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 this paper, Bayesian estimator for the parameter and reliability function of inverse Rayleigh distribution (IRD) were obtained Under three types of loss function, namely, square error loss function (SELF), Modified Square error loss function (MSELF) and Precautionary loss function (PLF),taking into consideration the  informative and non- informative  prior. The performance of such estimators was assessed on the basis of mean square error (MSE) criterion by performing a Monte Carlo simulation technique.

By use the notions pre-g-closedness and pre-g-openness we have generalized a class of separation axioms in topological spaces. In particular, we presented in this paper new types of regulαrities, which we named ρg­regulαrity and Sρg­regulαrity. Many results and properties of both types have been investigated and have illustrated by examples.

The main idea of this paper is to define other types of a fuzzy local function and study the advantages and differences between them in addition to discussing some definitions of finding new fuzzy topologies. Also in this research, a new type of fuzzy closure has been defined, where the relation between the new type and different types of fuzzy local function has been studied

   A comparison of double informative and non- informative priors assumed for the parameter of Rayleigh distribution is considered. Three different sets of double priors are included, for a single unknown parameter of Rayleigh distribution. We have assumed three double priors: the square root inverted gamma (SRIG) - the natural conjugate family of priors distribution, the square root inverted gamma – the non-informative distribution, and the natural conjugate family of priors - the non-informative distribution as double priors .The data is generating form three cases from Rayleigh distribution for different samples sizes (small, medium, and large). And Bayes estimators for the parameter is derived under a squared erro

In this paper, a robust adaptive sliding mode controller is designed for a mobile platform trajectory tracking.  The mobile platform is an example of a nonholonomic mechanical system. The presence of holonomic constraints reduces the number of degree of freedom that represents the system model, while the nonholonomic constraints reduce the differentiable degree of freedom. The mathematical model was derived here for the mobile platform, considering the existence of one holonomic and two nonholonomic constraints imposed on system dynamics. The partial feedback linearization method was used to get the input-output relation, where the output is the error functions between the position of a certain point on the platform

Students’ feedback is crucial for educational institutions to assess the performance of their teachers, most opinions are expressed in their native language, especially for people in south Asian regions. In Pakistan, people use Roman Urdu to express their reviews, and this applied in the education domain where students used Roman Urdu to express their feedback. It is very time-consuming and labor-intensive process to handle qualitative opinions manually. Additionally, it can be difficult to determine sentence semantics in a text that is written in a colloquial style like Roman Urdu. This study proposes an enhanced word embedding technique and investigates the neural word Embedding (Word2Vec and Glove) to determine which perfo

Extended calculations for sputtering yield through bombed Nickel – target by Xenon ions plasma are accomplished. The calculations include changing the input parameters: the energy of xenon ions plasma, the hit target angle of nickel target, thickness of the nickel target layer, and the slight change in the surface binding energy of Nickel. The program TRIM is used to accomplish these calculations. The results show that the sputtering yields directly dependent on these parameters. The change in angles of incidence plasma ions and energy leads to a significant change in the sputtering yields. On the other hand, the sputtering yields ore highly affected by changing target width and surface binding energy at fixed ion parameters.

In this research, the influence of the fermentation treatments and baking in Iraqi’s flour type (Ibaa 99, Al-rashed, Tamus, Abu-grabe) and Turkish flour type (Muaamel) on phytic acid was investigated. In whole wheat flour, the phytic acid was (1500, 1290, 1450, 1230, 1440 ( mg/ 100 g flour respectively, and the inorganic phosphorous was (29.18, 25.15, 23.89, 20.85, 22.83) mg/100 g flour respectively. The dough prepared from flour with a higher phytic acid content also contained higher amount of phytic acid. During fermentation, degradation of phytic acid occurred. The cumulative loss of phytic acid after fermentation in all type of dough was ~ 23, 22, 34, 26 and 27% respectively،While increased of inorganic phosphorous occurred. The c

Light naphtha one of the products from distillation column in oil refineries used as feedstock for gasoline production. The major constituents of light naphtha are (Normal Paraffin, Isoparaffin, Naphthene, and Aromatic). In this paper, we used zeolite (5A) with uniform pores size (5Aº) to separate normal paraffin from light naphtha, due to suitable pore size for this process and compare the behavior of adsorption with activated carbon which has a wide range of pores size (micropores and mesopores) and high surface area. The process is done in a continuous system - Fixed bed reactor- at the vapor phase with the constant conditions of flow rate 5 ml/min, temperature 180^oC, pressure 1.6 bar and 100-gram weight o