In this paper, we introduce an exponential of an operator defined on a Hilbert space H, and we study its properties and find some of properties of T inherited to exponential operator, so we study the spectrum of exponential operator e^T according to the operator T.

This paper proposes a new method to tune a fractional order PID controller. This method utilizes both the analytic and numeric approach to determine the controller parameters. The control design specifications that must be achieved by the control system are gain crossover frequency, phase margin, and peak magnitude at the resonant frequency, where the latter is a new design specification suggested by this paper. These specifications results in three equations in five unknown variables. Assuming that certain relations exist between two variables and discretizing one of them, a performance index can be evaluated and the optimal controller parameters that minimize this performance index are selected. As a case study, a third order linear time

Media is one of the main and effective factors; and it is a tool of crisis management equipment. Media is one of the most dangerous, effective and decisive weapons in modern conflicts; a tool for making events and influencing their events and trends as a means of reporting as the enormous capabilities of media which help media to move very quickly, and cross borders; and overcome obstacles, through many means of audio, reading and visual. As its ability, moreover, to influence the psychological and intellectual control of communities, and behaviors.

Intelligent media is, then, used in crises management and coverage. Crises have been existed with the presence of man on Earth. Thei

        Assimilation is defined ,by many phoneticians like  Schane ,Roach ,and many others, as a phonological process when there is a change of one sound into another because of  neighboring sounds.This study investigates the  phoneme assimilation as a phonological process in English and Arabic  and it is concerned specifically with the differences and similarities in both languages.   Actually ,this study reflects the different terms which are used  in Arabic to refer to this phenomenon and in this way it  shows whether the term 'assimilation ' can have the same meaning of  'idgham' in Arabic or not . Besides, in Arabic , this phenomenon is discussed from&nb

The interplay of species in a polluted environment is one of the most critical aspects of the ecosystem. This paper explores the dynamics of the two-species Lokta–Volterra competition model. According to the type I functional response, one species is affected by environmental pollution. Whilst the other degrades the toxin according to the type II functional response. All equilibrium points of the system are located, with their local and global stability being assessed. A numerical simulation examination is carried out to confirm the theoretical results. These results illustrate that competition and pollution can significantly change the coexistence and extinction of each species.

This review paper examines the crucial impact of YouTube on learning English as a Foreign Language. Recently, learners’ interaction and development of their skills have been improved due to the integration of digital platforms into language education. YouTube is regarded as one of the most prevalent platforms due to its accessibility, multimodal content, and capacity to simulate real-life communication. This study tackles thirty selected research articles from various cultural and institutional backgrounds to identify the pedagogical benefits and challenges associated with using YouTube in teaching English. Conventional methods of teaching English as a foreign language encounter difficulties in improving students’ engagement and