In this article, a new deterministic primality test for Mersenne primes is presented. It also includes a comparative study between well-known primality tests in order to identify the best test. Moreover, new modifications are suggested in order to eliminate pseudoprimes. The study covers random primes such as Mersenne primes and Proth primes. Finally, these tests are arranged from the best to the worst according to strength, speed, and effectiveness based on the results obtained through programs prepared and operated by Mathematica, and the results are presented through tables and graphs.

Semi-parametric models analysis is one of the most interesting subjects in recent studies due to give an efficient model estimation. The problem when the response variable has one of two values either 0 ( no response) or one – with response which is called the logistic regression model.

We compare two methods Bayesian and . Then the results were compared using MSe criteria.

A simulation had been used to study the empirical behavior for the Logistic model , with  different sample sizes and variances. The results using represent that the Bayesian method is better than the   at small samples sizes.

Multiple linear regressions are concerned with studying and analyzing the relationship between the dependent variable and a set of explanatory variables. From this relationship the values of variables are predicted. In this paper the multiple linear regression model and three covariates were studied in the presence of the problem of auto-correlation of errors when the random error distributed the distribution of exponential. Three methods were compared (general least squares, M robust, and Laplace robust method). We have employed the simulation studies and calculated the statistical standard mean squares error with sample sizes (15, 30, 60, 100). Further we applied the best method on the real experiment data representing the varieties of

 In this paper, an intelligent tracking control system of both single- and double-axis Piezoelectric Micropositioner stage is designed using Genetic Algorithms (GAs) method for the optimal Proportional-Integral-Derivative (PID) controller tuning parameters. The (GA)-based PID control design approach is a methodology to tune a (PID) controller in an optimal control sense with respect to specified objective function. By using the (GA)-based PID control approach, the high-performance trajectory tracking responses of the Piezoelectric Micropositioner stage can be obtained. The (GA) code was built and the simulation results were obtained using MATLAB environment. The Piezoelectric Micropositioner simulation model with th

Cover crops (CC) improve soil quality, including soil microbial enzymatic activities and soil chemical parameters. Scientific studies conducted in research centers have shown positive effects of CC on soil enzymatic activities; however, studies conducted in farmer fields are lacking in the literature. The objective of this study was to quantify CC effects on soil microbial enzymatic activities (β-glucosidase, β-glucosaminidase, fluorescein diacetate hydrolase, and dehydrogenase) under a corn (Zea mays L.)–soybean (Glycine max (L.) Merr.) rotation. The study was conducted in 2016 and 2018 in Chariton County, Missouri, where CC were first established in 2012. All tested soil enzyme levels were significantly different between 2016 and 2018

Vehicular Ad Hoc Networks (VANETs) are integral to Intelligent Transportation Systems (ITS), enabling real-time communication between vehicles and infrastructure to enhance traffic flow, road safety, and passenger experience. However, the open and dynamic nature of VANETs presents significant privacy and security challenges, including data eavesdropping, message manipulation, and unauthorized access. This study addresses these concerns by leveraging advancements in Fog Computing (FC), which offers lowlatency, distributed data processing near-end devices to enhance the resilience and security of VANET communications. The paper comprehensively analyzes the security frameworks for fog-enabled VANETs, introducing a novel taxonomy that c