This study presents a practical method for solving fractional order delay variational problems. The fractional derivative is given in the Caputo sense. The suggested approach is based on the Laplace transform and the shifted Legendre polynomials by approximating the candidate function by the shifted Legendre series with unknown coefficients yet to be determined. The proposed method converts the fractional order delay variational problem into a set of (n + 1) algebraic equations, where the solution to the resultant equation provides us the unknown coefficients of the terminated series that have been utilized to approximate the solution to the considered variational problem. Illustrative examples are given to show that the recommended approach is applicable and accurate for solving such kinds of problems.
It is widely accepted that early diagnosis of Alzheimer's disease (AD) makes it possible for patients to gain access to appropriate health care services and would facilitate the development of new therapies. AD starts many years before its clinical manifestations and a biomarker that provides a measure of changes in the brain in this period would be useful for early diagnosis of AD. Given the rapid increase in the number of older people suffering from AD, there is a need for an accurate, low-cost and easy to use biomarkers that could be used to detect AD in its early stages. Potentially, the electroencephalogram (EEG) can play a vital role in this but at present, no reliable EEG biomarker exists for early diagnosis of AD. The gradual s
... Show MoreA field-pilot scale slow sand filter (SSF) was constructed at Al-Rustamiya Sewage Treatment Plant (STP) in Baghdad city to investigate the removal efficiency in terms of Biochemical Oxygen Demand (BOD5), Chemical oxygen demand (COD), Total Suspended Solids (TSS) and Chloride concentrations for achieving better secondary effluent quality from this treatment plant. The SSF was designed at a 0.2 m/h filtration rate with filter area 1 m2 and total filter depth of 2.3 m. A filter sand media 0.35 mm in size and 1 m depth was supported by 0.2 m layer of gravel of size 5 mm. The secondary effluent from Al-Rustamiya STP was used as the influent to the slow sand filter. The results showed that the removal of BOD5, COD, TSS, and Chloride were
... Show MoreA novel analytical method is developed for the determination of azithromycin. The method utilizes continuous flow injection analysis to enhance the chemiluminescence system of luminol, H2O2, and Cr(III). The method demonstrated a linear dynamic range of 0.001–100 mmol L-1 with a high correlation coefficient (r) of 0.9978, and 0.001–150 mmol L-1 with a correlation coefficient (r) of 0.9769 for the chemiluminescence emission versus azithromycin concentration. The limit of detection (L.O.D.) of the method was found to be 18.725 ng.50 µL−1 based on the stepwise dilution method for the lowest concentration within the linear dynamic range of the calibration graph. The relative standard deviation (R.S.D. %) for n = 6 was less than 1.2%
... Show MoreThe necessary optimality conditions with Lagrange multipliers are studied and derived for a new class that includes the system of Caputo–Katugampola fractional derivatives to the optimal control problems with considering the end time free. The formula for the integral by parts has been proven for the left Caputo–Katugampola fractional derivative that contributes to the finding and deriving the necessary optimality conditions. Also, three special cases are obtained, including the study of the necessary optimality conditions when both the final time and the final state are fixed. According to convexity assumptions prove that necessary optimality conditions are sufficient optimality conditions.
... Show MoreIn this research, a simple experiment in the field of agriculture was studied, in terms of the effect of out-of-control noise as a result of several reasons, including the effect of environmental conditions on the observations of agricultural experiments, through the use of Discrete Wavelet transformation, specifically (The Coiflets transform of wavelength 1 to 2 and the Daubechies transform of wavelength 2 To 3) based on two levels of transform (J-4) and (J-5), and applying the hard threshold rules, soft and non-negative, and comparing the wavelet transformation methods using real data for an experiment with a size of 26 observations. The application was carried out through a program in the language of MATLAB. The researcher concluded that
... Show MoreThis study aims to derive a sustainable human development index for the Arab countries by using the principal components analysis, which can help in reducing the number of data in the case of multiple variables. This can be relied upon in the interpretation and tracking sustainable human development in the Arab countries in the view of the multiplicity of sustainable human development indicators and its huge data, beside the heterogeneity of countries in a range of characteristics associated with indicators of sustainable human development such as area, population, and economic activity. The study attempted to use the available data to the selected Arab countries for the recent years. This study concluded that a single inde
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The researcher shed light on a diet in Iraq before 2003 became in this period. And how the ration card has a variety of vocabulary and cover the need of the population of commodities and have a key role in saving Iraq from a real crisis in the period of economic siege, especially in light of the State's direction to support the agricultural sector, which in that period able to fill half of the market needs of food the basic. As well as providing strategic storage at the Ministry of Commerce enough for six months But after the events of 2003 and the crises that hit the country and the unstable security situation began to rise voices calling for reform of the ration card system as a system that is a burden on the
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