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.

The imposition of (state) policy on the South Kuril Islands.In the Pacific was a subject
of borders dispute between Japan and Soviet Union which appeared clearly afterthe second
Great War and during the cold war. Despite the end of the Cold War and the collapse of the
Soviet Union in 1991, this conflict has continued, thus both countries had to made a historic
and legitimate claims to demand the rights of sovereignty and ownership of four islands
occupied by the Soviet Union after World War II under the international conventions and
treaties, but these claims are proven failures through the continuation of the regional conflict.

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 discus throwing event is one of the complex events in athletics, and it is characterized by a performance method that depends on the principle of mechanical moments and requires high explosive capabilities of the thrower in addition to some physical specifications,which depends effectively and effectively on the biomechanical aspects in generating large moments during rotation. The importance of the research is highlighted by the interest in athletics, especially the effectiveness of the discus throw and the continuation of its development process, the importance of kinetic analysis in revealing the most important weaknesses and strengths of shooters, and the importance of explosive power And the moments generated in the rotation of the

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.

It highlights the importance of construction projects because of its significant role in the development of society, including the buildings FEDE projects to their importance to raise the level of education through the conclusion of the special to implementation and the establishment of schools of contracts at the country level, which requires the completion of the project at less time and within the cost specified and the best quality and may highlight the importance of time on all the elements of what has an important role in setting up the project for various reasons may be the need for the use of schools as soon as possible, but the reality showed exceeded the completion of those schools could be up to 6 years and there are some cont

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

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