In this paper, a discretization of a three-dimensional fractional-order prey-predator model has been investigated with Holling type III functional response. All its fixed points are determined; also, their local stability is investigated. We extend the discretized system to an optimal control problem to get the optimal harvesting amount. For this, the discrete-time Pontryagin’s maximum principle is used. Finally, numerical simulation results are given to confirm the theoretical outputs as well as to solve the optimality problem.
This paper presents new modification of HPM to solve system of 3 rd order PDEs with initial condition, for finding suitable accurate solutions in a wider domain.
Blockchain represents a new promising technology with a huge economic impact resulting from its uses in various fields such as digital currency and banking; malware represents a serious threat to users, and there are many differences in the effectiveness of antivirus software used to deal with the problem of malware. This chapter has developed a coefficient for measuring the effectiveness of antivirus software. This chapter evaluates the effectiveness of antivirus software by conducting tests on a group of protection programs using a folder containing an amount of data. These programs are applied to combat viruses contained in this folder. The study revealed that the effectiveness of antivirus software is as follows: AVG scored 0%,
... Show MoreThis paper deals with the thirteenth order differential equations linear and nonlinear in boundary value problems by using the Modified Adomian Decomposition Method (MADM), the analytical results of the equations have been obtained in terms of convergent series with easily computable components. Two numerical examples results show that this method is a promising and powerful tool for solving this problems.
The basic analytical formula for particle-hole state densities is derived based on the non-Equidistant Spacing Model (non-ESM) for the single-particle level density (s.p.l.d.) dependence on particle excitation energy u. Two methods are illustrated in this work, the first depends on Taylor series expansion of the s.p.l.d. about u, while the second uses direct analytical derivation of the state density formula. This treatment is applied for a system composing from one kind of fermions and for uncorrected physical system. The important corrections due to Pauli blocking was added to the present formula. Analytical comparisons with the standard formulae for ESM are made and it is shown that the solution reduces to earlier formulae providing m
... Show MoreIn this work, the occurrence conditions of both local Bifurcation and persistence were studied, Saddle-node bifurcation appears near fourth point, near the first point, the second point and the third point a transcritical bifurcation occurred but no pitchfork bifurcation happened near any of the four equilibrium points. In addition to study conditions for Hopf-bifurcation near positive stable point that is the fourth point. Besides discuss persistence occurrence as globally property of the food chain of three species include prey, first predator and top predator with impact of toxin in all species and harvesting effect on the predator’s only. Numerical results for the set of hypothe
A harvested prey-predator model with infectious disease in preyis investigated. It is assumed that the predator feeds on the infected prey only according to Holling type-II functional response. The existence, uniqueness and boundedness of the solution of the model are investigated. The local stability analysis of the harvested prey-predator model is carried out. The necessary and sufficient conditions for the persistence of the model are also obtained. Finally, the global dynamics of this model is investigated analytically as well as numerically. It is observed that, the model have different types of dynamical behaviors including chaos.
In this study, nano TiO2 was prepared with titanium isopropoxide (TTIP) as a resource to titanium oxide. The catalyst was synthesized using phosphotungstic acid (PTA) and, stearyl trimethyl ammonium bromide (STAB) was used as the structure-directing material. Characterization of the product was done by the X-ray diffraction (XRD), X-ray fluorescent spectroscopy (XRF), nitrogen adsorption/desorption measurements, Atomic Force Microscope (AFM) and Fourier transform infrared (FTIR) spectra, were used to characterize the calcined TiO2 nanoparticles by STAB and PWA. The TiO2 nanomaterials were prepared in three crystalline forms (amorphous, anatase, anatase-rutile). The results showed that the nanoparticles of anatase TiO2 have good cata
... Show MoreIn this study, nano TiO2 was prepared with titanium isopropoxide (TTIP) as a resource to titanium oxide. The catalyst was synthesized using phosphotungstic acid (PTA) and, stearyl trimethyl ammonium bromide (STAB) was used as the structure-directing material. Characterization of the product was done by the X-ray diffraction (XRD), X-ray fluorescent spectroscopy (XRF), nitrogen adsorption/desorption measurements, Atomic Force Microscope (AFM) and Fourier transform infrared (FTIR) spectra, were used to characterize the calcined TiO2 nanoparticles by STAB and PWA. The TiO2 nanomaterials were prepared in three crystalline forms (amorphous, anatase, anatase-rutile). The results showed that the
... Show MoreIn this study, we made a comparison between LASSO & SCAD methods, which are two special methods for dealing with models in partial quantile regression. (Nadaraya & Watson Kernel) was used to estimate the non-parametric part ;in addition, the rule of thumb method was used to estimate the smoothing bandwidth (h). Penalty methods proved to be efficient in estimating the regression coefficients, but the SCAD method according to the mean squared error criterion (MSE) was the best after estimating the missing data using the mean imputation method