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 near the vanishing and predator-free equilibrium points. The analytical results are then validated using a numerical approach. It is discovered that the cooperative hunting rate and conversion rate persistently affect the system. In contrast, the anti-predator rate leads to the extinction of the predator.
The goal of this study is to investigate the relationship between the student and the teacher and the student's behavior for a subject of the student in the intermediate stage, the sample contained (568) student, (266) male and (302) female.
The scale of student – teacher relationship was built according to a questionnaire pointed to a sample of the students, adding to that reviewing a number of previous scales and studies which was about the same topic, and in the same way a measure of student behavior was constructed.
Results showed that there was significant relation between the student's teacher relationship and student behavior, and the level of student- teacher relationship is higher than the average of the population that
<p>The objective of this paper is to study the dynamical behavior of an aquatic food web system. A mathematical model that includes nutrients, phytoplankton and zooplankton is proposed and analyzed. It is assumed that, the phytoplankton divided into two compartments namely toxic phytoplankton which produces a toxic substance as a defensive strategy against predation by zooplankton, and a nontoxic phytoplankton. All the feeding processes in this food web are formulating according to the Lotka-Volterra functional response. This model is represented mathematically by the set of nonlinear differential equations. The existence, uniqueness and boundedness of the solution of this model are investigated. The local and global stability
... Show MoreThis present work is concerned with one of the syntactic issues that has been researched by many linguists, grammarians, and specialists in Islamic studies, the estimated answer to a condition. However, this topic is researched this time by examining Imam Al-Qurtbi’s opinions in interpreting related ayas from the holly Quraan in his book (Collector of Quranic Rules) or its transliteration (Al-Jami’ Li Ahkam Al-Quran). Such a step involves commenting on, tracking what Al-Qurtbi said in this regard, discussing it from the points of view of other grammarians, and judging it accordingly, taking into account the apparent surface structures of the examples collected. To achieve this objective, the inductive analytical approach has be
... Show MoreIn this research, titanium dioxide nanoparticles (TiO2 NPs) were prepared through the sol-gel process at an acidic medium (pH3).TiO2 nanoparticles were prepared from titanium trichloride (TiCl3) as a precursor with Ammonium hydroxide (NH4OH) with 1:3 ratio at 50 °C. The resulting gel was dried at 70 °C to obtain the Nanocrystalline powder. The powder from the drying process was treated thermally at temperatures 500 °C and 700 °C. The crystalline structure, surface morphology, and particle size were studied by using X-ray diffraction (XRD), Atomic Force Microscopy (AFM), and Scanning Electron Microscope (SEM). The results showed (anatase) phase of titanium dioxide with the average grain size
... Show MoreIn this paper, a numerical model for fluid-structure interaction (FSI) analysis is developed for investigating the aeroelastic response of a single wind turbine blade. The Blade Element Momentum (BEM) theory was adopted to calculate the aerodynamic forces considering the effects of wind shear and tower shadow. The wind turbine blade was modeled as a rotating cantilever beam discretized using Finite Element Method (FEM) to analyze the deformation and vibration of the blade. The aeroelastic response of the blade was obtained by coupling these aerodynamic and structural models using a coupled BEM-FEM program written in MATLAB. The governing FSI equations of motion are iteratively calculated at each time step, through exchanging data between
... Show MoreA three species food web model involving a stage structure and cannibalism in the top predator species is proposed and studied. It is assumed that the prey species growth logistically in the absence of predator and the predation process occurred according to theLotka-Volterra functional response. The existence, uniqueness and bounded-ness of the solution of the model are investigated. The local and global stability conditions of all possible equilibrium points are established.The persistence conditions of the model are also determined. The local bifurcation near each of the equilibrium points is analyzed. The global dynamics of the model is investigated numerically and compared with the obtained analytical results. It is observed that the p
... Show MoreGiven that the Crimean and Congo hemorrhagic fever is one of the deadly viral diseases that occur seasonally due to the activity of the carrier “tick,” studying and developing a mathematical model simulating this illness are crucial. Due to the delay in the disease’s incubation time in the sick individual, the paper involved the development of a mathematical model modeling the transmission of the disease from the carrier to humans and its spread among them. The major objective is to comprehend the dynamics of illness transmission so that it may be controlled, as well as how time delay affects this. The discussion of every one of the solution’s qualitative attributes is included. According to the established basic reproductio
... Show MoreThis work is concerned with designing two types of controllers, a PID and a Fuzzy PID, to be used
for flying and stabilizing a quadcopter. The designed controllers have been tuned, tested, and
compared using two performance indices which are the Integral Square Error (ISE) and the Integral
Absolute Error (IAE), and also some response characteristics like the rise time, overshoot, settling
time, and the steady state error. To try and test the controllers, a quadcopter mathematical model has
been developed. The model concentrated on the rotational dynamics of the quadcopter, i.e. the roll,
pitch, and yaw variables. The work has been simulated with “MATLAB”. To make testing the
simulated model and the controllers m