We investigate mathematical models of the Hepatitis B and C viruses in the study, considering vaccination effects into account. By utilising fractional and ordinary differential equations, we prove the existence of equilibrium and the well-posedness of the solution. We prove worldwide stability with respect to the fundamental reproduction number. Our numerical techniques highlight the biological relevance and highlight the effect of fractional derivatives on temporal behaviour. We illustrate the relationships among susceptible, immunised, and infected populations in our epidemiological model. Using comprehensive numerical simulations, we analyse the effects of fractional derivatives and highlight solution behaviours. Subsequent investigatio

KE Sharquie, SA Al-Mashhadani, AA Noaimi, AA Hasan, Journal of Cutaneous and Aesthetic Surgery, 2012 - Cited by 19

Presents here in the results of comparison between the theoretical equation stated by Huang and Menq and laboratory model tests used to study the bearing capacity of square footing on geogrid-reinforced loose sand by performing model tests. The effects of several parameters were studied in order to study the general behavior of improving the soil by using the geogrid. These parameters include depth of first layer of reinforcement, vertical spacing of reinforcement layers, number of reinforcement layers and types of reinforcement layers The results show that the theoretical equation can be used to estimate the bearing capacity of loose sand.

The major cause of destruction during vertical vibration is the failure of the soil structure. The soil may fail due to loss of strength during continues vibration. The saturated sandy soil losses strength due to an increase in pore pressure, this phenomenon is called "liquefaction". Piled foundations are usually adopted as a foundation solution in potentially liquefiable soil under dynamic loading. In this research, 3D finite element model using PLAXIS Software was employed for pile foundation in saturated sandy soil. The results show the acceleration mobilization and velocity on the footing increases with increasing the intensity of dynamic loads and it becomes zero at maximum value of vertical settlement which indicates the end of the ti

    Soft clays are generally characterized by low shear strength, low permeability and high compressibility. An effective method to accelerate consolidation of such soils is to use vertical drains along with vacuum preloading to encourage radial flow of water.  In this research numerical modeling of prefabricated vertical drains with vacuum pressure was done to investigate the effect of using vertical drains together with vacuum pressure on the degree of saturation of fully and saturated-unsaturated soft soils.  Laboratory experiments were conducted by using a specially-designed large consolidometer cell where a central drain was installed and vacuum pressure was applied. All tests were conducted

The differential cross section for the Rhodium and Tantalum has been calculated by using the Cross Section Calculations (CSC) in range of energy(1keV-1MeV) . This calculations based on the programming of the Klein-Nashina and Rayleigh Equations. Atomic form factors as well as the coherent functions in Fortran90 language Machine proved very fast an accurate results and the possibility of application of such model to obtain the total coefficient for any elements or compounds.

A mathematical method with a new algorithm with the aid of Matlab language is proposed to compute the linear equivalence (or the recursion length) of the pseudo-random key-stream periodic sequences using Fourier transform. The proposed method enables the computation of the linear equivalence to determine the degree of the complexity of any binary or real periodic sequences produced from linear or nonlinear key-stream generators. The procedure can be used with comparatively greater computational ease and efficiency. The results of this algorithm are compared with Berlekamp-Massey (BM) method and good results are obtained where the results of the Fourier transform are more accurate than those of (BM) method for computing the linear equivalenc

           In this paper, the homotopy perturbation method (HPM) is presented for treating a linear system of second-kind mixed Volterra-Fredholm integral equations. The method is based on constructing the series whose summation is the solution of the considered system. Convergence of constructed series is discussed and its proof is given; also, the error estimation is obtained. Algorithm is suggested and applied on several examples and the results are computed by using MATLAB (R2015a). To show the accuracy of the results and the effectiveness of the method, the approximate solutions of some examples are compared with the exact solution by computing the absolute errors.

Iraqi oil crudes have some of the physical and chemical characteristics that distinguish it from other types of oil crudes in the world. Some of these features such us molecular composition, rheological, viscosity and emulsions are studied carefully by researchers. In this work, a comparative study of the linear and the non-linear optical properties for typical heavy and light crude oils of Iraqi origin was studied utilizing Z-scan technique. The He -Ne laser of wavelength 632.8 nm had been used for this purpose. These samples were collected from Basra and Kut oil fields. The values of the non-linear refractive index (n₂), non-linear absorption coefficient (β), and third-order electrical susceptibility (χ³) were e