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 complexes of para-chloranil as electron acceptor and the anions of amide, azide and cyanide as electron donors in aqueous ethanol as a solvent, were studied spectrophotometrically .     The reactions lead to the formation of charge transfer complexes. The CT complexes were stable in excess acceptor concentration, while they were underwent another transformations in excess donors concentrations.   Stoichiometries were determined, the molecular ratio was determined by continuous variation method (Job method) and is was  1:1 (donor: acceptor).   The maximum wavelength (λ max.), the energy (hÏ…CT), ionization potential (Ip) and activation energy (w ) of excited state f

This paper presents a comparison study on thermal performance conic cut twist tape inserts in laminar flow of nanofluids through a constant heat fluxed tube. Three tape configurations, namely, quadrant cut twisted tape (QCT), parabolic half cut twisted tape (PCT), and triangular cut twisted (VCT) of twist ratioy= 2.93 and cut depthde= 0.5 cm were used with 1% and 2% volume concentration of SiO₂/water and TiO

n this research, some thermophysical properties of ethylene glycol with water (H2O) and two solvent mixtures dimethylformamide/ water (DMF + H2O) were studied. The densities (ρ) and viscosities (η) of ethylene glycol in water and a mixed solvent dimethylformamide (DMF + H2O) were determined at 298.15 K, t and a range of concentrations from 0.1 to1.0 molar. The ρ and η values were subsequently used to calculate the thermodynamics of mixing including the apparent molar volume (ϕv), partial molar volume (ϕvo) at infinite dilution. The solute-solute interaction is presented by Sv results from the equation ∅_v=ϕ_v^o+S_v √m. The values of viscosity (B) coefficients and Falkenhagen coefficient(A) of the Jone-Dole equation and Gibbs free

This work studies the impact of input machining parameters of Electrical Discharge Machining (EDM) on the machining process performance. Tool steel O1 was selected as the workpiece material, copper as the electrode material, and kerosene as the dielectric medium. Experimental runs have been carried out with a Design of Experiment (DOE) technique. Twenty tests are accomplished with the current range of (18 to 24 Ampere), a pulse duration range of (150 to 200 µs), and a pulse-off time range of (25 to 75 µs). Based upon the experimental study's output results, the EDM parameter's effect (voltage of power supply, discharge current, pulse duration, and pulse pause interval) on the responses of the process represented by sur

The operating characteristics of optoelectronic devices depend critically on the properties physical of the constituent materials, interesting compound has been focused on this research formed from group III and V of the periodic table. Thin film n-InSb heterjuntion were successfully fabricated on p-Si substrates by thermal evaporation technique at different annealing temperature (as prepared, 400,500,600) °C. The effect of annealing temperature on the structural, surface morphology, optical and optoelectronic properties of InSb films were investigated and studied. The crystal structure of the film was characterized by X-ray diffraction and techniques. AFM techniques inspect the surface morphology of InSb films, the study presented the val

The synthesis of zeolite NaX from locally available kaolin has been studied. The operating conditions for zeolite NaX production from kaolin with good crystallinity were as follows; a gel formation step of metakaolin in alkaline medium in presence of additional silica to crystallize the zeolite was achieved at 60 oC for 1 hr,and with stirring. In ageing step of the reactants at room temperature for 5 days and crystallization step at 87±2 oC for 24 hr. The catalytic activity of catalyst prepared from local kaolin was studied by using cumene cracking as a model for catalytic cracking and compared with standard HY zeolite and HX zeolite catalysts. The activity test was carried out in a laboratory continuous flow unit with fixed bed reactor

Three strain of Bacillus cereus were obtained from soil sours Laboratories of Biology Department/ College of Science/ University of Baghdad. The bacteria secreted extracellular xylanase in liquid cultur the test ability of xylanase production from these isolates was studied semi quantitative and quantitative screening appeared that Bacillus cereus X3 was the highest xylanase producer. The enzyme was partial purification 191 fold from cultur by reached step by 4 U/mg proteins by ammonium sulfat precipitation 80%, Ion exchang DEAE-cellulos chromatography Characterization study of the partial purifation enzyme revealed that the enzyme had a optimum activity pH8 and activity was stable in the pH rang (8-10) for 30min. maximal activity was attai

In this study, detection of uricase production from Pseudomonas aeruginosa
isolates was done by applying colorimetric method, Uricase was purified from the
most potent isolate by precipitation using ammonium sulphate (80% saturation) then
purification was achieved using DEAE –Cellulose ion exchange and Sepharose 6B
gel filtration chromatography column, 16.4% of total enzyme was recovered with
specific activity 2337.5U/mg and 22.21folds of purification. Characterization of
uricase involved detection of optimal conditions for uricase activity, the maximal
activity was obtained at temperature 45ºC,while uricase appeared to be stable at
40ºC. Uricase showed optimal activity at pH 9 while pH stability was in the

The presence of alkaloids in Crassula ovata is a topic that is still unexplored, as there are no published studies on the matter. This study demonstrates the presence of an alkaloid compound (and its class) for the first time in Crassula ovata. The plant material was defatted with n-hexane, and a Soxhlet apparatus was used for the extraction process, while the acid-base method was used for the isolation of alkaloids from the chloroform fractions. The quaternary alkaloid was precipitated from the aqueous layer spontaneously, in high quantity. By using standard spectroscopic methods (including liquid chromatography - mass spectroscopy) we were able to clarify the structure of the precipi¬tated compound as a tetrahydroprotoberberine a