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

In the current study, we investigate the effect of  (La) substitution  instead of (Cu) on the properties of the superconductor compound  (Bi2Sr2Ca2Cu3-xLaxO10+δ)  with (x=0,0.05,0.1,0.15,0.2). The samples were  prepared  by solid state reaction method(SSR). Xray diffraction technique (XRD) was used to estimate the structural  properties of the specimens which show an orthorhombic crystalline structure for all the specimens.       The results show that the change in ( La) concentration  leads to decrease the concentration of (Bi-2223), increment in (Bi-2212 ) and(Bi-2201) with appearance of some impurities. Also decrease the critical temperature(Tc) with the increase

 In the current study, the definition of mapping of fuzzy neutrosophic generalized semi-continuous and fuzzy neutrosophic alpha has generalized mapping as continuous. The study confirmed some theorems regarding such a concept. In the following, it has been found relationships among fuzzy neutrosophic alpha generalized mapping as continuous, fuzzy neutrosophic mapping as continuous, fuzzy neutrosophic alpha mapping as continuous, fuzzy neutrosophic generalized semi mapping as continuous, fuzzy neutrosophic pre mapping as continuous and fuzzy neutrosophic γ mapping as continuous.

Total Quality Assurance Concept have appeared in Higher Education Institutions as a result of the continuous criticism for the lower quality of the outputs of these institutions and their inappropriacy to the needs of the job market. The faculty, i.e. teaching staff member, is one of the most important output for his/her responsibility to achieve the stated goals in higher education. This represents a problem that may influence the construction of society which has to limit his tasks, responsibilities, and competencies that should be found in a faculty, and evaluating his teaching profession in light of the prerequisites of the century to become an input to achieve quality assurance in Higher Education. Therefore, the present study aims

The main goal of this paper is to study and discuss a new class of meromorphici "functions[ which are multivalent defined by [fractional  calculus operators. Coefficients iestimates , radiisi of satarlikeness , convexityi and closed-to-iconvexity are studied. Also distortion iand closure theorems for the classi" ,  are considered.

  In this study, light elements for 13C , 16O for  (α,n) and (n,α) reactions as well as α-particle energy  from 2.7 MeV  to 3.08 MeV are used as far as the data of reaction cross sections are available. The more recent cross sections data of (α,n) and (n,α) reactions are reproduced in fine steps 0.02 MeV for  16O (n,α) 13C  in the specified energy range, as well as cross section (α,n)  values were derived from the published data of (n,α) as a function of α-energy in the same fine energy steps by using the principle inverse reactions. This calculation involves only the ground state of  13C , 16O  in the reactions 13C (α,n) 16O  and  16O (n,α) 13C.

         The purpose and goal of the research revolve around the diagnosis of intellectual capital as the logical indicator to study an effective human resource management practice and its influential role in determining the overall quality management of higher education institutions and scientific research in Baghdad.

       To achieve the purpose of the research, an upgraded standard questionnaire was used to collect data and distribute it to the selected sample in a statistical manner from the study population of (5) institutions affiliated with the Ministry of Higher Education and Scientific Resear

An R-module M is called ET-H-supplemented module if for each submodule X of M, there exists a direct summand D of M, such that T⊆X+K if and only if T⊆D+K, for every essential submodule K of M and T M. Also, let T, X and Y be submodules of a module M , then we say that Y is ET-weak supplemented of X in M if T⊆X+Y and (X⋂Y M. Also, we say that M is ET-weak supplemented module if each submodule of M has an ET-weak supplement in M. We give many characterizations of the ET-H-supplemented module and the ET-weak supplement. Also, we give the relation between the ET-H-supplemented and ET-lifting modules, along with the relationship between the ET weak -supplemented and ET-lifting modules.

Background & Objective: Breast cancer (BC) is the most prevalent disease among women around the world, considered the world's leading cause of death (15% of the total cancer deaths) in women in 2018. β-catenin is a multifunctional protein located in the cytoplasm and/or nucleus of the cell. Several studies suggested that β-catenin expression plays a critical role in cancer invasion and metastasis. This research sought to examine β-catenin expression in breast cancer and its associations with clinico-pathological features (such as histopathological types, grade, and invasion depth of tumor as well as lymph node involvement) and breast cancer patient survival. Methods:

In this paper we introduced a new type of integrals based on binary element sets “a generalized integral of Shilkret and Choquet integrals” that combined the two kinds of aggregation functions which are Shilkret and Choquet integrals. Then, we gave some properties of that integral. Finally, we illustrated our integral in a numerical example.
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