This paper deals with the mathematical method for extracting the Exponential Rayleighh  distribution based on mixed between the cumulative distribution function of Exponential distribution and  the cumulative distribution function of Rayleigh distribution using an application (maximum), as well as derived different statistical properties for  distribution, and present a structure of a new distribution based on a modified weighted version of Azzalini’s (1985) named Modified Weighted Exponential Rayleigh  distribution such that this new distribution is generalization of the  distribution and provide some special models of the  distribution, as well as derived different statistical properties for  distribution

In this paper, the species of the genus of Chlaenius Bonelli, 1810 (Coleoptera, Carabidae) were reviewed, and it was revealed that there are 21 confirmed species in Iraq; among them, the species of Chlaenius hamifer Chaudoir, 1856 was recorded for the first time in Iraq.
Diagnostic characters, a redescription of some of the morphological features, photographs and illustrations are provided for the new record species in this investigation.

The mathematical construction of an ecological model with a prey-predator relationship was done. It presumed that the prey consisted of a stage structure of juveniles and adults. While the adult prey species had the power to fight off the predator, the predator, and juvenile prey worked together to hunt them. Additionally, the effect of the harvest was considered on the prey. All the solution’s properties were discussed. All potential equilibrium points' local stability was tested. The prerequisites for persistence were established. Global stability was investigated using Lyapunov methods. It was found that the system underwent a saddle-node bifurcation near the coexistence equilibrium point while exhibiting a transcritical bifurcation

Background:The most common pattern of dyslipidemia in diabetic patients is increased triglyceride (TG) and decreased HDL cholesterol level, The concentration of LDL cholesterol in diabetic patients is usually not significantly different from non diabetic individuals, Diabetic patients may have elevated levels of non-HDL cholesterol [ LDL+VLDL]. However type 2 diabetic patients typically have apreponderance of smaller ,denser LDL particles which possibly increases atherogenicity even if the absolute concentration of LDL cholesterol is not significantly increased. The Third Adult Treatment Panel of the National Cholesterol Education Program (NCEP III) and the American Heart Association (AHA ) have designate diabetes as a coronary heart dis