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.

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.

Abstract:

        Organizations need today to move towards strategic innovation, which means the analysis of positions, especially the challenges faced by the change in the external environment, which makes it imperative for the organization that you reconsider their strategies and orientations and operations, a so-called re-engineering to meet those challenges and pressures. Now this research dilemma intellectual two-dimensional, yet my account in not Take writings and researchers effect strategic innovation in re-engineering business processes, according to science and to inform the researcher, and after the application represented in the non-application of such resear

Criticism is inherently impolite and a face-threatening act generally leading to conflicts among interlocutors. It is equally challenging for both native and non-native speakers, and needs pre-planning before performing it. The current research examines the production of non-institutional criticism by Iraqi EFL university learners and American native speakers. More specifically, it explores to what extent Iraqi EFL learners and American native speakers vary in (i) performing criticism, (ii) mitigating criticism, and (iii) their pragmatic choices according to the contextual variables of power and distance. To collect data, a discourse-completion task was used to elicit written data from 20 Iraqi EFL learners and 20 American native speaker

The present paper applies Fanon Psychological reading of the problem of the Black introduced in his book Black Skin White Mask to Crooks, The black Character in John Steinbeck’s  Of Mice and Men. The analysis of this character infers three essential points regarding the artistic achievement of the author. First, he uses a fictional character that offers a psychological interpretation of the black problem of alienation and loneliness in a way that does not disgrace the black. Second, he applies Fanon’s way of showing the various attitudes that the black adopts in contact with the white society. Third, he affirms that the black inferiority complex comes as a result of double proc

Back ground: During acrylic resin processing, the mold must be separated from the surface of the gypsum to prevent liquid resin from penetrating into the gypsum, and water from the gypsum seeping into the acrylic resin. For many years, tin foil was the most acceptable separating medium, and because it's difficult to apply, a tin-foil substitute is used. In this study, olive oil is used as an alternative to tin foil separating medium for first time, so the aim of the study was to evaluate its effect as a separating medium on some physical properties such as (surface roughness, water sorption and solubility) of acrylic resins denture base comparing it with those processed using tin-foil and tin foil substitute such as (cold mold seal) separat