The main goal of this paper is to introduce the higher derivatives multivalent harmonic function class, which is defined by the general linear operator. As a result, geometric properties such as coefficient estimation, convex combination, extreme point, distortion theorem and convolution property are obtained. Finally, we show that this class is invariant under the Bernandi-Libera-Livingston integral for harmonic functions.

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