The aim of this article is to solve the Volterra-Fredholm integro-differential equations of fractional order numerically by using the shifted Jacobi polynomial collocation method. The Jacobi polynomial and collocation method properties are presented. This technique is used to convert the problem into the solution of linear algebraic equations. The fractional derivatives are considered in the Caputo sense. Numerical examples are given to show the accuracy and reliability of the proposed technique.

In this paper we estimate the coefficients and scale parameter in linear regression model depending on the residuals are of type 1 of extreme  value distribution for the largest values . This can be regard as an improvement for the studies with the smallest values . We study two estimation methods ( OLS  & MLE ) where we resort to Newton – Raphson (NR) and Fisher Scoring methods to get MLE estimate because the difficulty of using the usual approach with MLE . The relative efficiency criterion is considered beside to the statistical inference procedures for the extreme value regression model of type 1 for largest values . Confidence interval , hypothesis testing for both scale parameter and regression coefficients

In this paper, an eco-epidemiological prey-predator system when the predator is subjected to the weak Allee effect, and harvesting was proposed and studied. The set of ordinary differential equations that simulate the system’s dynamic is constructed. The impact of fear and Allee’s effect on the system's dynamic behavior is one of our main objectives. The properties of the solution of the system were studied. All possible equilibrium points were determined, and their local, as well as global stabilities, were investigated. The possibility of the occurrence of local bifurcation was studied. Numerical simulation was used to further evaluate the global dynamics and understood the effects of varying parameters on the asymptotic behavior of t

The researchers have a special interest in studying  Markov  chains as one of the probability samples which has many applications in different fields. This study comes to deal with the changes issue that happen on budget expenditures by using statistical methods, and Markov chains is the best expression about that as they are regarded reliable  samples in the prediction process. A transitional matrix is built for three expenditure cases (increase ,decrease ,stability) for one of budget expenditure items (base salary) for three directorates (Baghdad ,Nineveh , Diyala) of one  of the ministries. Results are analyzed by applying  Maximum likelihood estimation  and Ordinary least squares  methods resulting

Background: Periodontium mainly exposed to injury by trauma or pathologic diseases, Aloe vera is a plant has many basic ingredients in its extracted gel that acts as wound healing accelerator in addition to that it's safe, and economical and without recordable of side effect. This study aimed is to evaluate the effect of topical application of Aloe vera on expression of syndecan -1 by periodontium tissue. Materials and methods: Thirty six male Albino rats were subjected for periodontium defect by electric scaler on the distal sides of both lower anterior teeth. The animals divided into two groups; control group (without treatment) and the experimental group treated with 1µLAloe vera gel/normal saline. Periodontal healing was examined at

Wildfire risk has globally increased during the past few years due to several factors. An efficient and fast response to wildfires is extremely important to reduce the damaging effect on humans and wildlife. This work introduces a methodology for designing an efficient machine learning system to detect wildfires using satellite imagery. A convolutional neural network (CNN) model is optimized to reduce the required computational resources. Due to the limitations of images containing fire and seasonal variations, an image augmentation process is used to develop adequate training samples for the change in the forest’s visual features and the seasonal wind direction at the study area during the fire season. The selected CNN model (Mob

The rise of Industry 4.0 and smart manufacturing has highlighted the importance of utilizing intelligent manufacturing techniques, tools, and methods, including predictive maintenance. This feature allows for the early identification of potential issues with machinery, preventing them from reaching critical stages. This paper proposes an intelligent predictive maintenance system for industrial equipment monitoring. The system integrates Industrial IoT, MQTT messaging and machine learning algorithms. Vibration, current and temperature sensors collect real-time data from electrical motors which is analyzed using five ML models to detect anomalies and predict failures, enabling proactive maintenance. The MQTT protocol is used for efficient com

This research work aims to the determination of molybdenum (VI) ion via the formation of peroxy molybdenum compounds which has red-brown colour with absorbance wave length at 455nm for the system of ammonia solution-hydrogen peroxide-molybdenum (VI) using a completely newly developed microphotometer based on the ON-Line measurement. Variation of responses expressed in millivolt. A correlation coefficient of 0.9925 for the range of 2.5-150 ?g.ml-1 with percentage linearity of 98.50%. A detection limit of 0.25 ?g.ml-1 was obtained. All physical and chemical variable were optimized interferences of cation and anion were studied classical method of measurement were done and compared well with newly on-line measurements. Application for the use

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