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 monitoring weld quality is increasingly important because great financial savings are possible because of it, and this especially happens in manufacturing where defective welds lead to losses in production and necessitate time consuming and expensive repair. This research deals with the monitoring and controllability of the fusion arc welding process using Artificial Neural Network (ANN) model. The effect of weld parameters on the weld quality was studied by implementing the experimental results obtained from welding a non-Galvanized steel plate ASTM BN 1323 of 6 mm thickness in different weld parameters (current, voltage, and travel speed) monitored by electronic systems that are followed by destructive (Tensile and Bending) and non

Pollen morphology of 4 species (A. aucheri , A. auriculata, A. caucasica, A. nova) belonging to the genus Arabis L. in Iraq was examined by light microscope and scanning electron microscope to determine the significance of pollen features as a taxonomic characters. The results showed pollen grains of the species were monades, homopolar, tricolpate, and with medium size, but the species varied in shapes (polar and equatorial view), colpus length and width, exine thickness and exine ornamentation. Pollen colors were brown convert to brownish yellow.

The aim of this study is to estimate the parameters and reliability function for kumaraswamy distribution of this two positive parameter  (a,b > 0), which is a continuous probability that has many characterstics with the beta distribution with extra advantages.

The shape of the function for this distribution and the most important characterstics are explained and estimated the two parameter (a,b) and the reliability function for this distribution by using the maximum likelihood method (MLE) and Bayes methods. simulation experiments are conducts to explain the behaviour of the estimation methods for different sizes depending on the mean squared error criterion the results show that the Bayes is bet

The focus of this paper is the presentation of a new type of mapping called projection Jungck zn- Suzuki generalized and also defining new algorithms of various types (one-step and two-step algorithms) (projection Jungck-normal N algorithm, projection Jungck-Picard algorithm, projection Jungck-Krasnoselskii algorithm, and projection Jungck-Thianwan algorithm). The convergence of these algorithms has been studied, and it was discovered that they all converge to a fixed point. Furthermore, using the previous three conditions for the lemma, we demonstrated that the difference between any two sequences is zero. These algorithms' stability was demonstrated using projection Jungck Suzuki generalized mapping. In contrast, the rate of convergenc

Within connected speech, RP speakers tend to shorten stressed long vowels end diphthongs in pre. Forties consonants in the same syllable on the basis of complementary Distribution, i.e., the phonological environment decides the influence of the forties plosives and fricatives, as far as they are in find position preceded by stressed long vowels and diphthongs, or particular voiced consonants plus vowels. The Iraqi learners, then, face.

The progress of network and multimedia technologies has been phenomenal during the previous two decades. Unauthorized users will be able to copy, retransmit, modify reproduction, and upload the contents more easily as a result of this innovation. Malicious attackers are quite concerned about the development and widespread use of digital video. Digital watermarking technology gives solutions to the aforementioned problems. Watermarking methods can alleviate these issues by embedding a secret watermark in the original host data, allowing the genuine user or file owner to identify any manipulation. In this study, lots of papers have been analyzed and studied carefully, in the period 2011–2022. The historical basis of the subject shou

Raising children occupies a prominent place in Islam as a step paving the way for the success of reform projects on the level of diverse human life, and for this reason the recommendation for education was mentioned in the mission entrusted to the Prophet (PBUH), the Almighty said:

(( هُوَ الَّذِي بَعَثَ فِي الْأُمِّيِّينَ رَسُولًا مِّنْهُمْ يَتْلُو عَلَيْهِمْ آيَاتِهِ وَيُزَكِّيهِمْ وَيُعَلِّمُهُمُ الْكِتَابَ وَالْحِكْمَةَ وَإِن كَانُوا مِن قَبْلُ لَفِي ضَلَالٍ مُّبِينٍ))  Jumaa verse /38

The topic of the research that is in your hands deals with the