The Caputo definition of fractional derivatives introduces solution to the difficulties appears in the numerical treatment of differential equations due its consistency in differentiating constant functions. In the same time the memory and hereditary behaviors of the time fractional order derivatives (TFODE) still common in all definitions of fractional derivatives. The use of properties of companion matrices appears in reformulating multilevel schemes as generalized two level schemes is employed with the Gerschgorin disc theorems to prove stability condition. Caputo fractional derivatives with finite difference representations is considered. Moreover the effect of using the inverse operator which transmit the memory and hereditary effects to other terms is examined. The theoretical results is applied to a numerical example. The calculated solution has a good agreement with the exact solution.
The plant licorice is considered important plants as nutritionally and medically and economically, as a rich in phytochemical, vitamins and minerals, and being widely available, Research indicated the presence of many nutrients such as (proteins, Carbohydrates, vitamins and minerals) as well as presence of Glycyrrhizin which responsible of sweet taste, that allowing the possibility to use it as natural intensity sweetener with few calories in Sweetening of many food. This research is aimed to study the Stability of Glycyrrhizin toward the various manufacturing conditions such as (thermal treatment, pH of foods and microwaves), so three factorial experiments was implemented to find out the Stability as following: 100C° - 121C° - Microwa
... Show MoreThe optimum conditions for production of fibrinolytic protease from an edible mushroom Pleurotus ostreatus grown on the solid medium , Sus medium, composed of Sus wastes (produced from extracted medicinal plant Glycyrrhiza glabra) were determined. Addition of 5% of Soya bean seeds meal in Sus medium recorded a maximum fibrinolytic protease activity resulting in 7.7 units / ml. The optimum moisture content of Sus medium supplemented with 5% Soya bean seeds meal was 60% resulting in 7.2 units / ml.Pleurotus ostreatus produced a maximum fibrinolytic protease activity when the spawn rate,pH of medium and incubation temperature were 2,6 and 30°C, respectively. The maximum fibrinolytic protease activity was 7.6 units / ml when incubat
... Show MoreThe main goal of the current research is to know -Environmental problems included in the content of the two science books (chemistry units) for intermediate stage
A list of environmental problems had been prepared and consisting of (8) main areas which are (air and atmosphere pollution, water pollution, soil pollution, energy, disturbance of biodiversity and environmental balance, waste management, food and medicinal pollution, investment of mineral wealth). Of which (60) sub-problems, at that time the researcher analyzed the two science books (two chemistry units) for the intermediate stage of the academic year (2020-2021) in light of the list that was prepared, and the validity and consisten
... Show MoreThe effect of applied current on protection of carbon steel in 0.1N NaCl solution (pH=7) was investigated under flow conditions (0-0.262 m/s) for a range of temperatures (35-55°C) using rotating cylinder electrode. Various values of currents were applied to protect steel from corrosion, these were Iapp.=Icorr., Iapp.=2Icorr. and Iapp.=2.4Icorr. under stationary and flow conditions. Corrosion current was measured by weight loss method. The variation of protection potential with time and rotation velocity at various applied currents was assessed. It is found that the corrosion rate of carbon steel increases with rotation velocity and
has unstable trend with temperature. The protection current required varies with temperature and it inc
This paper presents an investigation to the effect of the forming speed on healing voids that inhabit at various size in an ingot. The study was performed by using finite element method with bilinear isotropic material option, circular type voids were considered. The closure index was able to predict the minimum press force necessary to consolidate voids and the reduction. The simulation was carried out, on circular cross-section lead specials containing a central void of different size. At a time with a flat die, different ratio of inside to outside radius was taken with different speed to find the best result of void closure.
The stories of children in Iraq during the past two decades have received a number of important scientific studies. Despite tyranny of the historical study method on most of these studies, they have been and still are very important, because they have established a chronicle of this literary style that has been neglected and based not only on the academic level and serious in-depth university studies but also on the enclosed sight that doesn’t consider studied art as an innovation with its specificity and its typical technical components. While many of the public impressions and self-reflections contributed to the dominance of some of the provisions and concepts that were circulated as critical remarks and adopted by som
... Show MoreWith occurrence of any financial crises, regardless at global or regional levels such as the great economic crises during 1929 – 1933 and the Asian financial crises at the end of twentieth century as well as the current global financial crises that started during second half 2008, we acknowledge that there are some critics loudly articulated accusing accountants and auditors for disparences, and they are numerical partner of financial manipulation as well as corrupted administrators with the company's administrators that they are difficulty. At this point, many suggestions and recommendation for upgrading the accounting system has been made.  
... Show MoreWith the growing number of Internet users, public and private arts activities have become increasingly popular. Adolescents have begun to establish aesthetic taste and new cultural values. This category is the most affected one by the published images and ideas especially in the social networking space and specifically the Facebook. It is the most important problem in their cultural composition. This research aims to detect the problems of social networking sites in nurturing the aesthetic taste of adolescents. The researcher used the analytical descriptive approach to obtain accurate information describing the current situation or depicting the social reality of adolescents. The research concluded that the public discourse in social med
... Show MoreThis research aims to modify the components of stainless steel alloy by the method of surface engineering through the single diffusion coating technique in order to obtain new alloys with high efficiency in resisting harsh environmental conditions. Steam a mixture of sodium chloride ( ) and sodium sulfate ( ) at a temperature of 900 and then compare it with the base alloy. The results showed that the alloys produced in this way are very efficient. The results showed that the aluminum coating showed high efficiency in resisting oxidation and provided better protection for a longer time compared to the uncoated alloy due to the oxide crust layer formed with high adhesion as well as the aluminum-rich phases, whether the phase
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