Throughout this paper we study the properties of the composition operator
C
p1  o
p2  o…o
pn  induced by the composition of finite numbers of special
automorphisms of U,
pi  (z)  i
i
p z
1 p z


Such that pi  U, i  1, 2, …, n, and discuss the relation between the product of
finite numbers of automorphic composition operators on Hardy space H2 and some
classes of operators.

The research aims to know the impact of the innovative matrix strategy and the problem tree strategy in teaching mathematics to intermediate grade female students on mathematical proficiency. To achieve the research objectives, an experimental approach and a quasi-experimental design were used for two equivalent experimental groups. The first is studied according to the innovative matrix strategy, the second group is studied according to the problem tree strategy. The research sample consisted of (32) female students of the first intermediate grade, who were intentionally chosen after ensuring their equivalence, taking into several factors, most notably (chronological age, previous achievement, and intelligence test). The research tools con

The research addresses a fundamental Islamic jurisprudential Purposeful issue, which is (Sharia), and to indicate the impact of this on Islamic jurisprudence, deriving rulings and extracting purposes, and to repel the illusion that this issue is only doctrinal, and clarifying the aspects of similarities and links between them by explaining the origin of deriving the purposes of Islamic Law (Sharia) through the meanings and wisdom learned from the texts and the explanation of the rulings. The rulings of Islamic Law (Sharia) have urged bringing benefits and repelling harms, and that the path to do so is reason and its production. I began the research by defining the purposes of Islamic Law (Sharia), then defining the rule of rational right

The semiconductor ZnO is one of II – VI compound group, it is prepare as thin films by using chemical spray pyrolysis technique; the films are deposited onto glass substrate at 450 °C by using aqueous zinc chloride as a spray solution of molar concentration 0.1 M/L. Sample of the prepared film is irradiating by Gamma ray using CS 137, other sample is annealed at 550°C. The structure of the irradiated and annealed films are analyzed with X-ray diffraction, the results show that the films are polycrystalline in nature with preferred (002) orientation. The general morphology of ZnO films are imaged by using the Atomic Force Microscope (AFM), it constructed from nanostructure with dimensions in order of 77 nm.
The optical properties o

The research included the introduction to the research and its importance as knee joint is an important joint in the human body that is prone to injury. One such injury is knee roughness injury that occurs as a result of the stress of the knee joint and age. The importance of examining the need for the use of rehabilitation exercises, especially in the watercourse system, is highlighted by the fact that the aquatic environment is one of the most important factors helping to alleviate pain and rehabilitate the knee joint and thereby improve the mobility of those with knee roughness. The problem of research is that rehabilitation exercises have been developed in the watercourse system on the basis of scientific bases with a repetitive and sys

Background: Normal occlusal features of primary dentition are crucial for normal development of the permanent dentition. Breastfeeding is an important factor for both general and dental health of children. Aim: The aim of the present study is to assess the impact of the breastfeeding duration on the prevalence of normal occlusal features of the primary dentition among preschool children in Baghdad. Materials and Methods: The sample was 630 Iraqi children (270- boys, 360 girls), aged 3-5 years selected from four kindergartens in Baghdad city. The study was carried out through questionnaire and clinical examination. Normal occlusal features were examined as the presence or absence of interincisive spaces (IS) and primate spaces (PS), termi

The Films of CdTe:Zn were prepared on a glass by using vacuum vapor deposition technique .The x-ray diffraction pattern revealed that the films have polycrystalline with FCC structure and the preferred orientation was along (111) plane.  The films were exposed to a low dose of gamma ray.(5µCi for 30 days) Transmission and absorptance spectra were recorded in the range of (400-1100) nm before and after irradiation. It was found that irradiation has a clear effect on the optical and structural properties which include the transmition and absorption spectra, extinction coefficient, refractive index, and the energy gap.

 Additive aluminum powder to the polystyrene to prepare the composites Polystyrene– Aluminum.The samples were prepared by using mechanical  compressed method at low pressure and a temperature 120°C.         Measurements  of absorbance and reflectance spectra were carried out by UV-Visible  spectrophotometer , the effect of additive aluminum  on the optical band  gap Eop and  optical constants ( refractive index n, extinction coefficient k ,dielectric constant ε and optical conductivity σop)  were studied for the prepared composites .         Results showed a decrease in the Eop with increasing  perc