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 concept of the Extend Nearly Pseudo Quasi-2-Absorbing submodules was recently introduced by Omar A. Abdullah and Haibat K. Mohammadali in 2022, where he studies this concept and it is relationship to previous generalizationsm especially  2-Absorbing submodule and Quasi-2-Absorbing submodule, in addition to studying the most important Propositions, charactarizations and Examples. Now in this research, which is considered a continuation of the definition that was presented earlier, which is the Extend Nearly Pseudo Quasi-2-Absorbing submodules, we have completed the study of this concept in multiplication modules. And the relationship between the Extend Nearly Pseudo Quasi-2-Absorbing submodule and Extend Nearly Pseudo Quasi-2-Abs

Let  be a module over a commutative ring  with identity. In this paper we intoduce the concept of Strongly Pseudo Nearly Semi-2-Absorbing submodule, where a  proper submodule  of an -module  is said to be Strongly Pseudo Nearly Semi-2-Absorbing submodule of   if whenever , for implies that either  or , this concept is a generalization of 2_Absorbing submodule, semi 2-Absorbing submodule, and strong form of (Nearly–2–Absorbing, Pseudo_2_Absorbing, and Nearly Semi–2–Absorbing) submodules. Several properties characterizations, and examples concerning this new notion are given. We study the relation between Strongly Pseudo Nearly Semei-2-Absorbing submodule and (2_Absorbing, Nearly_2_Absorbing, Pseudo_2_Absorbing, and Nearly S

The optimum conditions for production of fibrinolytic protease from an edible mushroom Pleurotus ostreatus grown on the solid medium , Sus medium, composed of Sus wastes (produced from extracted medicinal plant Glycyrrhiza glabra) were determined. Addition of 5% of Soya bean seeds meal in Sus medium recorded a maximum fibrinolytic protease activity resulting in 7.7 units / ml. The optimum moisture content of Sus medium supplemented with 5% Soya bean seeds meal was 60% resulting in 7.2 units / ml.Pleurotus ostreatus produced a maximum fibrinolytic protease activity when the spawn rate,pH of medium and incubation temperature were 2,6 and 30°C, respectively. The maximum fibrinolytic protease activity was 7.6 units / ml when incubat

Background: Type 2 diabetes mellitus (T2DM) characterized by insulin resistance (IR) and progressive decline in functional beta (β) cell mass partially due to increased β cell apoptosis rate. Pancreatic stone protein /regenerating protein (PSP/reg) is produced mainly by the pancreas and elevated drastically during pancreatic disorder. Beta cells are experiencing apoptosis that stimulate the expression of PSP/reg gene in surviving neighboring cells, and that PSP/reg protein is subsequently secreted from these cells which could play a role in their regeneration.

Objectives: To analyze serum levels of PSP/reg protein in T2DM patients and evaluate its correlation with the microvasc

Two  series    of   1,n-alkylene    glycol   di [4{N(T-thiazolylazo­

nrethinyl)}2-metho y]     phenyl     ether     and     I ,n-alkylene      glycol di[4{N(r-benzo-thiazolylazomethinyl)}2-methoxy]phenyl ether were synthesize-d via rea tions  2-aminothiazole and  2-aminobenzothiazole with  dialdehyde • (which  are synthesized  from  .reaction  vanil.lin with

l ,n-dibromo   or   ehloro.   alkane   in  the   basic   me'dia   )   .  &nb