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

Background: The type of dental implant surface is one of many factors that determine the success of implant restoration. This study aimed to study the effect of mixture of nano titanium oxide with nanohydroxyapatite coating of screw shaped CPTi dental implant on bond strength at bone implant interface by torque removal test related to two healing periods (2 and 6 weeks). Materials and methods: Dip coating process was performed to get an even coating layer on CPTi screws. X-ray diffraction (XRD) analysis and microscopical examination were performed on the coating surfaces of the CPTi. The tibia of 10 white New Zealand rabbits was chosen as implantation sites. The tibia of each rabbit received two screws, one was coated with mixture of nanoT

Objective This study evaluated the effects of adding titanium oxide (TiO2) nanofillers on the tear strength, tensile strength, elongation percentage, and hardness of room-temperature-vulcanized (RTV) VST50F and high-temperature-vulcanized (HTV) Cosmesil M511 maxillofacial silicone elastomers. Methods Two types of maxillofacial elastomers, VST50F RTV and Cosmesil M511 HTV, were used. Nano-TiO2 powder was applied as a nanofiller. A total of 120 specimens were fabricated, 60 each of VST50F and Cosmesil M511. The specimens of each type of elastomer were divided into three equal groups on which tests were conducted for tear strength, tensile strength, and hardness i.e., 20 specimens were used for each test. Each group of 20 specimens was further

Concerns about the environment, the cost of energy, and safety mean that low-energy cold-mix asphalt materials are very interesting as a potential replacement for present-day hot mix asphalt. The main disadvantage of cold bituminous emulsion mixtures is their poor early life strength, meaning they require a long time to achieve mature strength. This research work aims to study the protentional utilization of waste and by-product materials as a filler in cold emulsion mixtures with mechanical properties comparable to those of traditional hot mix asphalt. Accordingly, cold mix asphalt was prepared to utilize paper sludge ash (PSA) and cement kiln dust (CKD) as a substitution for conventional mineral filler with percentages ranging fro

Microencapsulated of paraffin wax which acts as core material of phase change
material covered by polymer was prepared by using rabid (physical-chemical) with lower
energy (green) method. Prepolymer of condensed Melamine-Formaldehyde resin, was
solidified by heat effect gradually and surrounds the Paraffin wax as microcapsules. The
diameter of the prepared capsules was about (170-220) micron which has a proportion with
the prepolymer temperature, otherwise the thermal analysis appears as a best value of
enthalpy (ΔH) which was (12 J/gm) when the prepolymer temperature was (60˚C)

   A reseach is carried out by using Alumina material type α-Al2O3 which has partical size 63μm doped with different percentage weight of MgO (0.1%,0.3%and0.5%) and by using dry press method to prepare the samples ,A force press 50KN used and sintering to 1500oC with   soaking time  of  6 hours.        The physical properties were studied such as "Bulk density ,Porosity and water absorption "also the mechanical properties such as (hardness,compressive strength ), the result shows that the best ratio of maginsa(MgO) added to Alumina (Al2O3)is 0.5%and this  worked to improve   Physical and mechanical properties .

An in-depth experimental study of the matrix effect of antifreeze (ethylene glycol) and water contamination of engine oil through FT-IR spectroscopy. With a comparison of the percent by volume concentration of contaminated fresh 15W-40 engine oil, there appeared to be a noticeable reduction in the O–H stretching signal in the infrared spectrum when ethylene glycol based antifreeze was included as a contaminant. The contaminants of distilled water, a 50/50 mixture of water and commercial ethylene glycol antifreeze, and straight ethylene glycol antifreeze were compared and a signal reduction in the O–H stretch was clearly evident when glycol was present. Doubling the volume of the 50/50 mixture as compared to water alone still res

This paper presents a research for magnetohydrodynamic (MHD) flow of an incompressible generalized Burgers’ fluid including by an accelerating plate and flowing under the action of pressure gradient. Where the no – slip assumption between the wall and the fluid is no longer valid. The fractional calculus approach is introduced to establish the constitutive relationship of the generalized Burgers’ fluid. By using the discrete Laplace transform of the sequential fractional derivatives, a closed form solutions for the velocity and shear stress are obtained in terms of Fox H- function for the following two problems: (i) flow due to a constant pressure gradient, and (ii) flow due to due to a sinusoidal pressure gradient. The solutions for

This paper interest to estimation the unknown parameters for generalized Rayleigh distribution model based on censored samples of singly type one . In this paper the probability density function for generalized Rayleigh is defined with its properties . The maximum likelihood estimator method is used to derive the point estimation for all unknown parameters based on iterative method , as Newton – Raphson method , then derive confidence interval estimation which based on Fisher information matrix . Finally , testing whether the current model ( GRD ) fits to a set of real data , then compute the survival function and hazard function for this real data.

This paper including a gravitational lens time delays study for a general family of lensing potentials, the popular singular isothermal elliptical potential (SIEP), and singular isothermal elliptical density distribution (SIED) but allows general angular structure. At first section there is an introduction for the selected observations from the gravitationally lensed systems. Then section two shows that the time delays for singular isothermal elliptical potential (SIEP) and singular isothermal elliptical density distributions (SIED) have a remarkably simple and elegant form, and that the result for Hubble constant estimations actually holds for a general family of potentials by combining the analytic results with data for the time dela