It is well known that the spread of cancer or tumor growth increases in polluted environments. In this paper, the dynamic behavior of the cancer model in the polluted environment is studied taking into consideration the delay in clearance of the environment from their contamination. The set of differential equations that simulates this epidemic model is formulated. The existence, uniqueness, and the bound of the solution are discussed. The local and global stability conditions of disease-free and endemic equilibrium points are investigated. The occurrence of the Hopf bifurcation around the endemic equilibrium point is proved. The stability and direction of the periodic dynamics are studied. Finally, the paper is ended with a numerical simul

In this paper, a Cholera epidemic model is proposed and studied analytically as well as numerically. It is assumed that the disease is transmitted by contact with Vibrio cholerae and infected person according to dose-response function. However, the saturated treatment function is used to describe the recovery process. Moreover, the vaccine against the disease is assumed to be utterly ineffective. The existence, uniqueness and boundedness of the solution of the proposed model are discussed. All possible equilibrium points and the basic reproduction number are determined. The local stability and persistence conditions are established. Lyapunov method and the second additive compound matrix are used to study the global stability of the system.

This study has contributed to understanding a delayed prey-predator system involving cannibalism. The system is assumed to use the Holling type II functional response to describe the consuming process and incorporates the predator’s refuge against the cannibalism process. The characteristics of the solution are discussed. All potential equilibrium points have been identified. All equilibrium points’ local stability analyses for all time delay values are investigated. The system exhibits a Hopf bifurcation at the coexistence equilibrium, which is further demonstrated. The center manifold and normal form theorems for functional differential equations are then used to establish the direction of Hopf bifurcation and the stability of the per

Praise be to God, prayer, and peace be upon the Messenger of Allah and his God and his companions. The field of the judiciary to prove or invalidate some cases in the field of proof of descent and attachment to the plaintiff or exile, and other legal and judicial issues, especially in this era where the spread of previously unknown evidence, such as DNA, which was discovered in 1953, and the genetic fingerprint discovered 1984, blood analysis and a Saliva, sweat, poetry, etc. in the field of forensic evidence, in forensic medicine or medical expertise, it can be used to identify the killer, or verify his identity, using all the evidence in the scene, such as a point of blood or sweat, and the like So, as well as to prove the lineage is u

The research emphasizes importance of preliminary drawings in design of any product. Therefore, using of simulation as tools for visual thinking in developing drawing and design skills. So that practice of drawing by hand, considering shape of ideas in first stage of visualizations, and practice of its techniques and continuous training.
Hence, the research problem arose with the role of simulation method for developing preliminary sketches in the sample of students of the Product Design Department at the College of Design and Art, PNU, as it is important tool for visual thinking that helps the designer in designing and producing innovative artistic works.
Therefore, the research axes, a number of findings and recommendations were

In this study, the quality assurance of the linear accelerator available at the Baghdad Center for Radiation Therapy and Nuclear Medicine was verified using Star Track and Perspex. The study was established from August to December 2018. This study showed that there was an acceptable variation in the dose output of the linear accelerator. This variation was ±2% and it was within the permissible range according to the recommendations of the manufacturer of the accelerator (Elkta).

This paper is dealing with an experimental study to show the influence of the geometric characteristics of the vortex generators VG son the thickness of the boundary layer (∂) and drag coefficients (C_D) of the flat plate. Vortex generators work effectively on medium and high angles of attack, since they are "hidden" under the boundary layer and practically ineffective at low angles.

            The height of VGs relative to the thickness of the boundary layer enables us to study the efficacy of VGs in delaying boundary layer separation. The distance between two VGs also has an effect on the boundary layer if we take into

Social risks posed a great challenge to the development path in Iraq, which resulted in widening the development gaps, whether these gaps were between rural and embargoed areas, or between Iraqi governorates, and the gender gap. Besides, the nature of the reciprocal relationship between the social risks and the development process requires the adoption of development trends that are sensitive to the risks that take upon themselves the prompt and correct response to these risks, away from randomness and confusion that Iraq suffered from for decades. However, currently, the situation has differed a great deal. This is because the size and types of such gaps have widened and become more complicated than before; a matter which has led to hav