and the fractional free volume (F_h), and
thereby the microstructure of PU and EP. The results indicate that
the γ-dose increases the crystallinity in the amorphous regions of PU
and increas

The variety of ideas and freedom of expression among the authors who are looking for everything new that serves the goals of musical and aesthetic expression, which calls for the use of traditional musical instruments with the great composition of musical instruments known as the orchestra represents a great challenge in several aspects. The incompetence of some of these instruments or limited capabilities or its costly method of performance sometimes forbids its use permanently in this great composition. It was necessary to have some problems facing the composer and the player on the one hand and the recipient on the other hand, who must be looking for perfection. Among those instruments that are used regularly in the works of the orche