Gaslift reactors are employed in several bioapplications due to their characteristics of cost-effectiveness and high efficiency. However, the nutrient and thermal gradient is one of the obstacles that stand in the way of its widespread use in biological applications. The diagnosis, analysis, and tracking of fluid paths in external draft tube gaslift bioreactor-type are the main topics of the current study. Several parameters were considered to assess the mixing efficiency such as downcomer-to-rizer diameter ratio (Ded/Dr), the position of the diffuser to the height of bioreactor ratio (Pd/Lr), and gas bubble size (Db). The multiple regression of liquid velocity indicates the optimal setting: Ded/Dr is (0.5), Pd/Lr is (0.02), and Db

Gaslift reactors are employed in several bioapplications due to their characteristics of cost-effectiveness and high efficiency. However, the nutrient and thermal gradient is one of the obstacles that stand in the way of its widespread use in biological applications. The diagnosis, analysis, and tracking of fluid paths in external draft tube gaslift bioreactor-type are the main topics of the current study. Several parameters were considered to assess the mixing efficiency such as downcomer-to-rizer diameter ratio (Ded/Dr), the position of the diffuser to the height of bioreactor ratio (Pd/Lr), and gas bubble size (Db). The multiple regression of liquid velocity indicates the optimal setting: Ded/Dr is (0.5), Pd/Lr is (0.02), and Db

The aim of this article is to solve the Volterra-Fredholm integro-differential equations of fractional order numerically by using the shifted Jacobi polynomial collocation method. The Jacobi polynomial and collocation method properties are presented. This technique is used to convert the problem into the solution of linear algebraic equations. The fractional derivatives are considered in the Caputo sense. Numerical examples are given to show the accuracy and reliability of the proposed technique.

It is no secret to anyone that the Koran is a speech to people, and how it is not a speech to humans is a home to them and suitable for their understandings, and the people of rhetoric mean great care has never been before in the division of the Koranic discourse, followed by linguists and science of the Koran. After reading the letter, I followed it in the Holy Quran, taking advantage of what was written by former writers in language and interpretation. Thanks to God, I have done what I wanted. Perhaps one of the most important reasons that led me to write my research and optional for this topic; is related to the Koran. So I started to develop the research plan, and divided it as I saw it, I started to pave the way, and then divided it

Theatrical costume constitutes a peculiarity in the theatrical performance because of its ability to communicate and communicate with the rest of the visual elements of the show in highlighting the intellectual and dramatic values. Fashion developments in theatrical performance, the second: the design elements of costumes and their characteristics, the third, which includes research procedures, and the fourth, in which the research results and conclusions were presented, including:

• The play (Happening on the Farm) is considered one of the plays with educational, educational and aesthetic goals, as it carried in its formats the features of simplicity and diversity of the visual formal connotations of the child.
• The c

The progress of network and multimedia technologies has been phenomenal during the previous two decades. Unauthorized users will be able to copy, retransmit, modify reproduction, and upload the contents more easily as a result of this innovation. Malicious attackers are quite concerned about the development and widespread use of digital video. Digital watermarking technology gives solutions to the aforementioned problems. Watermarking methods can alleviate these issues by embedding a secret watermark in the original host data, allowing the genuine user or file owner to identify any manipulation. In this study, lots of papers have been analyzed and studied carefully, in the period 2011–2022. The historical basis of the subject shou