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 local resolving neighborhood  of a pair of vertices  for  and  is if there is a vertex  in a connected graph  where the distance from  to  is not equal to the distance from  to , or defined by . A local resolving function  of  is a real valued function   such that  for  and . The local fractional metric dimension of graph  denoted by , defined by  In this research, the author discusses about the local fractional metric dimension of comb product are two graphs, namely graph  and graph , where graph  is a connected graphs and graph  is a complate graph &

The research discussed the propositions of functional structures and the requirements for their transformation according to the variables of use and human interaction through the variables of functions with one form products، multifunctional variables، and transforming form in one product. The patterns of user’s interaction with products were discussed through the variables of functional type، starting from defining the types of functions in the industrial product structures to: practical functions، which were classified into: informational functions، ergonomic functions، use، handling، comfort، global، anthropometric adaptation and physical postures. While the interaction variables were discussed according to the meaning fun

 Morphological description and histological structure of the liver have been studied in Durra bird Melopsittacus undulatus. The liver is a bilobed organ , the left lobe with three secondary lobes and slightly larger than the right lobe which is elliptical in shape. Liver is surrounded by a capsule that consists of thin layer of connective tissue with no distinction between interlobular septa . The parenchyma tissue consists of hepatic cells arranged with thickness 2_1 cell. Portal area appears within the liver parenchyma tissue composed of hepatic artery, portal vein and bile duct and supported by connective tissue. A gallbladder was not noticed in this species.             

The purpose of this article is to introduce reverse engineering procedure (REP). It can achieved by developing an industrial mechanical product that had no design schemes throughout the 3D-Scanners. The aim of getting a geometric CAD model from 3D scanner is to present physical model. Generally, this used in specific applications, like commercial plan and manufacturing tasks. Having a digital data as stereolithography (STL) format. Converting the point cloud be can developed as a work in programming by producing triangles between focuses, a procedure known as triangulation. Then it could be easy to manufacture parts unknown documentation and transferred the information to CNC-machines. In this work, modification was proposed and used in RE

Finding orthogonal matrices in different sizes is very complex and important because it can be used in different applications like image processing and communications (eg CDMA and OFDM). In this paper we introduce a new method to find orthogonal matrices by using tensor products between two or more orthogonal matrices of real and imaginary numbers with applying it in images and communication signals processing. The output matrices will be orthogonal matrices too and the processing by our new method is very easy compared to other classical methods those use basic proofs. The results are normal and acceptable in communication signals and images but it needs more research works.

Find cares studying ways in the development of industrial products and designs: the way the progressive development (how typical) and root development (jump design), was the aim of the research: to determine the effectiveness of the pattern and the jump in the development of designs and industrial products. After a process of analysis of a sample of research and two models of contemporary household electrical appliances, it was reached a set of findings and conclusions including:1-leaping designs changed a lot of entrenched perceptions of the user on how the product works and its use and the size and shape of the product, revealing him about the possibilities of sophisticated relationships with the product, while keeping the typical desi

In this study, two types of mixes were adopted by using two grading of coarse aggregate. The practical side of this study was to produce no-fine aggregate concrete by using crushed clay brick aggregates. The durability of the produced concrete and internal sulfate attack was studied.      For durability assessment, it is found that the no-fine concrete made with crushed brick aggregate lost about (15-25) % of its compressive strength after being subjected to 60 cycles of wetting and drying with age 120 days. The curing condition showed that the water curing improved the compressive strength with a rate higher than that when sealed or air dry curing were used. The crushed brick no-fine concrete de

For a nonempty subset X of a group G and a positive integer m , the product of X , denoted by Xm ,is the set Xm = That is , Xm is the subset of G formed by considering all possible ordered products of m elements form X. In the symmetric group Sn, the class Cn (n odd positive integer) split into two conjugacy classes in An denoted Cn+ and Cn- . C+ and C- were used for these two parts of Cn. This work we prove that for some odd n ,the class C of 5- cycle in Sn has the property that = An n 7 and C+ has the property that each element of C+ is conjugate to its inverse, the square of each element of it is the element of C-, these results were used to prove that C+ C- = An exceptio