in this paper, we show that every element of a discrete module is a sum of two units if and only if its endomorphism ring has no factor ring isomorphic to $z_{2}$. we also characterize unit sum number equal to two for the endomorphism ring of quasi-discrete modules with finite exchange property.

Finitely-hollow lifting and hollow-weak modules are two generalizations of hollow module which is a weaker version module. In this paper, we have defined another generalization hollow-lifting namely finitely-hollow-weak (f-hollow-weak lifting) Various properties been seen found that, it not closed under quotients summands in general, so sufficient conditions provided f-hollow-weak property inhe...

A polypropylene hollow fiber membrane module is used for separating dissolved gases which contain dissolved oxygen from water. These dissolved gases can be used for underwater breathing. To be used for a human, the minimum amount of oxygen is essential. To increase separation of dissolved gases, much water and high surface area of hollow fibers are requested. For efficient separation system, pe...

membrane technology is used to separate water or solvents from salts or pollutants. this technique could be used for water treatment. for using of polyether sulfone (pes) hollow fiber membranes in water treatment processes, the pes hollow fiber membranes were prepared by dry-wet spinning method and heated in an oven at: 120°c, 150°c and 180°c. the effect of heating on performance of membranes w...

Solvent extraction of copper in hollow-fiber membrane contactors was investigated in this study. Extraction of copper is carried out conventionally using mixer-settlers. These contactors have some disadvantages such as consumption of high energy, dispersion of two phases and high operating costs. Membrane contactors can obviate the need for conventional contactors. The most favorable module use...

â a model is developed for separation of multicomponent gas mixtures in a countercurrent hollow fiber membrane module. while the model’s solution in countercurrent module usually involves in a time consuming iterative procedure, a proper initial guess is proposed for beginning the calculation and a simple procedure is introduced for correcting the guesses, hereby the cpu time is decreased ess...

Ten commercially available crude preparations of lipase from various microbial sources were adsorbed from aqueous buffers at several initial concentrations onto a bundle of hydrophobic hollow fibers made of poly(propylene) at pH 7.0 and 40 degrees C. The kinetics of adsorption were evaluated from measurements at various times of the protein content of the supernatant solution (using BSA as equi...