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.
The solar radiation plays an important role on the energy balance of the earthatmosphere, which is the main source of energy. Also the solar radiation is a main factor of all applications which use a solar energy as renewable energy source. The purpose of this research is to study the monthly average changes for solar radiation for the period from 1985 to 1989 by using satellite Antenna Alignment from (NASA). The result shows that the monthly average radiation changes from one year to another because of the changing of it component of atmosphere, (gases, clouds and Aerosols) and as an enhancement for this conclusion, we compared the results with the monthly average radiation at clear atmosphere where the change was slig
... Show MoreAn analytical and clinical study has been applied for measure the bioavailability of Zinc in serum of twenty adults healthy volunteers, using flame atomic absorption spectrophotometer (FAAS) at 213.9 nm. The calibration graph is linear in the ranges of 0.25-1.5 μg.mL-1 with correlation coefficient (R) 0.09996)μg.mL1-and molar absorpitivites 22957.76(L.mol1-cm-1.The concentration of Zinc determined in serum of all volunteers before and after administered orally a tablet of 50 mg zinc sulphate, produced by Samara drugs company (SDI). All data were subjected to statistical analysis by calculating accuracy, precision in addition to other parameters. The results indicate that the average maximum concentration (C-max ± SD) of blood zinc was 0.
... Show MoreThis article aims to establish and evaluate standards for critical equipment and materials in highway projects in Iraq. Delphi technique has been used to analyze, explore, and discover the main criteria and sub-criteria that affect equipment and materials in highway construction projects in Iraq. To determine the correct response to the criteria presented in this study, a program (IBM, SPSS/V25) was used to assess the main criteria and sub-criteria using the mean score (MS) and standard deviation (SD) technique, as well as to check reliability using Cronbach's alpha factor (α). The experts' qualifications and the extent to which the person is ready to commit are both important factors in panel selection. The design of a
... Show MoreComplex-valued regular functions that are normalized in the open unit disk are vastly studied. The current study introduces a new fractional integrodifferential (non-linear) operator. Based on the pre-Schwarzian derivative, certain appropriate stipulations on the parameters included in this con-structed operator to be univalent and bounded are investigated and determined.
Machine scheduling problems (MSP) are considered as one of the most important classes of combinatorial optimization problems. In this paper, the problem of job scheduling on a single machine is studied to minimize the multiobjective and multiobjective objective function. This objective function is: total completion time, total lead time and maximum tardiness time, respectively, which are formulated as are formulated. In this study, a mathematical model is created to solve the research problem. This problem can be divided into several sub-problems and simple algorithms have been found to find the solutions to these sub-problems and compare them with efficient solutions. For this problem, some rules that provide efficient solutio
... Show MoreIn this paper, a new technique is offered for solving three types of linear integral equations of the 2nd kind including Volterra-Fredholm integral equations (LVFIE) (as a general case), Volterra integral equations (LVIE) and Fredholm integral equations (LFIE) (as special cases). The new technique depends on approximating the solution to a polynomial of degree and therefore reducing the problem to a linear programming problem(LPP), which will be solved to find the approximate solution of LVFIE. Moreover, quadrature methods including trapezoidal rule (TR), Simpson 1/3 rule (SR), Boole rule (BR), and Romberg integration formula (RI) are used to approximate the integrals that exist in LVFIE. Also, a comparison between those methods i
... Show MoreWithin this research, The problem of scheduling jobs on a single machine is the subject of study to minimize the multi-criteria and multi-objective functions. The first problem, minimizing the multi-criteria, which include Total Completion Time, Total Late Work, and Maximum Earliness Time (∑𝐶𝑗, ∑𝑉𝑗, 𝐸𝑚𝑎𝑥), and the second problem, minimizing the multi-objective functions ∑𝐶𝑗 + ∑𝑉𝑗 +𝐸𝑚𝑎𝑥 are the problems at hand in this paper. In this study, a mathematical model is created to address the research problems, and some rules provide efficient (optimal) solutions to these problems. It has also been proven that each optimal solution for ∑𝐶𝑗 + ∑𝑉𝑗 + 𝐸𝑚𝑎𝑥 is an effic
... Show Moreproblems with its unobvious effect on scientific creativity and information. Problem solving is one of main goals of researchers because it develops their right logical thinking methods. The present study aims at measuring logical thinking among female it structures in the university mea swing problem solving among them ,identifying statically differences significance in logical thinking among female instructors in the university according to (Specialization Variable), identifying differences significance in problem Solving among female instructions in the university according to ( Specialization Variable) and identifying the Correlation between logical thinking and problem solving among female instructors in the university. The sample c
... Show MoreIn this paper, a new technique is offered for solving three types of linear integral equations of the 2nd kind including Volterra-Fredholm integral equations (LVFIE) (as a general case), Volterra integral equations (LVIE) and Fredholm integral equations (LFIE) (as special cases). The new technique depends on approximating the solution to a polynomial of degree and therefore reducing the problem to a linear programming problem(LPP), which will be solved to find the approximate solution of LVFIE. Moreover, quadrature methods including trapezoidal rule (TR), Simpson 1/3 rule (SR), Boole rule (BR), and Romberg integration formula (RI) are used to approximate the integrals that exist in LVFIE. Also, a comparison between those
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