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 electron correlation effect for inter-shell have been analysed in terms of Fermi hole and partial Fermi hole for Li-atom in the excited states (1s2 3p) and (1s2 3d) using Hartree-Fock approximation (HF). Fermi hole Δf(r12) and partial Fermi hole Δg(r12 ,r1) were determined in position space. Each plot of the physical properties in this work is normalized to unity. The calculation was performed using Mathcad 14 program.
Background: Tap waters play an important role in fulfilling the people needs for drinking and domestic purposes. Contaminate the tap water with different pollutants has become an issue of great concern for 90% of people who are depended on the tap water as the main source of drinking. Pollutants can make their way easily into the delivering pipes which suffer from the leaking resulting in decreasing the quality of water. Objective: Therefore, assess the water quality for drinking purpose by calculating the water quality index is an important tool to ascertain whether the water is suitable for human consumption or not. Methods: In the present work, the water quality of the Al-Salam, western region of Baghdad city, Iraq was investigated for 7
... Show MoreIn this theoretical paper and depending on the optimization synthesis method for electron magnetic lenses a theoretical computational investigation was carried out to calculate the Resolving Power for the symmetrical double pole piece magnetic lenses, under the absence of magnetic saturation, operated by the mode of telescopic operation by using symmetrical magnetic field for some analytical functions well-known in electron optics such as Glaser’s Bell-shaped model, Grivet-Lenz model, Gaussian field model and Hyperbolic tangent field model. This work can be extended further by using the same or other models for asymmetrical or symmetrical axial magnetic field
... Show Moreunacceptable social behaviors, particularly withdrawal behavior that appears in children with autism represent a major problem hindering the process of communication with those around them and therefore the process of mergence with them be difficult.
The withdrawal causes a real affect deficit for children with autism limits the possibility of development of their intellectual and mental growth due to their solitude and the weakness of their focus in the acquisition of pedagogical skills and lack the necessary social skills to maintain the relations of friendship and enjoyment of them.
withdrawal children fail to participate
... Show MoreThis paper presents an experimental study for strengthening existing columns against axial compressive loads. The objective of this work is to study the behavior of concrete square columns strengthening with circulation technique. In Iraq, there are significantly more reinforced rectangular and square columns than reinforced circular columns in reinforced concrete buildings. Moreover, early research studies indicated that strengthening of rectangular or square columns using wraps of CFRP (Carbon Fiber Reinforced Polymer) provided rather little enhancement to their load-carrying capacity. In this paper, shape modification technique was performed to modify the shape (cross section) of the columns from square columns into circular colu
... Show MoreThis paper concerns is the preparation and characterization of a bidentate ligand [4-(5,5- dimethyl-3-oxocyclohex-1-enylamino)-N-(5-methylisoxazol-3-yl) benzene sulfonamide]. The ligand was prepared from fusing of sulfamethoxazole and dimedone at (140) ºC for half hour. The complex was prepared by refluxing the ligand with a bivalent cobalt ion using ethanol as a solvent. The prepared ligand and complex were identified using Spectroscopic methods. The proposed tetrahedral geometry around the metal ions studied were concluded from these measurements. Both molar ratio and continuous variation method were studied to determine metal to ligand ratio (M:L). The M to L ratio was found to be (1:1). The adsorption of cobalt complex was carried out
... Show MoreAbstract Asthma is a complex disease defined by chronic airway inflammation and airflow limitation causing variable respiratory symptoms which include shortness of breath (SOB), wheezing, chest tightness and cough. Asthma guidelines advocate adding a second long acting bronchodilator to medium doses of inhaled corticosteroids (ICS) rather using high doses of ICS alone to control moderate to severe persistent asthma. The aim of this study was to evaluate the clinical outcomes of three medication regimens indicated for Iraqi patients suffering from persistent asthma. This study was interventional randomized clinical study conducted on a sample of adult Iraqi asthmatic patients in Baghdad City. The study com
... Show MoreMany waste materials can be repurposed effectively within asphalt concrete to enhance the performance and sustainability of pavement. One of these waste materials is sawdust ash (SDA). This study explores the beneficial use of SDA as a substitute for limestone dust (LD) mineral filler in asphalt concrete. The replacement rate was 0%, 15%, 30%, 45%, and 60% by weight of total mineral filler. Scanning electron microscopy (SEM) was employed to assess the surface morphology of Sawdust (SD), SDA, and LD. In addition, a series of tests, including Marshall stability and flow, indirect tensile strength,moisture susceptibility, and repeated uniaxial loading tests, were conducted to examine the performance characteristics of asphalt mixtures of diffe
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