The effect of superficial gas velocity within the range 0.01-0.164 m/s on gas holdup (overall, riser and down comer), volumetric oxygen mass transfer coefficient, liquid circulation velocity was studied in an internal loop concentric tubes airlift reactor (working volume 45 liters). It was shown that as the u_sg increases the gas holdup and also the liquid circulation velocity increase. Also it was found that increasing superficial gas velocity lead to increase the interfacial area that increases the overall oxygen mass transfer coefficient. The hydrodynamic experimental results were modeled with the available equations in the literature. The predicted data gave an acceptable accuracy with the empirical data.

The final

Market share is a major indication of business success. Understanding the impact of numerous economic factors on market share is critical to a company’s success. In this study, we examine the market shares of two manufacturers in a duopoly economy and present an optimal pricing approach for increasing a company’s market share. We create two numerical models based on ordinary differential equations to investigate market success. The first model takes into account quantity demand and investment in R&D, whereas the second model investigates a more realistic relationship between quantity demand and pricing.

In this study, a brand-new double transform known as the double INEM transform is introduced. Combined with the definition and essential features of the proposed double transform, new findings on partial derivatives, Heaviside function, are also presented. Additionally, we solve several symmetric applications to show how effective the provided transform is at resolving partial differential equation.

In this work, we first construct Hermite wavelets on the interval [0,1) with it’s product, Operational matrix of integration 2^k M×2^k M is derived, and used it for solving nonlinear Variational problems with reduced it to a system of algebric equations and aid of direct method. Finally, some examples are given to illustrate the efficiency and performance of presented method.

     The goal of the research is to develop a sustainable rating system for roadway projects in Iraq for all of the life cycle stages of the projects which are (planning, design, construction and operation and maintenance). This paper investigates the criteria and its weightings of the suggested roadway rating system depending on sustainable planning activities. The methodology started in suggesting a group of sustainable criteria for planning stage and then suggesting weights from (1-5) points for each one of it. After that data were collected by using a closed questionnaire directed to the roadway experts group in order to verify the criteria weightings based on the relative importance of the roadway related impacts