We study in this paper the composition operator of induced by the function ?(z)=sz+t where , and We characterize the normal composition operator C? on Hardy space H2 and other related classes of operators. In addition to that we study the essential normality of C? and give some other partial results which are new to the best of our knowledge.

In this research a study process to calculate the factor accumulation of gamma rays for aluminum and exporters cobalt 60 Mika Atktron volts and actively radiation Vdrh 1.406 Mika Bq been studying the effect of the angle of reimbursement and the distance between the shield and detector In measurements factor accumulation Adhrt results in line with the theoretical results published

The concept of epiform modules is a dual of the notion of monoform modules. In this work we give some properties of this class of modules. Also, we give conditions under which every hollow (copolyform) module is epiform.

The main purpose of this paper is to study some results concerning reduced ring with another concepts as semiprime ring ,prime ring,essential ideal ,derivations and homomorphism ,we give some results a bout that.

ABSTRACT: BACKGROUND: Infantile haemangioma one of the most common tumour of new borns , a safe and effective treatment options are under ongoing research . OBJECTIVE: The authors show the effectiveness and safety of low dose propranolol as a method for infantile haemangioma treatment . METHOD: In this study twenty- four patients with infantile haemangioma in different anatomical locations were treated with oral propranolol and the result were assessed in a retrospective analysis of the results patients were kept on 0.25 mg/kg/day for one month , then on 0.5mg/kg/day in 2 divided doses for another one month , in the third month the dose will be increased to 1 mg/kg/day in 2 divided doses , then the propranolol were given in a maintenance do

After Zadeh introduced the concept of z-number scientists in various fields have shown keen interest in applying this concept in various applications. In applications of z-numbers, to compare two z-numbers, a ranking procedure is essential.  While a few ranking functions have been already proposed in the literature there is a need to evolve some more good ranking functions.  In this paper, a novel ranking function for z-numbers is proposed- "the Momentum Ranking Function"(MRF). Also, game theoretic problems where the payoff matrix elements are z-numbers are considered and the application of the momentum ranking function in such problems is demonstrated.

In the present work, a z-scan technique was used to study the nonlinear optical properties, represented by the nonlinear refractive index and nonlinear absorption coefficients of nanoparticles cadmium sulfide thin film. The sample was prepared by the chemical bath deposition method. Several testing were done including, x-ray, transmission and thickness of thin film. z-Scan experiment was performed at two wavelengths (1064 nm and 532 nm) and different energies. The results showed the effect of self-focusing in the material at higher intensities, which evaluated n2 to be (0.11-0.16) cm2/GW. The effect of two-photon absorption was studied, which evaluated β to be (24-106) cm/GW. In addition, the optical limiting behavior has been studied.

The investigation of determining solutions for the Diophantine equation  over the Gaussian integer ring for the specific case of  is discussed. The discussion includes various preliminary results later used to build the resolvent theory of the Diophantine equation studied. Our findings show the existence of infinitely many solutions. Since the analytical method used here is based on simple algebraic properties, it can be easily generalized to study the behavior and the conditions for the existence of solutions to other Diophantine equations, allowing a deeper understanding, even when no general solution is known.