The interplay of predation, competition between species and harvesting is one of the most critical aspects of the environment. This paper involves exploring the dynamics of four species' interactions. The system includes two competitive prey and two predators; the first prey is preyed on by the first predator, with the former representing an additional food source for the latter. While the second prey is not exposed to predation but rather is exposed to the harvest. The existence of possible equilibria is found. Conditions of local and global stability for the equilibria are derived. To corroborate our findings, we constructed time series to illustrate the existence and the stability of equilibria numerically by varying the different values

In this paper, the process for finding an approximate solution of nonlinear three-dimensional (3D) Volterra type integral operator equation (N3D-VIOE) in R³ is introduced. The modelling of the majorant function (MF) with the modified Newton method (MNM) is employed to convert N3D-VIOE to the linear 3D Volterra type integral operator equation (L3D-VIOE). The method of trapezoidal rule (TR) and collocation points are utilized to determine the approximate solution of L3D-VIOE by dealing with the linear form of the algebraic system. The existence of the approximate solution and its uniqueness are proved, and illustrative examples are provided to show the accuracy and efficiency of the model.

Mathematical Subject Classificat

    Building a geological model is an essential and primary step for studying the reservoir’s hydrocarbon content and future performance. A three-dimensional geological model of the Asmari reservoir in Abu- Ghirab oil field including structure, stratigraphy, and reservoir petrophysical properties, has been constructed in the present work. As to underlying Formations, striking slip faults developed at the flank and interlayer normal. Abu Ghirab oilfields are located on the eastern anticlinal band, which has steadily plunged southward. 3D seismic interpretation results are utilized to build the fault model for 43 faults of the Asmari Formation in Abu Ghirab Oilfield. A geographic facies model with six different rock facies types

This work was conducted to study the extraction of eucalyptus oil from natural plants (Eucalyptus camadulensis leaves) by organic solvents. the effects of the main operating parameters were studied; type of solvent (n-hexane and ethanol), time to reach equilibrium, the temperature (45°C to 65°C) for n-hexane and (45°C to 75°C) for ethanol, solvent to solid ratio (5:1 to 8:1 (v/w)), agitation speed (0 to 900 rpm) and the particle size (0.5 to 2.5 cm) of fresh leaves to find the best processing conditions for the achieving maximum oil yield. The concentration of eucalyptus oil in solvent was measured by using UV-spectrophotometer. The results (for n-hexane) showed that the agitation speed of 900 rpm, temperature 65°C with solvent to soli

Diarrhea is one of the most commonly encountered minor ailments in the community pharmacies. It is associated with significant morbidity and mortality. However, the majority of pharmacists in Iraq did not manage diarrheal cases in a proper way. Therefore, the current study aimed to evaluate the benefit of a new mobile application (diarrhea management step by step) to improve the pharmacist's role in the management of diarrhea. The study was conducted from 21th September to 21th October 2021 using a pre-post design via a simulated patient (SP) technique. A validated diarrhea scenario was presented to each pharmacist by the SP twice, once before and the other after giving the mobile application to the pharmacist. Furthermore, pharmaci

      The objective of this research is employ the special cases of  function  trapezoid in the composition of fuzzy sets to make decision within the framework of the theory of games traditional to determine the best strategy for the mobile phone networks in the province of  Baghdad and Basra, has been the adoption of different periods of the  functions belonging to see the change happening in the matrix matches and the impact  that the strategies  and decision-making  available to each player and the impact on  societ

Hydrocarbon production might cause changes in dynamic reservoir properties. Thus the consideration of the mechanical stability of a formation under different conditions of drilling or production is a very important issue, and basic mechanical properties of the formation should be determined.
There is considerable evidence, gathered from laboratory measurements in the field of Rock Mechanics, showing a good correlation between intrinsic rock strength and the dynamic elastic constant determined from sonic-velocity and density measurements.
The values of the mechanical properties determined from log data, such as the dynamic elastic constants derived from the measurement of the elastic wave velocities in the material, should be more a

n this research, several estimators concerning the estimation are introduced. These estimators are closely related to the hazard function by using one of the nonparametric methods namely the kernel function for censored data type with varying bandwidth and kernel boundary. Two types of bandwidth are used: local bandwidth and global bandwidth. Moreover, four types of boundary kernel are used namely: Rectangle, Epanechnikov, Biquadratic and Triquadratic and the proposed function was employed with all kernel functions. Two different simulation techniques are also used for two experiments to compare these estimators. In most of the cases, the results have proved that the local bandwidth is the best for all the types of the kernel boundary func