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.

Longitudinal data is becoming increasingly common, especially in the medical and economic fields, and various methods have been analyzed and developed to analyze this type of data.

In this research, the focus was on compiling and analyzing this data, as cluster analysis plays an important role in identifying and grouping co-expressed subfiles over time and employing them on the nonparametric smoothing cubic B-spline model, which is characterized by providing continuous first and second derivatives, resulting in a smoother curve with fewer abrupt changes in slope. It is also more flexible and can pick up on more complex patterns and fluctuations in the data.

The longitudinal balanced data profile was compiled into subgroup

Iraq is highly dependent on international markets to provide food for its residents. As imported food prices are highly dependent on crude oil prices in global markets, any shock in oil prices will have an impact on food consumption in the country. As a result, it is essential to study the demand for imported food at every time period. To the best of our knowledge as researchers, as not even a single study is available in the literature, this paper is considered the first to study the demand for imported food groups in Iraq. Therefore, the main objective of this research is to estimate demand elasticities for several imported food categories in Iraq. This study uses an Almost Ideal Demand System model to analyze the demand for imported f

The research aims to answer the questions that revolve in the mind of mankind about how to create creation, how it existed prior to creation, who created existence, and the characteristics of that presence. The researcher also wanted to show that the culture of Imam Ali (peace be upon him) In the book of Adam, peace be upon him, God has punished Adam (peace be upon him) for not having sinned. Because his wife is the one who fed him the fruit of the tree, and this is contrary to what was stated in the sermon of Imam (peace be upon him) who Z Adam (peace be upon him) is the one who trusted Satan and Gwighth.

We note that the approach of the rhetoric has pointed to the creation of angels and did not refer to

The research aims to answer the questions that revolve in the mind of mankind about how to create creation, how it existed prior to creation, who created existence, and the characteristics of that presence. The researcher also wanted to show that the culture of Imam Ali (peace be upon him) In the book of Adam, peace be upon him, God has punished Adam (peace be upon him) for not having sinned. Because his wife is the one who fed him the fruit of the tree, and this is contrary to what was stated in the sermon of Imam (peace be upon him) who Z Adam (peace be upon him) is the one who trusted Satan and Gwighth.We note that the approach of the rhetoric has pointed to the creation of angels and did not refer to the creation of Eve and the class

In this research, a mathematical model of tumor treatment by radiotherapy is studied and a new modification for the model is proposed as well as introducing the check for the suggested modification. Also the stability of the modified model is analyzed in the last section.

An innovative desalination method called electrosorption or capacitive deionization (CDI) has significant benefits for wastewater treatment. This process is performed by using a carbon fiber electrode as a working electrode to remove hexavalent chromium ions from an aqueous solution. The pH, NaCl concentration, and cell voltage were optimized using the Box-Behnken experimental design (BDD) in response surface methodology (RSM) to study the effects and interactions of selected variables. To attain the relationship between the process variables and chromium removal, the experimental data were subjected to an analysis of variance and fitted with a quadratic model. The optimum conditions to remove Cr(VI) ions were: pH of 2, a cell voltage of 4.