A complete metric space is a well-known concept. Kreyszig shows that every non-complete metric space  can be developed into a complete metric space , referred to as completion of .

We use the b-Cauchy sequence to form  which “is the set of all b-Cauchy sequences equivalence classes”. After that, we prove  to be a 2-normed space. Then, we construct an isometric by defining the function from  to ; thus  and  are isometric, where  is the subset of  composed of the equivalence classes that contains constant b-Cauchy sequences. Finally, we prove that  is dense in ,  is complete and the uniqueness of  is up to isometrics

      Let R be a commutative ring with unity. And let E be a unitary R-module. This paper introduces the notion of 2-prime submodules as a generalized concept of 2-prime ideal, where proper submodule H of module F over a ring R is said to be 2-prime if , for r R and x F implies that  or . we prove many properties for this kind of submodules, Let H is a submodule of module F over a ring R then H is a 2-prime submodule if and only if [N ] is a 2-prime submodule of E, where r R. Also, we prove that if F is a non-zero multiplication module, then [K: F] [H: F] for every submodule k of F such that H K. Furthermore, we will study the basic properties of this kind of submodules.

The main goal of our research is to synthesize novel nano Zn²⁺ complex with the 8-(2-(dansyl chloride)azo) adenine (LA) ligand as a pH sensor because of its advantageous properties, obtained from a single molecule. The Zn²⁺- LA complex was based on the production of an intensely dark purple-colored substance with λ_max at 552 nm. Molar ratio of Zn²⁺- LA complex is a 1:2 in aqueous buffer. The optimum concentration (0.3) mM, pH (2-5.5), and time (0-3) hr at pH=5.5, that in the studies followed Lambert-law Beer'

CdO:NiO/Si solar cell film was fabricated via deposition of CdO:NiO in different concentrations 1%, 3%, and 5% for NiO thin films in R.T and 723K, on n-type silicon substrate with approximately 200 nm thickness using pulse laser deposition. CdO:NiO/n-Si solar cell photovoltaic properties were examined under 60 mW/cm2 intensity illumination. The highest efficiency of the solar cell is 2.4% when the NiO concentration is 0.05 at 723K.

CZTS / CdS / ZnO / ITO solar cell was studied using Solar Cell Capacitance Simulato-1D (SCAPS-1D) program. We performed an improvement on the theoretical cell by increasing the doping and thickness of some layers. As a result, the efficiency was shifted from 2.18% to 6.17% and several back reflection layers (BSL) were introduced on the enhanced cell until. We obtained a highest conversion efficiency of 13.99%.  The best reflection layer (CZTSSe) was combined with the best buffer layer (CdSe), with thickness of 0.9µm, on the enhanced cell. Thereby, we obtained a cell with a conversion efficiency of 16.53%. A second improvement was made to the best obtained cell, where the CZTSSe with thickness of 0.05µm and the CdSe with thickness

Background:The most common pattern of dyslipidemia in diabetic patients is increased triglyceride (TG) and decreased HDL cholesterol level, The concentration of LDL cholesterol in diabetic patients is usually not significantly different from non diabetic individuals, Diabetic patients may have elevated levels of non-HDL cholesterol [ LDL+VLDL]. However type 2 diabetic patients typically have apreponderance of smaller ,denser LDL particles which possibly increases atherogenicity even if the absolute concentration of LDL cholesterol is not significantly increased. The Third Adult Treatment Panel of the National Cholesterol Education Program (NCEP III) and the American Heart Association (AHA ) have designate diabetes as a coronary heart dis

     In this paper, the performance of a silicon cell with a Fresnel lens (FL) for building a solar photovoltaic concentrator system was evaluated; the solar concentrator is a Fresnel lens, which is a point concentrator made of  polymethyl-methacrylate (PMMA) as a thin lens for the optics system.

As the radiation from the sun on the solar cell is concentrated to the levels of solar radiation  of 750, 1300, 1930, 2600, 4250, 7250, and 10500) W/m², the work was conducted at the midday in summer weather conditions, with ambient temperatures ranging 40-45 °C. The evaluation was performed in three cases; each case was conducted in succession. The performance of the cell was evaluated first wit

     We introduce in this paper, the notion of a 2-quasì-prime module as a generalization of quasi-prime module, we know that a module E over a ring R is called quasi-prime module, if (0) is quasi-prime submodule. Now, we say that a module E over ring R is a 2-quasi-prime module if (0) is 2-quasi-prime submodule, a proper submodule K of E is 2-quasi-prime submodule if whenever ,  and , then either  or .

Many results about these kinds of modules are obtained and proved, also, we will give a characterization of these kinds of modules.