This paper treats the interactions among four population species. The system includes one mutuality prey, one harvested prey and two predators. The four species interaction can be described as a food chain, where the first prey helps the second harvested prey. The first and the second predator attack the first and the second prey, respectively, according to Lotka-Volterra type functional responses. The model is formulated using differential equations. One equilibrium point of the model is found and analysed to reveal a threshold that will allow the coexistence of all species. All other equilibrium points of the system are located, with their local and global stability being assessed. To back up the conclusions of the mathema

The interplay of predation, competition between species and harvesting is one of the most critical aspects of the environment. This paper involves exploring the dynamics of four species' interactions. The system includes two competitive prey and two predators; the first prey is preyed on by the first predator, with the former representing an additional food source for the latter. While the second prey is not exposed to predation but rather is exposed to the harvest. The existence of possible equilibria is found. Conditions of local and global stability for the equilibria are derived. To corroborate our findings, we constructed time series to illustrate the existence and the stability of equilibria numerically by varying the different values

In this paper, we made comparison among different parametric ,nonparametric and semiparametric estimators for partial linear regression model users parametric represented by ols and nonparametric methods represented by cubic smoothing spline estimator and Nadaraya-Watson estimator, we study three nonparametric regression models and samples sizes  n=40,60,100,variances used σ²=0.5,1,1.5 the results  for the first model show that N.W estimator for partial linear regression model(PLM) is the best followed the cubic smoothing spline estimator for (PLM),and the results of the second and the third model show that the best estimator is C.S.S.followed by N.W estimator for (PLM) ,the

In this paper, the general framework for calculating the stability of equilibria, Hopf bifurcation of a delayed prey-predator system with an SI type of disease in the prey population, is investigated. The impact of the incubation period delay on disease transmission utilizing a nonlinear incidence rate was taken into account. For the purpose of explaining the predation process, a modified Holling type II functional response was used. First, the existence, uniform boundedness, and positivity of the solutions of the considered model system, along with the behavior of equilibria and the existence of Hopf bifurcation, are studied. The critical values of the delay parameter for which stability switches and the nature of the Hopf bifurcat

An ecological model consisting of prey-predator system involving the prey’s fear is proposed and studied. It is assumed that the predator species consumed the prey according to prey square root type of functional response. The existence, uniqueness and boundedness of the solution are examined. All the possible equilibrium points are determined. The stability analysis of these points is investigated along with the persistence of the system. The local bifurcation analysis is carried out. Finally, this paper is ended with a numerical simulation to understand the global dynamics of the system.

The research tried to show the importance of  Administrative Control being one of the important means in administrative work; they work on the review and audit work done and error handling explored in the work and prevent the occurrence and ascertain the extent of implementation of the planned targets, and therefore this is reflected in raising the efficiency of the performance of the tax examiner and complete the work as soon as possible and the highest efficiency and reduce the gaps that may occur between the parties of the tax settling accounts and dealt with in the theoretical side of the search to the research problem, namely with whether operating management oversight to improve the performance and increase the efficiency of t

At the beginning of the nineties increased responsibility of the auditor to the community as the demand for auditing the environmental performance for the economic units in addition to audit the financial performance. With the aim of preserving the environment and reducing the damagse as  aresult of the negative effects of the activities of these units.

The researh deal with two sides the first one identifies the theoretical framework of the concept of environmental audits, requirements, methods, types of procedures, and duties of  the auditor in conducting  environmental audits. It also deals with the concept of the enviro

In The Bluest Eye (1970), the American-African writer, Toni Morrison explores how
Western standards of ideal beauty are created and propagated with and among the black
community. The novel not only portrays the lives of those whose dark skinned and Negroid
features blight their lives; it also shows how the standard of white beauty, when imposed on
black youth, can drastically damage one’s self-love and esteem which usually occurs when
beauty goes unrecognized. Morrison in this novel focuses on the damage that the black
women characters suffer through the construction of femininity in a racialised society where
whiteness is used as a standard of beauty.

Kurdish language multifunctional morphemes indicate the different functional morphological, syntactical, and semantic tasks of the morphemes. The present study discusses the multifunctional task of the Morpheme Le in Kurdish Language. The Morpheme Le has marginally been included in other studies, yet up to the present times, there has not been a research inclusively dedicated to thoroughly discuss and clarify its multifunctional aspects. The present study is divided into two chapters: Chapter one discusses the theoretical aspect of chapter two that is entirely concerned with the practical aspect of the morpheme Le. The first part of chapter one sheds light on the morphological aspect of the morpheme while part two discusses