In this paper, we present new algorithm for the solution of the nonlinear high order multi-point boundary value problem with suitable multi boundary conditions. The algorithm is based on the semi-analytic technique and the solutions are calculated in the form of a rapid convergent series. It is observed that the method gives more realistic series solution that converges very rapidly in physical problems. Illustrative examples are provided to demonstrate the efficiency and simplicity of the proposed method in solving this type of multi- point boundary value problems.

In this paper, a new technique is offered for solving three types of linear integral equations of the 2nd kind including Volterra-Fredholm integral equations (LVFIE) (as a general case), Volterra integral equations (LVIE) and Fredholm integral equations (LFIE) (as special cases). The new technique depends on approximating the solution to a polynomial of degree  and therefore reducing the problem to a linear programming problem(LPP), which will be solved to find the approximate solution of LVFIE. Moreover, quadrature methods including trapezoidal rule (TR), Simpson 1/3 rule (SR), Boole rule (BR), and Romberg integration formula (RI) are used to approximate the integrals that exist in LVFIE. Also, a comparison between those methods i

The catalytic cracking of three feeds of extract lubricating oil, that produced as a by-product from the process of furfural extraction of lubricating oil base stock in AL-Dura refinery at different operating condition, were carried out at a fixed bed laboratory reactor. The initial boiling point for these feeds was 140 ºC for sample (1), 86 ºC for sample (2) and 80 ºC for sample (3). The catalytic cracking processes were carried out at temperature range 325-400 ºC and initially at atmospheric pressure after 30 minutes over 9.88 % HY-zeolite catalyst load. The comparison between the conversion at different operating conditions of catalytic cracking processes indicates that a high yield was obtained at 375°C, according to gasoline pr

The influence and hazard of fire flame are one of the most important parameters that affecting the durability and strength of structural members. This research studied the influence of fire flame on the behavior of reinforced concrete beams affected by repeated load. Nine self- compacted reinforced concrete beams were castellated, all have the same geometric layout (0.15x0.15x1.00) m, reinforcement details and compressive strength (50 Mpa).

To estimate the effect of fire flame disaster, four temperatures were adopted (200, 300, 400 and 500) ^oC and two method of cooling were used (graduated and sudden). In the first cooling method, graduated, the tested beams were leaved to cool in air while in the seco

In this study, we used Bayesian method to estimate scale parameter for the normal distribution. By considering three different prior distributions such as the square root inverted gamma (SRIG) distribution and the non-informative prior distribution and the natural conjugate family of priors. The Bayesian estimation based on squared error loss function, and compared it with the classical estimation methods to estimate the scale parameter for the normal distribution, such as the maximum likelihood estimation and th

Undoped and Iodine (I)–doped chrome oxide (Cr2O3)thin films have been prepared by chemical spray pyrolysis technique at substrate temperatures(773K) on glass substrate. Absorbance and transmittance spectra have been recorded as a function of wavelength in the range (340-800 nm) in order to study the optical properties such as reflectance, Energy gap of allowed direct transition, extinction coefficient refractive index, and dielectric constant in real and imagery parts all as a function of wavelength. It was found that all the investigated parameters affect by the doping ratios.

The optimization calculations are made to find the optimum properties of combined quadrupole lens consist of electrostatic and magnetic lenses to produce achromatic lens. The modified bell-shaped model is used and the calculation is made by solving the equation of motion and finding the transfer matrices in convergence and divergence planes, these matrices are used to find the properties of lens as the magnification and aberrations coefficients. To find the optimum values of chromatic and spherical aberrations coefficients, the effect of both the excitation parameter of the lens (n) and the effective length of the lens into account as effective parameters in the optimization processing

The influence and hazard of fire flame are one of the most important parameters that affecting the durability and strength of structural members. This research studied the influence of fire flame on the behavior of reinforced concrete beams affected by repeated load. Nine self- compacted reinforced concrete beams were castellated, all have the same geometric layout (0.15x0.15x1.00) m, reinforcement details and compressive strength (50 Mpa). To estimate the effect of fire flame disaster, four temperatures were adopted (200, 300, 400 and 500) oC and two method of cooling were used (graduated and sudden). In the first cooling method, graduated, the tested beams were leaved to cool in air while in the second method, sudden, water splash was use