We investigate the interaction of proton with a solid target, describing the wake effects by taking fitted parameters with experimental values of energy loss function ELF for copper using the dielectric function of random phase approximation (RPA). The results exhibited a damped oscillatory behavior in the longitudinal direction behind the projectile. In addition, the wake potential becomes asymmetric around the z-axis with proton velocity values higher than Fermi velocity, as well as it depends on the position of projectile in cylindrical coordinates.

      Predicting the visibility of the lunar crescent drew great attention during the Middle Ages, especially among Muslims, because the dates of religious practices in Islam and calendars, in addition to being aware of the motion of the moon in its orbit, are based on the lunar month.

 This paper aims to study the development of crescent visibility criteria from ancient times through the medieval period to the modern update. Some basics and astronomical terms related to crescent visibility are presented and then a comprehensive view of crescent visibility criteria is examined by surveying about 54 published research papers related to the issue of crescent visibility. Each research paper is summarized, classified, and the re

In the current review, an updated list of dark beetle species (Coleoptera, Tenebrionidae) recorded in Iraq was given. The current paper is based on previous studies in the literature and contains all dark beetles referred to in Iraq, except for the species within the Pimelinae subfamily. The investigation of this review showed the presence of 89 species belonging to 34 genera within five subfamilies. This work included mentioning the basionyms and synonyms for genera and species with their global distribution, as well as, correcting the scientific names that were mentioned in the previous checklists.

    In this paper, we introduce the bi-normality set, denoted by , which is an extension of the normality set, denoted by  for any operators  in the Banach algebra . Furthermore, we show some interesting properties and remarkable results. Finally, we prove that it is not invariant via some transpose linear operators.

This paper is an attempt to demonstrate the syntactic behavior of -ly adverbs and -ly adjectives. It mainly deals with -ly as an inflectional suffix that forms adverbs and adjectives It is hypothesized that there are differences between adjective-forming –ly and adverb-forming –ly.The researcher first made general and specific observations about the morphological processes of -ly adverbs and -ly adjectives. Since the study focuses on a linguistic phenomenon, its data is a set of -ly adverbs and -ly adjectives used as examples to support the hypothesis. The importance of studying the syntactic behavior of -ly stems from the fact that thousands of English adjectives and adverbs are created by adding the suffix "-ly" to their roots

In this work, nonlinear diabetes controlled model with and without complications in a population is considered. The dynamic behavior of diabetes in a population by including a constant control is studied and investigated. The existence of all its possible fixed points is investigated as well as the conditions of the local stability of the considered model are set. We also find the optimal control strategy in order to reduce the number of people having diabetes with complications over a finite period of time. A numerical simulation is provided and confirmed the theoretical results.