In this paper,  a Sokol-Howell prey-predator model involving strong Allee effect is proposed and analyzed. The existence, uniqueness, and boundedness are studied. All the five possible equilibria have been are obtained and their local stability conditions are established. Using Sotomayor's theorem, the conditions of local saddle-node and transcritical and pitchfork bifurcation are derived and drawn. Numerical simulations are performed to clarify the analytical results

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

The Qur'an is an inexhaustible source for researchers, and all of them find a rich material for its research, and no wonder in it is the book of the greatest Arabic. Quranic research has been an attempt to extract the secret in the miracle of the Koran, and not the Quranic miracle is limited to the word and its meaning, but that the miracle extends to include every sound in motion or silent; the sound performance of the Quranic text increases the meaning of beauty and earns the word heartbeat, Souls; and this may be due to the beauty of voice in the performance and harmony between sounds and words, and harmony between the exits and descriptions, or the tides of the tides,
Based on the above and to show the miraculous aspects of the Qu

Background: Debonding orthodontic brackets and removal of residual bonding material from the enamel surface include critical steps that may cause enamel damage. The aim of the present study was to evaluate and compare the site of bond failure and enamel surface damage after debonding of three types of esthetic brackets (composite, ceramic, sapphire) bonded with light cure composite and resin-modified glass ionomer adhesive. Materials and methods: Seventy two maxillary premolars teeth were divided into three groups each group consisted of 24 teeth according to the type of brackets. Each group was subdivided into two subgroups (12 teeth for each) according to the bonding material that was used. After 7 days of bonding procedure, the brackets

Background: The presence of anatomic variations within the maxillary sinus such as septa has been reported to increase the risk of sinus membrane perforation during sinus elevation procedure for implant placement. This study aimed to measure the septal heights and correlate it with different types of septa. Material and methods: Thirty patients (15 males and 15 females) with partially edentulous maxillae and mean age (35) years were enrolled in this study. Sixty sinuses scanned with Spiral multislice Computed Tompgraphy, septal height measured after evaluation of septal type whether it was primary or secondary. Results: The results showed that 72.5 % of the septa detected were primary and this is statistically significant when compared w

The study showed significant differences between the average weight lens and the average amount protein in the lens between that Kestrel Falco tinnunculus L. and the Collared Dove Streptopelia decaocto F. , also the study electrical migration of lens proteins having one bundle of crystalline –? in Kestrel compared with three bundles in Collared Dove, two bundles of crystalline – ? in both , and crystalline – ? appeared as one bundle in both birds.

Abstract\

In this research we built a mathematical model of the transportation problem  for data of General Company for Grain Under the environment of variable demand ,and situations of incapableness to determining the supply required quantities as a result of economic and commercial reasons, also restrict flow of grain amounts was specified to a known level by the decision makers to ensure that the stock of reserves for emergency situations that face the company from decrease, or non-arrival of the amount of grain to silos , also it took the capabilities of the tanker into consideration and the grain have been restricted to avoid shortages and lack of processing capability, Function has been adopted