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

In this paper, a mathematical model is proposed and studied to describe the spread of shigellosis disease in the population community. We consider it divided into four classes namely: the 1^st class consists of  unaware susceptible individuals, 2^nd class of infected individuals, 3^rd class of aware susceptible individuals and 4^th class are people carrying bacteria. The solution existence, uniqueness as well as bounded-ness are discussed for the shigellosis model proposed. Also, the stability analysis has been conducted for all possible equilibrium points. Finally the proposed model is studied numerically to prove the analytic results and discussing the effects of the external sources for dis

The internet, unlike other traditional means of communication, has a flexibility to stimulate the user and allows him to develop it. Perhaps, the reason for the superiority of the internet over other traditional means of communication is the possibility of change and transmission from one stage to another in a short period. This means that the internet is able to move from the use to the development of the use and then the development of means and innovation as the innovation of the internet is a logical product of the interaction of the user with the network. The internet invests all the proposals and ideas and does not ignore any even if it is simple. This is represented in social networking sites which in fact reflects personal emotio

This work represents development and implementation a programmable model for evaluating pumping technique and spectroscopic properties of solid state laser, as well as designing and constructing a suitable software program to simulate this techniques . A study of a new approach for Diode Pumped Solid State Laser systems (DPSSL), to build the optimum path technology and to manufacture a new solid state laser gain medium. From this model the threshold input power, output power optimum transmission, slop efficiency and available power were predicted. different systems configuration of diode pumped solid state laser for side pumping, end pump method using different shape type (rod,slab,disk) three main parameters are (energy transfer efficie

This research aimed at recognizing the properties of curricula that fitted to preeminent and talent students. Many types of these curricula were exposed, enrichment curriculum was explained as one of alternatives of available curricula.
The research used the analytical methodology for local and international literature in the field of preeminent and talent education to meet the properties of curricula that fitted to this special group of students. Many results was obtained as:
• This type of school enrichment curriculum consists of three levels( general discovery activities, individual and groups training activities, and individual or groups real problems).
• Investigation the effectively both sides of brain: right and left,