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

Both traditional and novel techniques were employed in this work for magnetic shielding evaluation to shed new light on the magnetic and aromaticity properties of benzene and 12 [n]paracyclophanes with n = 3–14. Density functional theory (DFT) with the B3LYP functional and all-electron Jorge-ATZP and x2c-TZVPPall-s basis sets was utilized for geometry optimization and magnetic shielding calculations, respectively. Additionally, the 6-311+G(d,p) basis set was incorporated for the purpose of comparing the magnetic shielding results. In addition to traditional evaluations such as NICS/NICSzz-Scan, and 2D-3D σiso(r)/σzz(r) maps, two new techniques were implemented: bendable grids (BGs) and cylindrical grids (CGs) of ghost atoms (Bqs). BGs a

Algae have been considered a sources task of biofuels, which is a future alternative to fossil fuels, and this lead the environmental studies concerned with the lifting of curves or growth rates and time of replication of different kinds of algae, as well as algae cells in response to different environmental conditions, whether chemical or physical, to assess their impact on the composition of these cells and the extent of affected components that make up the living, especially fatty acid ,total fats, proteins and carbohydrates, Gbrha. Green Chlorococcum humicola showed a different response when treated with an average of agriculture Chu-10 and Chu-13 which used as control media,Compared with the degree of its response when exposed to e

In this work was prepared three different types of modified screen printed carbon electrode (SPCEs) with drops casted method, the used carbone nanomaterials were the MWCNT, functionalized –MWCNT (f-MWCNT) and After several experiments were made to find an appropriate ratio to make good GOT/f-MWCNT nanocomposite, and found the suspension mixture (1:1) from GOT/f-MWCNT (f-MWCNT-GOT). The electrical and physical properties were performed with cyclic voltammeter technique, and studied the maximum current response, the effective surface area, effect of the pH value and the determination of active surface area for MWCNT-SPCE , f-MWCNT-SPCE and f-MWCNT-GOT/SPCE as (0.04 cm2), (0.119 cm2) and (0.115 cm2) respectively, the surface coverage concent

To determine the abilities of salivary E‐cadherin to differentiate between periodontal health and periodontitis and to discriminate grades of periodontitis.