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

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.

Numerous academic and critical studies concerned with the language of poetry, with the differences and diversity in these studies and the critical methods. , the study tries to study this modern approach in the language Iraqi and Arabic poetry according to analyzing and following the functional dimension of the language, regardless of its poetic value which should be on them, as each poetic experience has its own language, thestudy came to investigate the variety of poetry samples, poets from different and far generations. - in an attempt to give an image Career dimension of language, the center of intellectual transformations that have affected the experience of Arabic poetry generally, and the level of language to be exact, as a tool f

The polygamy as a social was known before Islam, has kept Islam on this system after it organized and put his controls and conditions, as justice between wives and the ability to alimony, it was not the purpose of satisfying the instinct of man and enjoyment, but his goal nominal than that, because it addresses problems humanity has goals noble, so the pluralism overlap of the fabric of families belonging to governance and benefits for women and men and society, which leads to increased ties of love between people of the same society and thus increases the cohesion and importance of the topic and its association with financial conditions have emerged as needed so you viewed in the second scientific Conference of the Department social Ser