Fear, harvesting, hunting cooperation, and antipredator behavior are all important subjects in ecology. As a result, a modified Leslie-Gower prey-predator model containing these biological aspects is mathematically constructed, when the predation processes are described using the Beddington-DeAngelis type of functional response. The solution's positivity and boundedness are studied. The qualitative characteristics of the model are explored, including stability, persistence, and bifurcation analysis. To verify the gained theoretical findings and comprehend the consequences of modifying the system's parameters on their dynamical behavior, a detailed numerical investigation is carried out using MATLAB and Mathematica. It is discovered that the

   In this paper, we find the two solutions of two dimensional stochastic Fredholm integral equations contain two gamma processes differ by the parameters in two cases and equal in the third are solved by the Adomain decomposition method. As a result of the solutions probability density functions and their variances at the time t are derived by depending upon the maximum variances of each probability density function with respect to the three cases. The auto covariance and the power spectral density functions are also derived. To indicate which of the three cases is the best, the auto correlation coefficients are calculated.

Asphaltene is a component class that may precipitate from petroleum as a highly viscous and sticky material that is likely to cause deposition problems in a reservoir, in production well, transportation, and in process plants. It is more important to locate the asphaltene precipitation conditions (precipitation pressure and temperature) before the occurring problem of asphaltene deposition to prevent it and eliminate the burden of high treatment costs of this problem if it happens. There are different models which are used in this flow assurance problem (asphaltene precipitation and deposition problem) and these models depend on experimental testing of asphaltene properties. In this study, the used model was equation of

    The experiment was conducted in twodifferentsplaces, one of this experiment in the field was not under salt stress  and the other experiment field was under salt stress.Those experiments were conducted in college of AgricultureDiyalaUniversity  atautmyseason  (2015  - 2016)to study  the salt stress by usingseeds soaking with Hydrogen Peroxide and foliar application in different concentrations ofAbscisic acid.The experiment  statistical design as RCBD was with three replicates.Soaking the seeds withHydrogen  Peroxidetreatments  0 , 10 , 15 ,  20  mmol.L-1.  Three Abscisic acid levels0 , 15 , 30 mg.L1.α -Tocopherol, Catalase Enzyme, Membrane Stability Index,prolin

In this work, new di-acid monomers 4, 4’-di-carboxillic-4”-bromo-2”, 6”-dimethyl triphenylamine (Ma), 4, 4’- di-carboxylic -4”-chloro-2”, 6”-dimethyl triphenylamine (Mb) and 4, 4’- di-carboxylic -2”,4”-dichloro-6”-methyl triphenylamine (Mc) were synthesized by reaction of p-cyanobenzofluride with three different aromatic amines (4-bromo,2,6-dimethyl aniline, 4-chloro,2,6-dimethyl aniline and 2,4 dichloro, 6- methyl aniline )  via aromatic nucleophilc substitution method to form three di cyano intermediates 4, 4’-Dicyano-4”-bromo-2”, 6”-dimethyl triphenylamine (Da), 4,

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

Volterra – Fredholm integral equations (VFIEs) have a massive interest from researchers recently. The current study suggests a collocation method for the mixed Volterra - Fredholm integral equations (MVFIEs)."A point interpolation collocation method is considered by combining the radial and polynomial basis functions using collocation points". The main purpose of the radial and polynomial basis functions is to overcome the singularity that could associate with the collocation methods. The obtained interpolation function passes through all Scattered Point in a domain and therefore, the Delta function property is the shape of the functions. The exact solution of selective solutions was compared with the results obtained

In this paper, a discrete SIS epidemic model with immigrant and treatment effects is proposed. Stability analysis of the endemic equilibria and disease-free is presented. Numerical simulations are conformed the theoretical results, and it is illustrated how the immigrants, as well as treatment effects, change current model behavior

Globally, the COVID-19 pandemic’s development has presented significant societal and economic challenges. The carriers of COVID-19 transmission have also been identified as asymptomatic infected people. Yet, most epidemic models do not consider their impact when accounting for the disease’s indirect transmission. This study suggested and investigated a mathematical model replicating the spread of coronavirus disease among asymptomatic infected people. A study was conducted on every aspect of the system’s solution. The equilibrium points and the basic reproduction number were computed. The endemic equilibrium point and the disease-free equilibrium point had both undergone local stability analyses. A geometric technique was used

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