We study in this paper the composition operator that is induced by ?(z) = sz + t. We give a characterization of the adjoint of composiotion operators generated by self-maps of the unit ball of form ?(z) = sz + t for which |s|?1, |t|<1 and |s|+|t|?1. In fact we prove that the adjoint is a product of toeplitz operators and composition operator. Also, we have studied the compactness of C? and give some other partial results.

The numerical investigation has been performed to study the radiation affected steady state laminar mixed convection induced by a hot inner varied positions circular core in a horizontal rectangular channel for a fully developed flow. To examine the effects of thermal radiation on thermo fluid dynamics behavior in the eccentric geometry channel, the generalized body fitted co-ordinate system is introduced while the finite difference method is used for solving the radiative transport equation. The governing equations which used are continuity, momentum and energy equations. These equations are normalized and solved using the Vorticity-Stream function. After validating numerical results for the case without radiation, the detailed radiatio

    The article analyzes the ideological and genre features of L. Ulitskaya's work "The Plague, or OOI in the City", examines the features of building an artistic whole, ways of creating images of characters and their characteristics, stylistic features of the work.

We investigate mathematical models of the Hepatitis B and C viruses in the study, considering vaccination effects into account. By utilising fractional and ordinary differential equations, we prove the existence of equilibrium and the well-posedness of the solution. We prove worldwide stability with respect to the fundamental reproduction number. Our numerical techniques highlight the biological relevance and highlight the effect of fractional derivatives on temporal behaviour. We illustrate the relationships among susceptible, immunised, and infected populations in our epidemiological model. Using comprehensive numerical simulations, we analyse the effects of fractional derivatives and highlight solution behaviours. Subsequent investigatio

  Amidst the changes resulting from the subject matter of expression in art. The necessity of searching for the expressive features of thought that leaves different imprints with aesthetic features and values which called for re-modifying the expressive vision of contemporary drawings. Therefore, this research has been concerned with the study of (abstract expressive features in the drawings of (Serwan Baran) and (Eric Barto) - a comparative study), and the research includes four chapters. The first chapter is devoted to explaining the research problem, its importance, need, purpose, and limits, then determining the most important terms mentioned in it. Where the research problem dealt with the subject of abstract expressive feature

Diabetic retinopathy is one of most important complications of diabetes mellitus that can be treated by Nd:YAG laser. Laser is used in ophthalmic practice for photocoagulation and photodisruption. The purpose of this study is to evaluate changes in immunological ,hematological and biochemical values after treatment of diabetic retinopathy by laser. Blood samples from 10 patients suffering from diabetic retinopathy were taken before and after laser treatment to coagulate retina to prevent leakage and hemorraghe to avoid deterioration of vision.In group one (4 patients = 40%), blood tests were done one day after treatment. In group two (6 patients =60%) tests were done 7 days after treatment with laser. The study showed no clear changes in

        Environmental risk growing Become challenge "and a matter of controversy and concern to many of those concerned with environment, social, economic, and the same happens with the administrative rather than in isolation for this movement, as the issues of climate change Disturbed and troubled him, especially after what caused the risk of destruction, and irresponsibility , chaos, and the futility of resources, crops, fields,  nature and homes and reactors, and after what happened in Japan from the scourge of "Hurricane tsunami " and earthquakes successive accompanied him and what became of him by surprise catastrophic affected the economy and the univ