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.

This field experiment, was conducted to investigate a comparison of two methods for harvesting potatoes: mechanical and handy when using moldboard and chisel plow for primary tillage and three different distances for planting tubers in the rows 15, 25, and 35 cm in silt clay loam soil south of Baghdad. The factorial experiment followed a randomized complete block design with three replications using L.S.D. 5 % and 1 %. Mechanical harvest recorded the best valid potato tubers at 88.78 %, marketable yield of 31.74 ton. ha-1, efficiency lifted 95.68 %, tubers damage index 28.41, speeding up the harvesting process and reducing time and effort. Handy harvest gave the least damage to potato tubers, 6.02 %, and unlifted potato tubers, 4.32 %. Howe

This study evaluated the knowledge and practice of breast self-examination (BSE), among a sample of educated Iraqi women. The study sample comprised 858 women aged 18–62 years affiliated to 6 major Iraqi universities, categorized according to occupation as teaching staff (11.5%), administrative staff (18.0%) and students (70.5%). Data were collected by a self-completed questionnaire. In all, 93.9% of the women had heard about BSE, the main source of information was television (39.9%), doctors (18.4%) and the awareness campaign of the Iraqi National Breast Cancer Research Programme (11.6%). Only 53.9% of the women practised BSE; the most common excuses by those that did not were lack of knowledge of the significance of BSE (42.0%) and lack

There are many techniques that can be used to estimate the spray quality traits such as the spray coverage, droplet density, droplet count, and droplet diameter. One of the most common techniques is to use water sensitive papers (WSP) as a spray collector on field conditions and analyzing them using several software. However, possible merger of some droplets could occur after they deposit on WSP, and this could affect the accuracy of the results. In this research, image processing technique was used for better estimation of the spray traits, and to overcome the problem of droplet merger. The droplets were classified as non-merged and merged droplets based on their roundness, then the merged droplets were separated based on the average non-m

Gymnastics is one of the most interesting games in terms of organizing various world championships and tournaments. Their basic skills and their technical development, especially those with high difficulty levels that rely on basic and complex skills, are the basic skills of gymnastics are the main pillar to be developed and therefore high-difficulty skills will not depend on basic skills, which should reach the stage of the automatic mechanism. Retention) in order to move on to training and developing another skill for the difficulty of movements as well as the smooth flow of performance, ie the degrees of difficulty of each skill specific to your gym and The researcher used the experimental method and The research community determin

The topic of supra.topological.spaces considered one of the important topics because it is a generalization to topological.spaces. Many researchers have presented generalizations to supra open sets such as supra semi.open and supra pre.open sets and others. In this paper, the concept of δ∼open sets was employed and introduced in to the concept of supra topology and a new type of open set was extracted, which was named S∼δ∼open. Our research entails the utilization of this category of sets to form a new concepts in these spaces, namely S∼δ∼limit points and S∼δ∼derive points, and examining its relationship with S∼open and S∼reg∼open. Based on this class of sets, we have introduced other new concepts such as S∼isolate

Singapore has invested its human resources for the development of the country since earlier times, so it has directed attention to the education sector. Education and development complement each other, as investment in education has contributed over several years to the development of Singapore economy and has made it one of the strongest economies in Asia and the world. Despite the obstacles that faced educational policies in Singapore, the presence of a wise leadership capable of overcoming difficulties and solving them, and providing the appropriate atmosphere for the development of education has contributed significantly to making it one of the most advanced educational systems in the world, and making this system the main pillar for