In this work, a class of stochastically perturbed differential systems with standard Brownian motion of ordinary unperturbed differential system is considered and studied. The necessary conditions for the existence of a unique solution of the stochastic perturbed semi-linear system of differential equations are suggested and supported by concluding remarks. Some theoretical results concerning the mean square exponential stability of the nominal unperturbed deterministic differential system and its equivalent stochastically perturbed system with the deterministic and stochastic process as a random noise have been stated and proved. The proofs of the obtained results are based on using the stochastic quadratic Lyapunov function meth

The two parameters of Exponential-Rayleigh distribution were estimated using the maximum likelihood estimation method (MLE) for progressively censoring data. To find estimated values for these two scale parameters using real data for COVID-19 which was taken from the Iraqi Ministry of Health and Environment, AL-Karkh General Hospital. Then the Chi-square test was utilized to determine if the sample (data) corresponded with the Exponential-Rayleigh distribution (ER). Employing the nonlinear membership function (s-function) to find fuzzy numbers for these parameters estimators. Then utilizing the ranking function transforms the fuzzy numbers into crisp numbers. Finally, using mean square error (MSE) to compare the outcomes of the survival

Many objective optimizations (MaOO) algorithms that intends to solve problems with many objectives (MaOP) (i.e., the problem with more than three objectives) are widely used in various areas such as industrial manufacturing, transportation, sustainability, and even in the medical sector.  Various approaches of MaOO algorithms are available and employed to handle different MaOP cases. In contrast, the performance of the MaOO algorithms assesses based on the balance between the convergence and diversity of the non-dominated solutions measured using different evaluation criteria of the quality performance indicators. Although many evaluation criteria are available, yet most of the evaluation and benchmarking of the MaOO with state-of-art a

The Log-Logistic distribution is one of the important statistical distributions as it can be applied in many fields and biological experiments and other experiments, and its importance comes from the importance of determining the survival function of those experiments. The research will be summarized in making a comparison between the method of maximum likelihood and the method of least squares and the method of weighted least squares to estimate the parameters and survival function of the log-logistic distribution using the comparison criteria MSE, MAPE, IMSE, and this research was applied to real data for breast cancer patients. The results showed that the method of Maximum likelihood best in the case of estimating the paramete

   In this work, a novel technique to obtain an accurate solutions to nonlinear form by multi-step combination with Laplace-variational approach (MSLVIM) is introduced. Compared with the  traditional approach for variational it overcome all difficulties and enable to provide us more an accurate solutions with extended of the convergence region as well as covering to larger intervals which providing us a continuous representation of approximate analytic solution and it give more better information of the solution over the whole time interval. This technique is more easier for obtaining the general Lagrange multiplier with reduces the time and calculations. It converges rapidly to exact formula with simply computable terms wit

In this research, salbutamol sulphate (SAS) has been determined by a simple, rapid and sensitive spectrophotometric method. Salbutamol sulphate in this method is based on the coupling of SAS with diazotized ρ- bromoaniline reagent in alkaline medium of Triton X-100 (Tx) to form an orange azo dye which is stable and water-soluble. The azo dye is exhibiting maximum absorption at 441 nm. A 10 - 800 µg of SAS is obeyed of Beer^'s law in a final volume of 20 ml, i.e., 0.5- 40 ppm with ε, the molar absorptivity of 48558 L.mol^-1.cm^-1 and Sandell's sensitivity index of 0.01188 µg.cm^-2. This new method does not need solvent extraction or temperature control which is well applied to determine SAS in d

Based on the diazotization-coupling reaction, a new, simple, and sensitive spectrophotometric method for determining of a trace amount of (BPF) is presented in this paper. Diazotized metoclopramide reagent react with bisphenol F produces an orange azo-compound with a maximum absorbance at 461 nm in alkaline solution. The experimental parameters were optimized such as type of alkaline medium, concentration of NaOH, diazotized metoclopramide amount, order additions, reaction time, temperature, and effect of organic solvents to achieve the optimal performance for the proposed method. The absorbance increased linearly with increasing bisphenol F concentration in the range of 0.5-10 μg mL^-1 under ideal conditions, with a correlati

Abstract

            Rayleigh distribution is one of the important distributions used for analysis life time data, and has applications in reliability study and physical interpretations. This paper introduces four different methods to estimate the scale parameter, and also estimate reliability function; these methods are Maximum Likelihood, and Bayes and Modified Bayes, and Minimax estimator under squared error loss function, for the scale and reliability function of the generalized Rayleigh distribution are obtained. The comparison is done through simulation procedure, t

In this study, an unknown force function dependent on the space in the wave equation is investigated. Numerically wave equation splitting in two parts, part one using the finite-difference method (FDM). Part two using separating variables method. This is the continuation and changing technique for solving inverse problem part in (1,2). Instead, the boundary element method (BEM) in (1,2), the finite-difference method (FDM) has applied. Boundary data are in the role of overdetermination data. The second part of the problem is inverse and ill-posed, since small errors in the extra boundary data cause errors in the force solution. Zeroth order of Tikhonov regularization, and several parameters of regularization are employed to decrease error

This researchpaper includes the incorporation of Alliin at various energy levels and angles 

With Metformin using Gaussian 09 and Gaussian view 06. Two computers were used in this work. Samples were generated to draw, integrate, simulate and measure the value of the potential energy surface by means of which the lowest energy value was (-1227.408au). The best correlation compound was achieved between Alliin and Metformin through the low energy values where the best place for metformin to b