The method of operational matrices based on different types of polynomials such as Bernstein, shifted Legendre and Bernoulli polynomials will be presented and implemented to solve the nonlinear Blasius equations approximately. The nonlinear differential equation will be converted into a system of nonlinear algebraic equations that can be solved using Mathematica®12. The efficiency of these methods has been studied by calculating the maximum error remainder ( ), and it was found that their efficiency increases as the polynomial degree (n) increases, since the errors decrease. Moreover, the approximate solutions obtained by the proposed methods are compared with the solution of the 4th order Runge-Kutta method (RK4), which gives very good agreement. In addition, the convergence of the proposed approximate methods is given based on one of the Banach fixed point theorem results.
In this work, enhancement to the fluorescence characteristics of laser dye solutions hosting highly-pure titanium dioxide nanoparticles as random gain media. This was achieved by coating two opposite sides of the cells containing these media with nanostructured thin films of highly-pure titanium dioxide. Two laser dyes; Rhodamine B and Coumarin 102, were used to prepare solutions in hexanol and methanol, respectively, as hosts for the nanoparticles. The nanoparticles and thin films were prepared by dc reactive magnetron sputtering technique. The enhancement was observed by the narrowing of fluorescence linewidth as well as by increasing the fluorescence intensity. These parameters were compared to those of the dye only and the dye solution
... Show MoreThe seedlings of vegetables are exposed to stress states, especially through the first period, due to injuring their roots by transplanting or heavy rain , so it is necessary to provide an available nutrient to recover the growth and increase their early yield, which means more income for farmers. In this regard, an experiment was conducted in the College of Agricultural Engineering Sciences, Agriculture Faculty, University of Baghdad, Iraq to study the effect of different types and concentrations of mineral fertilizers as starter solutions by using high nitrogen (N), high phosphorus (P) and neutral fertilizers (Q) at three levels which were 4 g/l (S1), 8 g/l (S2) and 12 g/l (S3) on broccoli growth and yield. The results showed tha
... Show MoreA comparative study was done on the adsorption of methyl orange dye (MO) using non-activated and activated corn leaves with hydrochloric acid as an adsorbent material. Scanning electron microscopy (SEM) and Fourier Transform Infrared spectroscopy (FTIR) were utilized to specify the properties of adsorbent material. The effect of several variables (pH, initial dye concentration, temperature, amount of adsorbent and contact time) on the removal efficiency was studied and the results indicated that the adsorption efficiency increases with the increase in the concentration of dye, adsorbent dosage and contact time, while inversely proportional to the increase in pH and temperature for both the treated and untreated corn leav
... Show MoreThe seedlings of vegetables are exposed to stress states, especially through the first period, due to injuring their roots by transplanting or heavy rain , so it is necessary to provide an available nutrient to recover the growth and increase their early yield, which means more income for farmers. In this regard, an experiment was conducted in the College of Agricultural Engineering Sciences, Agriculture Faculty, University of Baghdad, Iraq to study the effect of different types and concentrations of mineral fertilizers as starter solutions by using high nitrogen (N), high phosphorus (P) and neutral fertilizers (Q) at three levels which were 4 g/l (S1), 8 g/l (S2) and 12 g/l (S3) on broccoli growth and yield. The results showed tha
... Show MoreThis research is concerned with the re-analysis of optical data (the imaginary part of the dielectric function as a function of photon energy E) of a-Si:H films prepared by Jackson et al. and Ferlauto et al. through using nonlinear regression fitting we estimated the optical energy gap and the deviation from the Tauc model by considering the parameter of energy photon-dependence of the momentum matrix element of the p as a free parameter by assuming that density of states distribution to be a square root function. It is observed for films prepared by Jackson et al. that the value of the parameter p for the photon energy range is is close to the value assumed by the Cody model and the optical gap energy is which is also close to the value
... Show MoreIn this research, A thin film of Rhodamine B dye and TiO2 Nanoparticles doped in PMMA Polymer has been prepared by a casting method. The sample was spectrum absorption by UV-Vis. The nonlinear optical properties were measured by Z- scan technique using Nd:YAG laser with (1064 nm) wavelength. The nonlinear refractive index (n2) and nonlinear absorption coefficient (β) were estimated for the thin film for different energies of the laser, n2 and β were decreased with increasing intensity of incident laser beam. Also, the type of β was two-photon absorption and n2 negative nonlinear reflective.
In this paper, we established a mathematical model of an SI1I2R epidemic disease with saturated incidence and general recovery functions of the first disease I1. Considering the basic reproduction number, we obtained conditions for both disease-free and co-existing cases. The equilibrium points local stability is verified by using the Routh-Hurwitz criterion, while for the global stability, we used a suitable Lyapunov function to analyze the endemic spread of the positive equilibrium point. Moreover, we carried out the local bifurcation around both equilibrium points (disease-free and co-existing), where we obtained that the disease-free equilibrium point undergoes a transcritical bifurcation. We conduct numerical simulations that suppo
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