In This paper, we have been approximated Grűnwald-Letnikov Derivative of a function having m continuous derivatives by Bernstein Chlodowsky polynomials with proving its best approximation. As well as we have been solved Bagley-Torvik equation and Fokker–Planck equation where the derivative is in Grűnwald-Letnikov sense.
Background: The potential use of zinc oxide and other metal oxide nanoparticles in biomedical are gaining interest in the scientific and medical communities, largely due to the physical and chemical properties of these nanomaterials. The present work revealed the effect of zinc oxide nanoparticles (ZnONPs) on the total salivary peroxidase enzyme activity of human saliva in comparison to de-ionized water. Materials and methods: Forty eight unstimulated saliva samples were collected from dental students/University of Baghdad 18-22 years. Then measure the total salivary peroxidase activity first without any addition to human saliva as a control, second with dilution the saliva with de-ionized water, and third with zinc oxide nanoparticles in c
... Show MoreBackground: 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 MoreThe technique of plant tissue culture has been used to In vitro micropropagation of Spilanthes acmella (L.) Murr. It is an ornamental and medicinal plant not cultivated in Iraq. Seeds were sterilized and cultuared on full strength Murashige and Skoog medium(1962)(MS). Naphthalene acetic acid (NAA), 6- furfuryl aminopurine (Kin.) growth regulators were used at the Initiation stage.The combination between IAA and Kin. was used in multiplication stage. IAA was used for rooting the shoots. Results showed that 1.5% sodium hypochlorite for 15 min was very effective for disinfecting and survival. Nodes exhibited relatively highest response as compared with apical meristems and leaflets culture. Supplying the culture medium with 1 mg/L.
... Show MoreAn acidic environment causes surface changes of resin composites. Filler particlesize and filler distribution also have a direct effect on these surface changes. This invitro study evaluated the influence of Pepsi Cola drink on the surface roughness ofComposan LCM and Composan Ceram over time. Sixteen disc shaped specimens(10mm diameter, 2mm thickness) of each resin composite were fabricated, therebyforming two groups (n= 8). Surface roughness (Ra) was analyzed after 24 hrs beforeexposure to beverage. The specimens were submitted to a five minutes immersion inPepsi Cola three times daily interrupted by immersion in deionized distilled water (37C˚). Surface roughness measurements were done at 10, 30, and 60 days intervals. Datawere
... Show MoreBackground: The aims of the study were to evaluate the unclean/clean root canal surface areas with a histopathological cross section view of the root canal and the isthmus and to evaluate the efficiency of instrumentation to the isthmus using different rotary instrumentation techniques. Materials and Methods:The mesial roots of thirty human mandibular molars were divided into six groups, each group was composed of five roots (10 root canals)which prepared and irrigated as: Group one A: Protaper system to size F2 and hypodermic syringe, Group one B: Protaper system to size F2 and endoactivator system, Group two A:Wave One small then primary file and hypodermic syringe, Group two B:Wave One small then primary file and endoactivator system, Gr
... Show MoreIn 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.
The purpose of this study was to evaluate the epidemiological characteristics of the mandibular fractures relating to gender, age, the etiology of injury, and the rendered treatment modalities and complications. The data of the patients who sustained mandibular fractures were retrieved and were analyzed retrospectively, and based on these data a descriptive analysis was conducted. A total of 112 patients were included in this study; the most common cause was road traffic accidents (RTAs) followed by assaults and missile injuries. The most frequently involved age group was 11 to 20 years, treatment modalities included conservative, closed reduction and indirect fixation, and open reduction and internal fixation (ORIF) in 11.6, 79.5, and 8.9%
... Show MoreIn the 20th century, the concept of "sarcasm" has relatively prevailed, and in this sense, it is a method in the art of conversation that wants to keep the question about the intended meaning, that is, "saying something and suggesting its opposite."
There are other concepts that indicate that sarcasm is saying something in a way that provokes the recipient of the statement an infinite number of different interpretations, with multiple readers of different interpretations. While the philosophy of irony stands by the standards of things, exaggeration or minimization, this manipulation takes place within the enjoyment. However, it's a method to present sharp criticism in an atmosphere of criticism that differs from generation to gener
We investigate mathematical models of the Hepatitis B and C viruses in the study, considering vaccination effects into account. By utilising fractional and ordinary differential equations, we prove the existence of equilibrium and the well-posedness of the solution. We prove worldwide stability with respect to the fundamental reproduction number. Our numerical techniques highlight the biological relevance and highlight the effect of fractional derivatives on temporal behaviour. We illustrate the relationships among susceptible, immunised, and infected populations in our epidemiological model. Using comprehensive numerical simulations, we analyse the effects of fractional derivatives and highlight solution behaviours. Subsequent investigatio
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