In this paper, the dynamics of scavenger species predation of both susceptible and infected prey at different rates with prey refuge is mathematically proposed and studied. It is supposed that the disease was spread by direct contact between susceptible prey with infected prey described by Holling type-II infection function. The existence, uniqueness, and boundedness of the solution are investigated. The stability constraints of all equilibrium points are determined. In addition to establishing some sufficient conditions for global stability of them by using suitable Lyapunov functions. Finally, these theoretical results are shown and verified with numerical simulations.

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 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

In this study, active knife and fixed knife of single-row disc silage machine has three different clearance C1, C2 and C3 (1, 3 and 5 mm) and it is tried in three different working speed V1, V2 and V3 (1.8, 2.5 and 3.7 km / h) and PTO speed (540 min-1) and machine's fuel consumption (l/h), average power consumption (kW), field energy consumption (kW/da), product energy consumption (kW/t), field working capacity (da/h), product working capacity (t/h) and Chopping size distribution characteristics of the fragmented material were determined. It has been found that knife-counter knife clearances smaller than 3 mm (1 mm) and larger (5 mm) have a negative effect on machine performance in general. In terms of fuel and power consumptions, the m

This study presents the effect of laser energy on burning loss of magnesium from the holes' drilled in aluminum alloy 5052. High energy free running pulsed Nd:Glass laser of 300 µs pulse duration has been used to perform the experiments. The laser energy was varied from 1.0 to 8.0 Joules, The drilling processes have been carried out under atmospheric pressure and vacuum inside a specially designed chamber. Microhardness of the blind drilled holes has been investigated .The results indicated that the magnesium loss could be manipulated by adjusting the focusing conditions of the laser beam. Almost, the obtained holes were free of cracks with low taper and low sputter deposition. .The holes performed under atmospheric conditions have high

The present study aims at finding out the (effect of the Caroll’s pattern on the second intermediate class pupils' achievement in geography)

The partial experimental design of two groups, experimental and control, with pre-post tests is used. The sample is represented in (74) female pupils. The sample is divided into two groups (38) experimental group and (36) control one. The sample is selected from first intermediate  class pupils    ( Am Salama Secondary School for girls) \ Baghdad\ Al-karkh-1, for academic year 2015-2016.

The researcher has equalized the two groups in several variables: the previous achievement tests, intelligence, age in months, the scor

Background and aim: Pomegranate is a medicinal herb that can promote healing of periodontal tissue through differentiation of mesenchymal cells both in vivo and in vitro. Therefore, this study is to investigate the effect of oral supplementation of Punicagranatum L. peel extract on bone defect in rabbit. Methods: Forty five male rabbits were divided into 3 groups; group 1; baseline group(5 rabbits) left without bone defect. Group 2; study group (20 rabbits) with bone defect model that received daily 1ml of oral supplementation of pomegranate peel extract (PoPx). Group 3; control group (20 rabbits) with bone defect model that received distilled water. Bone defect was done into facial plate of lower right central incisor. Blood biopsies by