In the context of normed space, Banach's fixed point theorem for mapping is studied in this paper. This idea is generalized in Banach's classical fixed-point theory. Fixed point theory explains many situations where maps provide great answers through an amazing combination of mathematical analysis. Picard- Lendell's theorem, Picard's theorem, implicit function theorem, and other results are created by other mathematicians later using this fixed-point theorem. We have come up with ideas that Banach's theorem can be used to easily deduce many well-known fixed-point theorems. Extending the Banach contraction principle to include metric space with modular spaces has been included in some recent research, the aim of study proves some pro

Abstract. The main technique for removing bacteria from water for various applications is chemical disinfection. However, this method has many disadvantages such as producing disinfectant by-products (DBPs), biofilm formation and either rendering the water unpotable (at high residual disinfection) or leaving a potential for lethal diseases such as Cholera (if the residual disinfection is too low). Recently, a process was developed for continuous removal of bacteria from water using the principle of froth flotation through compressed air only without any chemicals (Hassan, 2015). This work examines the extent to which chemical free froth flotation can purify drinking water. The experiments were carried out using two flotation columns

Health and environmental factors as well as operational difficulties are major challenges facing the development of an anaerobic digestion process. Some of these problems relate to the use of sludge collected from primary and secondary clarifier units in wastewater treatment plants for laboratory purposes.

The present study addresses the preparation of sludge for laboratory purposes by using a mixture that consists of the digested sludge, which is less pathogenic, compared to the collected sludge from the primary or secondary clarifier, and food wastes. The sludge has been tested experimentally for 19 and 32 days under mesophilic conditions. The results show a steady methane production rate from the anaerobic dig

Electrochemical decolorization of direct black textile dye was studied in the presence of sodiumhydroxide (NaCl). Electrochemical cell occupy about 1 liter of working electrolyte supplied with graphiteelectrodes for both anode and cathode was constructed for this purpose. Decolorization percent, treatment time, power consumption, and pH were studied as a function of the applied voltage and salt concentration. Results show that decolorization increase with increasing salt concentration and applied voltage. Best decolorization of 86% can be achieved after 17 min at 7 volt and 5 g/l salt concentration. Further decolorization can be achieved but this will be accompanied with a sharp increase in power consumption. No significant decrease

Simulated annealing (SA) has been an effective means that can address difficulties related to optimization problems. is now a common discipline for research with several productive applications such as production planning. Due to the fact that aggregate production planning (APP) is one of the most considerable problems in production planning, in this paper, we present multi-objective linear programming model for APP and optimized by . During the course of optimizing for the APP problem, it uncovered that the capability of was inadequate and its performance was substandard, particularly for a sizable controlled problem with many decision variables and plenty of constraints. Since this algorithm works sequentially then the current state wi