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.
Background: Secretory Immunoglobulin A (SIgA) is a subclass of Immunoglobulin A (IgA), It is an antibody that plays an important role in mucosal immunity. It is the main immunoglobulin found in mucous secretions from mammary glands, tear glands and salivary glands, every pathologic process in the body involves the immune system, and periodontal inflammation is one of them and is not an exception. Material and methods: this study was consisted of 60 healthy male participants of an age ranged between (35-50) years old ; 25 of them with generalized moderate chronic periodontists(Clinical Attachment Loss equal to 3-4mm at ≥ 30% of the sites; 20 participants with plaque induced gingivitis and 15 participants had clinically healthy pe
... Show MoreSurvival analysis is widely applied to data that described by the length of time until the occurrence of an event under interest such as death or other important events. The purpose of this paper is to use the dynamic methodology which provides a flexible method, especially in the analysis of discrete survival time, to estimate the effect of covariate variables through time in the survival analysis on dialysis patients with kidney failure until death occurs. Where the estimations process is completely based on the Bayes approach by using two estimation methods: the maximum A Posterior (MAP) involved with Iteratively Weighted Kalman Filter Smoothing (IWKFS) and in combination with the Expectation Maximization (EM) algorithm. While the other
... Show MoreThe study aimed to determine of some Optimum conditions for bioremediation and removing of seven mineral elements included hexavalent chromium, nickel, cobalt, cadmium, lead, iron and copper as either alone or in group by living and heat treated cells of baker’s yeast Saccharomyces cerevisiae. The dried baker's yeast from Aldnaamaya China Company was used in this study. Biochemical tests was used to ensure yeast belonging to S. cerevisiae and then used to remove the mentioned mineral elementes under different conditions which included incubation period, pH, and temperature. It was found that the best of these conditions was 60 minutes for duration of incubation, 6 for pH, 25 ᵒC for temperature. During the study the behavior of living
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Abstract
Due to the momentum of winning in the streets of the city of Baghdad as a result of the large number of checkpoints so felt researcher to conduct a field visit to find out the main reasons that led to this congestion and to find practical solutions to mitigate wastage winning the arrival time citizen to where you want the least possible time.
This research aims to overcome the difficulties experienced by citizens to reach their places of work and reduce waste at the time of service and waiting time as well as reduce the cost of waiting.
Has emerged study a set of conclusions, including the use of model queue (G / G / C) and the mome
... Show MoreThis paper is devoted to an inverse problem of determining discontinuous space-wise dependent heat source in a linear parabolic equation from the measurements at the final moment. In the existing literature, a considerably accurate solution to the inverse problems with an unknown space-wise dependent heat source is impossible without introducing any type of regularization method but here we have to determine the unknown discontinuous space-wise dependent heat source accurately using the Haar wavelet collocation method (HWCM) without applying the regularization technique. This HWCM is based on finite-difference and Haar wavelets approximation to the inverse problem. In contrast to othe
There is no doubt that Jane Austen is one of the most studied authors of the late 18th and early 19th centuries. Her female characters have been extensively studied and they seem to have aroused much interest as manifestations of the conduct of their time. Her heroines have realized that there were many mistakes in the rules of conduct that controlled and restricted their behaviors. Thus, they have found no fault in correcting these mistakes, by behaving naturally without acting. Elizabeth Bennet the heroine of Pride and Prejudice and Marianne Dashwood of Sense and Sensibility are the chosen examples of that kind of women.
The current research dealt with the issue of organizational skillfulness as an entry point to reach strategic agility. The study has been tested in Iraq's mobile operators - Asia Cell, Zain Iraq and Cork Telecom. The study was applied to a sample of (93) managers distributed at various levels of management (board members, general managers, commissioners, department managers, people managers, unit managers, office managers). The survey used the questionnaire as a key tool for collecting data and information as well as personal interviews. It has sought to test a number of hypotheses related to correlation and influence relationships between the variables of the study, in order to answer the questions related to the problem of stud
... Show MoreThis paper aims to study the fractional differential systems arising in warm plasma, which exhibits traveling wave-type solutions. Time-fractional Korteweg-De Vries (KdV) and time-fractional Kawahara equations are used to analyze cold collision-free plasma, which exhibits magnet-acoustic waves and shock wave formation respectively. The decomposition method is used to solve the proposed equations. Also, the convergence and uniqueness of the obtained solution are discussed. To illuminate the effectiveness of the presented method, the solutions of these equations are obtained and compared with the exact solution. Furthermore, solutions are obtained for different values of time-fractional order and represented graphically.
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 and Objective: Public demand for procedures to rejuvenate photodamaged facial skin have stimulated the use of fractional CO2 laser as a precise and predictable treatment modality. The purpose of this study was to assess the effect of fractional CO2 laser system for reducing periorbital rhytids.
Materials and Methods: twenty seven subjects with mild periocular wrinkles, and photoaged skin of the face were prospectively treated two to three times (according to clinical response) in the periorbital area with a fractional CO2 laser device equipped with a scanning hand piece. Improvements in eyelid wrinkles was evaluated clinically and photographically. Subjects also scored satisfaction and
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