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 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

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 present work presents design and implementation of an automated two-axis solar tracking system using local materials with minimum cost, light weight and reliable structure. The tracking system consists of two parts, mechanical units (fixed and moving parts) and control units (four LDR sensors and Arduino UNO microcontroller to control two DC servomotors). The tracking system was fitted and assembled together with a parabolic trough solar concentrator (PTSC) system to move it according to information come from the sensors so as to keep the PTSC always perpendicular to sun rays. The experimental tests have been done on the PTSC system to investigate its thermal performance in two cases, with tracking system (case 1) and without trackin

The sculpture composing of iron materials is being considered most important raw material that has been used by the modern artist ,especially period of post –modernism. The works of the two artists ( SALIH AL-QARAGHULI and AHMED AL-BAHRANI) the most important works that entailed to be studied for being using iron material in most of their sculpturing works; in works of Al-Quraghuli, we find ores composing of iron wires , animals threads and remaining of trash and to be assembled in a sculptured text with unique style in Arab Home. Moreover, we find huge works of (al-Bahrani) represented into formations characterized with its ironic flexibility, its abstracted engineering forms. Al-Bahrani solely has used iron plates represented in its

   The research deals with the relationship between supplier evaluation (single variable) and family brand strategy (single variable) a case study in the battery factory\Al-Waziriya, and the fact that the industrial sector represents a cornerstone for building the country’s economy of and their development. The research has been selected on this basis. The problem stems from the lack of business understanding of the real role played by the assessment of the suppliers' and its strong impact on its reputation and position in the market. The research gains its importance by moving away from traditional marketing style in terms of characteristics related to the resource itself, and the service provided by the factory to c

Purpose – measure the relationship between operation management strategies as an independent variable on the customer's delight as an approved variable.

Design/methodology/approach – The research sample vocabulary included sales representatives and customers of the researched markets at a rate of (100%). The recovery rate is (95) Customers and (95) delegates for the products for the factory in neighbourhood (Banooks and Karrada ) regions were randomly chosen from an open community in these two residential areas. Statistical methods were used (arithmetic media, standard deviations, t-test,  correlation coefficient (Horst), simple regression analysis).

Findings – The people in charge of the factory management nee

Nano-crystalline iron oxide nanoparticles (magnetite) was synthesized by open vessel ageing process. The iron chloride solution was prepared by mixing deionized water and iron chloride tetrahydrate. The product was characterized by X-Ray, Surface area and pore volume by Brunauer-Emmet-Teller, Atomic Force Microscope (AFM) and Fourier Transform Infrared Spectroscopy(FTIR)  .  The results showed that the XRD in compatibility of the prepared iron oxide (magnetite) with the general  structure of standard iron oxide, and in Fourier Transform Infrared Spectroscopy, it is strong crests in 586 bands, because of  the expansion vibration manner related to the metal oxygen absorption band (Fe–O bonds in the crystals of iron ox

The possibility of using zero-valent iron as permeable reactive barrier in removing lead from a contaminated groundwater was investigated. In the batch tests, the effects of many parameters such as contact time between adsorbate and adsorbent (0-240 min), initial pH of the solution (4-8), sorbent dosage (1-12 g/100 mL), initial metal concentration (50-250 mg/L), and agitation speed
(0-250 rpm) were studied. The results proved that the best values of these parameters achieve the maximum removal efficiency of Pb+2 (=97%) were 2 hr, 5, 5 g/100 mL, 50 mg/L and 200 rpm respectively. The sorption data of Pb+2 ions on the zero-valent iron have been performed well by Langmuir isotherm model in compared with Freundlich model under the studied

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