Nonlinear differential equation stability is a very important feature of applied mathematics, as it has a wide variety of applications in both practical and physical life problems. The major object of the manuscript is to discuss and apply several techniques using modify the Krasovskii's method and the modify variable gradient method which are used to check the stability for some kinds of linear or nonlinear differential equations. Lyapunov function is constructed using the variable gradient method and Krasovskii’s method to estimate the stability of nonlinear systems. If the function of Lyapunov is positive, it implies that the nonlinear system is asymptotically stable. For the nonlinear systems, stability is still difficult even though the Lyapunov methods are applied. There has to find a positive definite Lyapunov function, and its derivative function has to be negative definite. A new approach had been tested in several …
Monetary policy occupies a prominent role in achieving monetary stability by adjusting the growth rates of the number of available means of payment in line with changes in the size of the gross domestic product in the country and expressed by the monetary stability coefficient agreed upon by the International Monetary Fund, a term that hides the fact that there is a rate of change in the volume of commodity or real production which expresses the levels of aggregate supply in the economy, which corresponds to the quantities of cash in circulation, which represent a net purchasing power and stimulate aggregate demand, which completes the picture of the existence of the market mechanism, expressed by the monetary or economic stability
... Show MoreBackground: The present study was carried out to compare shear bond strength of sapphire bracket bonded to zirconium surface after using different methods of surface conditioning and assessment of the adhesive remnant index. Materials and methods: The sample composed of 40 zirconium specimens divided into four groups; the first group was the control, the second group was conditioned by sandblast with aluminum oxide particle 50 μm, the third and fourth group was treated by (Nd: YAG) laser (1064nm)(0.888 Watt for 5 seconds) for the 1st laser group and (0.444 Watt for 10 seconds) for the 2nd laser group. All samples were coated by z-prime plus primer. A central incisor sapphire bracket was bonded to all samples with light cure adhesive res
... Show MoreBackground: the primary objective for many researches carried out in dental implantology was to reduce the period needed for functional implant loading, simvastatin (cholesterol lowering medication) had many pleiotropic effects, one of which was increasing bone density around titanium implants (1) and subsequently establishing faster osseointegrated dental implants (2,3). This study aims to reduce the period of time needed to establish secondary stability of dental implant measured in ISQ (Implant Stability Quotient) by investigating the effect of orally administered simvastatin on bone. Materials and methods: simvastatin tablets (40mg/day for three months) were administered orally for 11 healthy women aged (40-51) years old who received 1
... Show MoreIn the present study a new synthesis method has been introduced for the decoration of platinum(Pt) on the functionalized graphene nanoplatelet (GNP) and also highlighted the preparation method of nanofluids. GNP–Pt uniform nanocomposite was produced from a simple chemical reaction procedure, which included acid treatment for functionalization of GNP. The surface characterization was performed by various techniques such as XRD, FESEMand TEM. The effective thermal conductivity, density, viscosity, specific heat capacity and stability of functionalized GNP–Pt water based nanofluids were investigated in different instruments. The GNP–Pt hybrid nanofluids were prepared by dispersing the nanocomposite in base fluid without adding any surfac
... Show MoreWater quality planning relies on Biochemical Oxygen Demand BOD. BOD testing takes five days. The Particle Swarm Optimization (PSO) is increasingly used for water resource forecasting. This work designed a PSO technique for estimating everyday BOD at Al-Rustumiya wastewater treatment facility inlet. Al-Rustumiya wastewater treatment plant provided 702 plant-scale data sets during 2012-2022. The PSO model uses the daily data of the water quality parameters, including chemical oxygen demand (COD), chloride (Cl-), suspended solid (SS), total dissolved solids (TDS), and pH, to determine how each variable affects the daily incoming BOD. PSO and multiple linear regression (MLR) findings are compared, and their perfor
... Show MoreWater quality planning relies on Biochemical Oxygen Demand BOD. BOD testing takes five days. The Particle Swarm Optimization (PSO) is increasingly used for water resource forecasting. This work designed a PSO technique for estimating everyday BOD at Al-Rustumiya wastewater treatment facility inlet. Al-Rustumiya wastewater treatment plant provided 702 plant-scale data sets during 2012-2022. The PSO model uses the daily data of the water quality parameters, including chemical oxygen demand (COD), chloride (Cl-), suspended solid (SS), total dissolved solids (TDS), and pH, to determine how each variable affects the daily incoming BOD. PSO and multiple linear regression (MLR) findings are compared, and their performance is evaluated usin
... Show MoreOne of the main causes for concern is the widespread presence of pharmaceuticals in the environment, which may be harmful to living things. They are often referred to as emerging chemical pollutants in water bodies because they are either still unregulated or undergoing regulation. Pharmaceutical pollution of the environment may have detrimental effects on ecosystem viability, human health, and water quality. In this study, the amount of remaining pharmaceutical compounds in environmental waters was determined using a straightforward review. Pharmaceutical production and consumption have increased due to medical advancements, leading to concerns about their environmental impact and potential harm to living things due to their increa
... Show MoreMethods of estimating statistical distribution have attracted many researchers when it comes to fitting a specific distribution to data. However, when the data belong to more than one component, a popular distribution cannot be fitted to such data. To tackle this issue, mixture models are fitted by choosing the correct number of components that represent the data. This can be obvious in lifetime processes that are involved in a wide range of engineering applications as well as biological systems. In this paper, we introduce an application of estimating a finite mixture of Inverse Rayleigh distribution by the use of the Bayesian framework when considering the model as Markov chain Monte Carlo (MCMC). We employed the Gibbs sampler and
... Show MoreIn this paper, point estimation for parameter ? of Maxwell-Boltzmann distribution has been investigated by using simulation technique, to estimate the parameter by two sections methods; the first section includes Non-Bayesian estimation methods, such as (Maximum Likelihood estimator method, and Moment estimator method), while the second section includes standard Bayesian estimation method, using two different priors (Inverse Chi-Square and Jeffrey) such as (standard Bayes estimator, and Bayes estimator based on Jeffrey's prior). Comparisons among these methods were made by employing mean square error measure. Simulation technique for different sample sizes has been used to compare between these methods.