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

          Whatever forms embodied in nature or in the product by forming elements, Kahadjom, fonts, and colors that characterized that her aesthetic and expressive values ​​evoked to multiple indications of which are unequivocal, including what is iconic. Each one of these constituent elements of her form of extreme importance

Require senior management of the state when developing the strategy the general budget to the clarity of the reasons that are based upon the ministries in the preparation of estimates of expenditure for the next year to justify the spending, and in the absence of targets, the ministry or government unit would not be in front, but be guided by the size of expenditure for the last year in addition to the percentage of represented an increase of appropriations required for the next year in light of the fiscal policy of the state, so the requested increase in appropriations to meet the desired increase in some of its activities and to meet the increase in salaries and prices. So must be available to the Ministry of criteria that coul

Aim: The current study was aimed to determine the relationship between the orthodontic force applied by monobloc and the salivary level of alkaline phosphatase (ALP) and lactate dehydrogenase (LDH) enzymes, considering the time factor after insertion of the appliance and whether there is a correlation between these enzymes. Materials and methods: A sample of 28 growing patients requiring orthodontic treatment with myofunctional appliance (Monoblock) was taken for the current study with an age range 9 to 12 years,all patients had Angle's class II division 1 malocclusion with no or mild crowding, the sample was selected using simple random sampling. Only 16 subjects (10 males and 6 females) were included who follow certain inclusion criteria.

This work presents a five-period chaotic system called the Duffing system, in which the effect of changing the initial conditions and system parameters d, g and w, on the behavior of the chaotic system, is studied. This work provides a complete analysis of system properties such as time series, attractors, and Fast Fourier Transformation Spectrum (FFT). The system shows periodic behavior when the initial conditions xi and yi equal 0.8 and 0, respectively, then the system becomes quasi-chaotic when the initial conditions xi and yi equal 0 and 0, and when the system parameters d, g and w equal 0.02, 8 and 0.09. Finally, the system exhibits hyperchaotic behavior at the first two conditions, 0 and 0, and the bandwidth of the chaotic

This research addresses a problem manifested in a main question: what is the role of the digital media in marketing the artistic products? in order to determine the role played by the digital media in  the disclosure and promotion of  the artistic product, its price and places of distribution, as the basic elements of the marketing mixture. 

                This is a descriptive research in which the researcher used the survey method to check the opinions of a sample chosen according to the (proportion) method from the research community represented by instructors and students of the college of Fine Arts- University of Dayala. 

P. aeruginosa is a famous bacterium that causes several diseases and has a high ability to be a multidrug resistant organism that is linked with the formation of biofilm. This study aimed to investigate tssC1 gene role in the resistance of different antibiotics in the presence of biofilm. We constructed biofilm for the isolates under the study and showed the effect of different antibiotics on biofilm formation and maturation. The presence of the gene was detected through achieving PCR reaction. Finally, tssC1 gene variation was determined through sequencing and aligning the sequencing products. The results showed that most of the isolates (80%) formed biofilm that played a role in the resistance of different antibiotics which could

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

The main aim of this paper is to introduce the concept of a Fuzzy Internal Direct Product of fuzzy subgroups of group . We study some properties and prove some theorems about this concept ,which is very important and interesting of fuzzy groups and very useful in applications of fuzzy mathematics in general and especially in fuzzy groups.