The discussion in this paper gives several theorems and lemmas on the Sums of Squares of consecutive Carol Numbers. These theorems are proved by using the definition of carol numbers and mathematical induction method. Here the matrix form and the recursive form of sum of squares of consecutive Carol numbers is also given. The properties of the Carol numbers are also derived.
words of God the Quranic text , is genera words have many faces and connotations a ccording to references, cutures and Ages.That the Quranic text is fixed , But the connotations are moveable the scientists agreed about the miracle of the Qurantic text , But they differd of the Position of miracLe including the muatazala and Al- Ashaira who have adopted the idea of sytem and miracle of linguistic . Most of them were lingustics, grammerians and writers as: AL- Jahith, AL- Faraa Abivbeida , Ibn kutaba , AL -Rumani , AL -katabi , AL- Bakilaai , AL- Gargani and Others.
They also differed in what the words of Allaah mean . Is the Quranic text creature or updated ,it is the issue that exhausted the effort.of muslim scientists though its imbo
The idea of a homomorphism of a cubic set of a KU-semigroup is studied and the concept of the product between two cubic sets is defined. And then, a new cubic bipolar fuzzy set in this structure is discussed, and some important results are achieved. Also, the product of cubic subsets is discussed and some theorems are proved.
In this contribution, density functional theory-based calculations have been carried out to assess the electronic, photocatalytic and optical properties of Ce1-xTixO2 system. Ti incorporation leads to a decrease of Ce 4f states and enhancement of Ti 3d states in the bottom of conduction band. Furthermore, it was found that doping ceria with Ti-like transition metals could evidently shift the absorption of pure CeO2 towards higher wavelength range. These findings can provide some new insights for designing CeO2-based photocatalysts with high photocatalytic performance. To the best of our knowledge, this investigation calculates Mullikan’s charge transfer of Ce1-xTixO2 system for the first time. Charge transfer reveals an ionic bond between
... Show Morehe dairy industry is one of the industrial activities classified within the food industries in all phases of the dairy industry, which leads to an increase in the amount of wastewater discharged from this industry. The study was conducted in the Abu Ghraib dairy factory, classified as one of the central factories in Iraq, located in the west of Baghdad governorate, with a design capacity of 22,815 tons of dairy products. The characteristics of the liquid waste generated from the factory were determined for the following parameters biological oxygen demand (BOD5), Chemical oxygen demand (COD), total suspended solids (TSS), pH, nitrate, phosphate, chloride, and sulfate with an average value of (1079, 1945, 323, 9.2, 24, 2
... Show MoreMeasurements of Hall effect properties at different of annealing temperature have been made on polycrystalline Pb0.55S0.45 films were prepared at room temperature by thermal evaporation technique under high vacuum 4*10-5 torr . The thickness of the film was 2?m .The carrier concentration (n) was observed to decrease with increasing the annealing temperature. The Hall measurements showed that the charge carriers are electrons (i.e n-type conduction). From the observed dependence on the temperature, it is found that the Hall mobility (µH), drift velocity ( d) carrier life time ( ), mean free path (?) were increased with increasing annealing temperature
Thermal conductivity of compacted bentonite is one of the most important properties where this type of clay is proposed for use as a buffer material. In this study, Lee's disc method was used to measure the thermal conductivity of compacted bentonite specimens. The experimental results have been analyzed to observe the three major factors affecting the thermal conductivity of bentonite buffer material. While the clay density reaches to a target value, the measurement is taken to evaluate the thermal conductivity. By repeating this procedure, a relationship between clay dry density and thermal conductivity has been established in specimens after adjusting the water contents of the bentonite by placing its specimens in a drying oven for diffe
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