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: Radiation therapy reported to be an effective in palliating pain. Objective: To describe roles of palliative radiotherapy in controlling pain in metastatic cancerous patients, and evaluation of radio-therapy doses in pain management. Methods: A prospective observational study carried out at the Baghdad Radiotherapy and Nuclear Medicine Center/Baghdad Medical City Complex, Baghdad, Iraq, from 1st of December 2018 to 30th of May 2019. 88 Patients, were included. Patients were assessed before applying radiotherapy, and at the end of treatment. Pain scoring used from 0 to 10. Kaplan Meier survival curve used. Result: The mean±SD of age was 55.44±11.1 years, and the most frequent age group was 41-50years as 37(42.1%). Breas
... Show MoreThe digital dermatoglyphics were studied in 120 females derived from northern region of Iraq (60 Arabs and 60 Kurds). Two kinds of analyses were perfomed : Quantitative and Qualtative. The unilateral and bilateral analyses for dermal ridge counts in each digital and the overall did not reveal any significant difference when t-test was used. A high correlation coefficients were revealed in this study between homologous and adjacent digits, moreover, significant differences were revealed between Arabian and Kurdish samples in both analyses when Fisher Z transform test was used, but the significant differences in the bilateral analysis exceed the ones in the unilateral. This indicates the importance of the former analysis in detecting the vari
... Show MorePorcelain is one of the most important ceramic materials with a wide range of traditional and technical applications. Since most mixtures of porcelain have a high sintering temperature, bentonite has been added in this research to improve the characteristics of sintering and burning. The porcelain mixture consisted of the following Iraqi raw materials: 30% wt kaolin, 30 wt% non-plastic clay (grog), 10% wt sodium feldspar, 10 wt% potassium feldspar and 20 wt% flint. After the mechanical mixing process and transfer the powder mixture to the slurry by adding distilled water, then different weight percentage of the sodium bentonite(0, 2.5, 5, 7.5 and 10) wt% was added. The specimens were prepared by using the solid casting m
... Show Morein this paper the second order neutral differential equations are incestigated are were we give some new suffucient conditions for all nonoscillatory
In this paper, a sufficient condition for stability of a system of nonlinear multi-fractional order differential equations on a finite time interval with an illustrative example, has been presented to demonstrate our result. Also, an idea to extend our result on such system on an infinite time interval is suggested.
In Libya, there are multiple sources of pollution, one of which is animal waste. The anaerobic digestion (AD) of organic wastes to produce biogas has the advantage of producing valuable, renewable energy while reducing the environmental impact of these wastes. Cowmanure have the potential to produce biogas due to their high organic content. This study aimed to study different concentrations for the feedstock (1:1 and 2:1 cow manure: water v/v) to monitor which one gives higher biogas production. A plastic tank with a capacity of 72 liters and a feedstock volume of 60 liters was used to create a pilot scale. The biogas was analyzed using a GC device at the end of the experiment in the Zawiya Oil Refining Company. The result indicated that th
... Show MoreBackground: The Titanium and its alloys are suitable for dental implant and medical applications. Biocompatibility of the materials is a major factor in determining the success of the implant and has a great impact on their rate of osseointegration. The aim of this study was to evaluate the biocompatibility and cytotoxicity of Ti2AlC in comparison to CPTi & Ti6Al7Nb in rabbits. Materials and Methods: 10 male New Zealand White rabbits, weighing (2-2.5 kg), aged (10-12 months) were used in this study. Cylindrical implants were prepared from the study materials (CPTi, Ti6Al7Nb and Ti2AlC) with (8mm) height and (3mm) diameter for the evaluation of tissue response and disc specimens were prepared with (6 mm) diameter and (2 mm) thickness for ev
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