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.
Background: With the increased in the demands of adult orthodontics, the challenge of direct bonding to non-enamel surface (zirconium) had been increased. The present study was carried out to compare the shear bond strength of three different brackets (stainless steel, sapphire and composite) bonded to zirconium surface and study the mode of bond failure. Materials and methods: The sample was comprised of 30 models (8mm *6mm*1.5mm) of full contour zirconium veneers. They were divided into three groups according to the brackets type; all samples were treated first by sandblast with aluminum oxide particle 50 µm then coated by z-prime plus primer. A central incisor bracket of each group was bonded to the prepared zirconium surface with lig
... Show MoreBackground: This study was done to assist X-ray diffraction and biocompatability of glass ionomer cement reinforced by different ratios of Hydroxyapatite. Materials and Methods: The powder of glass ionomer cement reinforced by different ratios of Hydroxyapatite were used to get X-ray diffraction pattern by X-ray diffraction machine, While for biocompatibility test, A polyethylene tubes containing glass ionomer cement reinforced by different ratios of Hydroxyapatite were implanted on the dorsal submucosal site of Rabbit's tissues and histological slide were prepared for histopathological study. Results: X-ray diffraction test showed that all elements of glass ionomer cement reinforced by different ratios of Hydroxyapatite were react with eac
... Show MoreABSTRACT : A new ligand [ 2- (3-acetylthioureido)-3-phenylpropanoic acid (APA) is synthesized by reaction of acetyl isothiocyanate with phenylalanine (1:1). It is characterized by micro elemental analysis (C.H.N.S.), FT-IR, (UV-Vis) and 1H and 13CNMR spectra. Some metals ions complexes of this ligand were prepared and characterized by FT-IR, UV-Visible spectra, conductivity measurements, magnetic susceptibility and atomic absorption. From results obtained, the following formula [M(APA)2] where M2+ = Mn, Co, Ni, Cu, Zn, Cd and Hg, the proposed molecular structure for these complexes as tetrahedral geometry, except copper complex is has square planer geometry.
Radiation treatment has long been the conventional approach for treating nasopharyngeal cancer (NPC) tumors due to its anatomic features, biological characteristics, and radiosensitivity. The most common treatment for nasopharyngeal carcinoma is radiotherapy. This study aimed to assess the better quality of radiotherapy treatment techniques using intensity-modulated radiotherapy (IMRT) and volumetric-modulated arc therapy (VMAT). The VMAT and IMRT are comparative techniques. Forty patients with nasopharyngeal carcinoma and forwarded for radiotherapy were treated with both advanced techniques, IMRT and VMAT, using eclipse software from Varian. The x-ray energy was set at 6 MV. The total prescribed dose was 70 Gy. The results show that the
... Show MoreIn this research, a group of gray texture images of the Brodatz database was studied by building the features database of the images using the gray level co-occurrence matrix (GLCM), where the distance between the pixels was one unit and for four angles (0, 45, 90, 135). The k-means classifier was used to classify the images into a group of classes, starting from two to eight classes, and for all angles used in the co-occurrence matrix. The distribution of the images on the classes was compared by comparing every two methods (projection of one class onto another where the distribution of images was uneven, with one category being the dominant one. The classification results were studied for all cases using the confusion matrix between every
... Show MoreThis study presents certain modifications done to the conditions set by Searle
(1969: 57) concerning the speech act of promising in order to render them to selected
sayings of Prophet Muhammad (P.B.U.H.) and Jesus Christ (P.B.U.H.) and to
political texts. These modifications make the conditions of the speech act of
promising appropriate for sincere promises made by the Messengers of God since
they deliver their Messages of God but they are unable, as Messengers, to fulfill
God’s promises which they make as part of their Messages and by representatives of
States who deliver speeches on behalf of their Governments. These are the only two
situations where the speakers can make promises and do not fulfill these prom
The effect of metal nanoparticles on the anaerobic digestion of sludge and the sludge bacterial community are still not well-understood, and both improvements and inhibitions have been reported. This study investigated the impact of 2, 10, and 30 mg/g TS silver and copper oxide nanoparticles (AgNPs and CuONPs) on the mesophilic anaerobic digestion of sludge and the bacterial community structure. The reactors were monitored for changes in tCOD, sCOD, TS, VS, biogas generation, and cell viability. Also, the relative abundance and taxonomic distribution of the bacterial communities were analyzed at the phylum and genus levels, including the genera involved in anaerobic digestion. Both AgNPs and CuONPs exhibited some inhibition on anaer
... Show MoreBackground: Denture cleansing was an important step that could prevent the spread of infection and improve a patient's health, the durability of the dentures, and the overall quality of life; therefore, it was necessary to choose a suitable cleanser that, in addition to being effective, did not have an unfavorable effect on the qualities of the denture base resin itself when used for an extended period. For this purpose, this study aimed to evaluate the effect of tea tree oil (TTO) on Candida albicans adhesion and the surface roughness property of poly(methyl methacrylate) denture material after immersion in TTO. Methods: A total of 55 heat-cured acrylic resin specimens were used for C. albicans adherence and surface roughness tests. The
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