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 research، a comparison has been made between the robust estimators of (M) for the Cubic Smoothing Splines technique، to avoid the problem of abnormality in data or contamination of error، and the traditional estimation method of Cubic Smoothing Splines technique by using two criteria of differentiation which are (MADE، WASE) for different sample sizes and disparity levels to estimate the chronologically different coefficients functions for the balanced longitudinal data which are characterized by observations obtained through (n) from the independent subjects، each one of them is measured repeatedly by group of  specific time points (m)،since the frequent measurements within the subjects are almost connected an

Nonlinear time series analysis is one of the most complex problems ; especially the nonlinear autoregressive with exogenous variable (NARX) .Then ; the problem of model identification and the correct orders determination considered the most important problem in the analysis of time series . In this paper , we proposed splines  estimation method for model identification , then we used three criterions for the correct orders determination. Where ; proposed method used to estimate the additive splines for model identification , And the rank determination depends on the additive property  to avoid the problem of curse dimensionally . The proposed method is one of the nonparametric methods , and the simulation results give a

In this paper, 3D simulation of the global coronal magnetic field, which use observed line of sight component of the photosphere magnetic field from (MDI/SOHO) was carried out using potential field model. The obtained results, improved the theoretical models of the coronal magnetic field, which represent a suitable lower boundary conditions (Bx, By, Bz) at the base of the linear force-free and nonlinear force free models, provides a less computationally expensive method than other models. Generally, very high speed computer and special configuration is needed to solve such problem as well as the problem of viewing the streamline of the magnetic field. For high accuracy special mathematical treatment was adopted to solve the computation comp

 In this study, we derived the estimation for Reliability of the Exponential distribution based on the Bayesian approach. In the Bayesian approach, the parameter of the Exponential distribution is assumed to be random variable .We  derived  posterior distribution the parameter of the Exponential distribution under four types priors distributions for the scale parameter of the Exponential distribution is: Inverse Chi-square distribution, Inverted Gamma distribution, improper distribution, Non-informative distribution. And the estimators for Reliability is obtained using the two proposed loss function in this study which is based on the natural logarithm for Reliability function .We used simulation technique, to compare the

This study we have made a subject of fanny podcast in electronic media, as a new way to express different issues by the public, This study focuses started on how to address social issues in Alegria by ANAS TINA vidéo on the youtube network , you are to know the trends of young amateur about the various issues dealt with as well as the most important methods used to convince browsers.
The researcher used the survey method based on studying 10 episodes videos of blogger ANAS TINA.
The result of the study found that the most important issues are the abduction of children, teaching in Algeria; women in Algeria, The negative aspects of the issues addressed have been established in order to direct public opinion and awareness of ph

The purpose of this article is to improve and minimize noise from the signal by studying wavelet transforms and showing how to use the most effective ones for processing and analysis. As both the Discrete Wavelet Transformation method was used, we will outline some transformation techniques along with the methodology for applying them to remove noise from the signal. Proceeds based on the threshold value and the threshold functions Lifting Transformation, Wavelet Transformation, and Packet Discrete Wavelet Transformation. Using AMSE, A comparison was made between them , and the best was selected. When the aforementioned techniques were applied to actual data that was represented by each of the prices, it became evident that the lift

This paper deals with an analytical study of the flow of an incompressible generalized Burgers’ fluid (GBF) in an annular pipe. We discussed in this problem the flow induced by an impulsive pressure gradient and compare the results with flow due to a constant pressure gradient. Analytic solutions for velocity is earned by using discrete Laplace transform (DLT) of the sequential fractional derivatives (FD) and finite Hankel transform (FHT). The influences of different parameters are analyzed on a velocity distribution characteristics and a comparison between two cases is also presented, and discussed in details. Eventually, the figures are plotted to exhibit these effects.

The current study aims to compare between the assessments of the Rush model’s parameters to the missing and completed data in various ways of processing the missing data. To achieve the aim of the present study, the researcher followed the following steps: preparing Philip Carter test for the spatial capacity which consists of (20) items on a group of (250) sixth scientific stage students in the directorates of Baghdad Education at Al–Rusafa (1^st, 2^nd and 3^rd) for the academic year (2018-2019). Then, the researcher relied on a single-parameter model to analyze the data. The researcher used Bilog-mg3 model to check the hypotheses, data and match them with the model. In addition