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

The present work involved preparation of new hetro cyclic polyacrylamides (1-9) using reaction of polyacryloyl chloride with 2-aminobenzothiazole which prepeard by thiocyanogen method in the presence of a suitable solvent and amount tri ethyl amine (Et3N) with heating. The structure confirmation of polymers were proved using FT-IR,1H-NMR,C13NMR and UV spectroscopy.Other physical properties including softening and melting points, and solubility of the polymers were also measured.

B3LYP density functional is utilized for probing the effect of decorating Al, Ga, and In on the sensing performance of a boron phosphide nanotube (BPNT) in detecting the 2-chloroethanol (CHE) molecule. We predict that the interaction of pure BPNT with CHE is physisorption, and the sensing response (SR) of BPNT is approximately 6.3. The adsorption energy of CHE is about − 26.3 to − 91.1, − 96.6, and − 100.3 kJ/mol, when the Al, Ga, and In metals are decorated on the BPNT surface, respectively. This indicates that the decorated metals significantly strength the interaction. Also, the corresponding SR meaningfully rises to 19.4, 41.0, and 93.4, indicating that by increasing the atomic number of metals, the sensitivity i

In this study forty mature albino rats were used wich were randomly divided into five groups ,four groups were adminstrated Phoenix dactylifera pollen grains suspension at concertenrations (18,54,108,and 216)mg/ kg body weight by oral administration while the fifth group was considered as a control group.Experiment continued for 40 days then rats were sacrificed and samples of blood were collected for determination of some biochemical parameters (total protein ,total cholesterol ,LDLc and HDLc).Testis were removed for preparation histological sections to measures the diameters of seminferous tubules ,thickness of seminiferous epithelium and the numbers of spermatogenic cells.

Coupling reaction of 2-amino benzoic acid with 8-hydroxy quinoline gave bidentate azo ligand. The prepared ligand has been identified by Microelemental Analysis,1HNMR,FT-IR and UV-Vis spectroscopic techniques. Treatment of the prepared ligand with the following metal ions (ZnII,CdII and HgII) in aqueous ethanol with a 1:2 M:L ratio and at optimum pH, yielded a series of neutral complexes of the general formula [M(L)2]. The prepared complexes have been characterized by using flame atomic absorption, (C.H.N) Analysis, FT-IR and UV-Vis spectroscopic methods as well as conductivity measurements. The nature of the complexes formed were studied following the mole ratio and continuous variation methods, Beer's law obeyed over a concentration range

Coupling reaction of 2-amino benzoic acid with 8-hydroxy quinoline gave bidentate azo ligand. The prepared ligand has been identified by Microelemental Analysis,1HNMR,FT-IR and UV-Vis spectroscopic techniques. Treatment of the prepared ligand with the following metal ions (ZnII,CdII and HgII) in aqueous ethanol with a 1:2 M:L ratio and at optimum pH, yielded a series of neutral complexes of the general formula [M(L)2]. The prepared complexes have been characterized by using flame atomic absorption, (C.H.N) Analysis, FT-IR and UV-Vis spectroscopic methods as well as conductivity measurements. The nature of the complexes formed were studied following the mole ratio and continuous variation methods, Beer's law obeyed over a concentration range

Coupling reaction of 2-amino benzoic acid with 8-hydroxy quinoline gave bidentate azo ligand. The prepared ligand has been identified by Microelemental Analysis,1HNMR,FT-IR and UV-Vis spectroscopic techniques. Treatment of the prepared ligand with the following metal ions (ZnII,CdII and HgII) in aqueous ethanol with a 1:2 M:L ratio and at optimum pH, yielded a series of neutral complexes of the general formula [M(L)2]. The prepared complexes have been characterized by using flame atomic absorption, (C.H.N) Analysis, FT-IR and UV-Vis spectroscopic methods as well as conductivity measurements. The nature of the complexes formed were studied following the mole ratio and continuous variation methods, Beer's law obeyed over a concentration ra