Adsorption and ion exchange are examples of fixed-bed sorption processes that show transient behavior. This means that differential equations are needed to design them. As a result, numerical methods are commonly utilized to solve these equations. The solution frequently used in analytical methods is called the Thomas solution. Thomas gave a complete solution that adds a nonlinear equilibrium relationship that depends on second-order reaction kinetics. A computational approach was devised to solve the Thomas model. The Thomas model's validity was established by conducting three distinct sets of experiments. The first entails the adsorption of acetic acid from the air through the utilization of activated carbon. Following

It was known that every left (?,?) -derivation is a Jordan left (?,?) – derivation on ?-prime rings but the converse need not be true. In this paper we give conditions to the converse to be true.

A trademark is one of the most valuable elements in advertising. At the same time, it is a guarantee for both the producer and the consumer. It prevents the mixing of products with a certain mark with similar products bearing another mark; and creates confidence in the goods of the product.

With the increase in the types of goods and products and the emergence of similar goods, producers have turned to the use of the brand to identify their products and seek perfection in manufacture to maintain quality and continuous improvement which ensures good reputation and fame.

Hence, commercials for goods and services focused on the brand because they give in-depth connotations with the recipients of these ads. T

One of the crucial public health problems worldwide is the urinary tract infections (UTIs) that are derived from uropathogenic bacteria (UPBs). Slime layer is known to have the ability to permit bacteria to achieve smooth surfaces attachment like catheters and prosthetic implants which in turn, facilitate biofilm formation and may cause lethal infections. On the other hand, Extended-spectrum beta-lactamase (ESBL) production is considered a growing concern among UPBs due to the limiting of the treatment options and contributes to resistance toward antibiotics. The principal study's point is the finding out the slime layer and ESBL production in Escherichia coli and Klebsiella pneumoniae of uropathogenic origin. Ten ready isolates (five isola

This large book represents the research and is marked (Compilers of Hanbali jurisprudence of the Abbasid era). It includes, between its covers, a large group of scholars of the Islamic nation, with its great jurists and mujtahids, from the followers of the school of (Ahmed bin Hanbal) in the fundamentals and branches, and specific to the sciences of the Qur’an, its jurisprudence, and the narrators of the hadiths of the Noble Prophet The best of creation (Muhammad) peace and blessings be upon him, and it also includes a large number of reciters and ascetics, who are known for their abundance of authorship, especially with regard to the collection and numbers of classifications, and they are too large to be counted by number! But can we

The method of work is not a method made by grammarians. We have found more than guidance from the ancients and contemporaries; That to the corruption of meaning; or to apparent cost Not accepted by good linguistic taste.

The concept of bipolar fuzzy ideals in a TM-algebra was introduced and some properties of these ideals are investigated. Also, a few relations between a bipolar fuzzy ideal and T-ideal are discussed. A new bipolar fuzzy set with a homomorphism of TM-algebra is defined. The Cartesian product of bipolar fuzzy T-ideals in Cartesian product TM-algebras is given.