In this paper, we study the incorporation of the commensalism interaction and harvesting on the Lotka–Volterra food chain model. The system provides one commensal prey, one harvested prey, and two predators. A set of preliminary results in local bifurcation analysis around each equilibrium point for the proposed model is discussed, such as saddle-node, transcritical and pitchfork. Some numerical analysis to confirm the accruing of local bifurcation is illustrated. To back up the conclusions of the mathematical study, a numerical simulation of the model is carried out with the help of the MATLAB program. It can be concluded that the system's coexistence can be achieved as long as the harvesting rate on the second prey population is

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

Because of the experience of the mixture problem of high correlation and the existence of linear MultiCollinearity between the explanatory variables, because of the constraint of the unit and the interactions between them in the model, which increases the existence of links between the explanatory variables and this is illustrated by the variance inflation vector (VIF), L-Pseudo component to reduce the bond between the components of the mixture.

    To estimate the parameters of the mixture model, we used in our research the use of methods that increase bias and reduce variance, such as the Ridge Regression Method and the Least Absolute Shrinkage and Selection Operator (LASSO) method a

Derivational word formation process is one of the most substantial linguistic procedures that solves many problems in the translation of the language new vocabulary and helps to comprehend the smallest language component that not simply semantically and structurally explain the elements  of both Russian and Arabic but also enables translators to comprehend the derivational method procedures of both languages. It also reveals the structural aspects of translation equivalences, cognitive and semantic foundations of translation. The rapid development of languages and the appearance of a new vocabulary like ṭabaʿa "print → ṭābiʿat "printer", kataba "to write" → kātib → kātibat, rafaʿa "to raise" → rāfiʿat "a crane" d

The current research aims to find out ( the effectiveness of the structural model of learning in the acquisition of geographical concepts at the first grade average students ) , and achieving the goals of research has been formulating the null hypothesis of the following :

    " There is no difference statistically significant when Mistoi (0.5 ) between the mean scores of the collection of students in the experimental group that is studying the general geographical principles " Bonmozj constructivist learning " and the mean scores of the control group , which is considering the same article ," the traditional way " to acquire concepts.

The researcher adopted th

An environmentally friendly technique was used to prepare titanium dioxide@ silver (core shell) (TiO₂@Ag NPs) using chard leaf extract, a natural stabilizer and reductant. A nanocomposite (NCs) of TiO₂@Ag supported by halloysite nanotubes (HNTs), TiO2@Ag/HNT NCs, was prepared under microwave irradiation. The microwave technique is used to accelerate the reaction and enhance the homogeneity of nanoparticle distribution. Spectroscopic and structural analyses were performed on the resulting nanocomposite. X-ray diffraction (XRD) revealed a clear crystalline structure with grain sizes ranging from 7 to 15 nm, with an average of ~11 nm, the transmission electron microscope (TEM) revealed that the size of nanoparticles in the TiO₂@Ag/HNT N

The aim of the research is to identify the cognitive method (rigidity flexibility) of third-stage students in the collage of Physical Education and Sports Sciences at The University of Baghdad, as well as to recognize the impact of using the McCarthy model in learning some of skills in gymnastics, as well as to identify the best groups in learning skills, the experimental curriculum was used to design equal groups with pre test and post test and the research community was identified by third-stage students in academic year (2020-2021), the subject was randomly selected two divisions after which the measure of cognitive method was distributed to the sample, so the subject (32) students were distributed in four groups, and which the pre te

Abstract---The aim of the current research is to identify the level of logical reasoning skills in chemistry students at the Faculty of Education for Pure Sciences/ Ibn Al-Haytham for the academic year (2021-2022). The differences in their level of skills according to the gender variable (males and females) and the academic stages (first- second - third - fourth). The descriptive approach was adopted because it corresponds to the nature of the research objectives. The research sample consisted of (400 )students selected in a relatively random stratified way. The researcher constructed a logical reasoning test, which includes (6) sub-skills , which is (proportional - probabilistic- synthetic- deductive- logic- variable adjustment). The psych