هناك دائما حاجة إلى طريقة فعالة لتوليد حل عددي أكثر دقة للمعادلات التكاملية ذات النواة المفردة أو المفردة الضعيفة لأن الطرق العددية لها محدودة. في هذه الدراسة ، تم حل المعادلات التكاملية ذات النواة المفردة أو المفردة الضعيفة باستخدام طريقة متعددة حدود برنولي. الهدف الرئيسي من هذه الدراسة هو ايجاد حل تقريبي لمثل هذه المشاكل في شكل متعددة الحدود في سلسلة من الخطوات المباشرة. أيضا ، تم افتراض أن مقام النواة لن يكون صفرا أبدا أو أن يكون له قيمة عقدية بسبب اختيارالعقد المحددة لمتغيري النواة الوحيدين. مع متعددات حدود برنولي من الدرجة 4 و 8 كمثال على ذلك، يوفر النهج الحالي حلا قريبا جدا من الحل الدقيق في أمثلة الاختبار. بينما. يثبت الحجم المتواضع جدا للأخطاء في أمثلة الاختبار فعالية الاستراتيجية الحالية. أيضا ، فإن السهولة التي يمكن بها تنفيذ برنامج الكمبيوتر تجعل هذه التقنية فعالة للغاية. هدف آخر هو تحديد كفاءة الطريقة المقترحة من خلال مقارنتها بأساليب مختلفة. يظهر أن الحل التقريبي للمعادلات التكاملية ذات النواة المفردة أو المفردة الضعيفة يتقارب بشدة مع الحل المضبوط للمعادلات باستخدام متعددة حدود برنولي وهو متفوق على تلك الموجودة في الأساليب الأخرى المذكورة. هذا يضمن الأصالة والدقة العالية للطريقة المقترحة. كذلك تمت مناقشة تقارب الحل. تم تنفيذ البرامج باستخدام برنامج ال MATLAB النسخة 2018a .
The removal of boron from aqueous solution was carried out by electrocoagulation (EC) using magnesium electrodes as anode and stainless steel electrodes as cathode. Several operating parameters on the removal efficiency of boron were investigated, such as initial pH, current density, initial boron ion concentration, NaCl concentration, spacing between electrodes, electrode material, and presence of carbonate concentration. The optimum removal efficiency of 91. 5 % was achieved at a current density of 3 mA/cm² and pH = 7 using (Mg/St. St. ) electrodes, within 45 min of operating time. The concentration of NaCl was o. 1 g/l with a 0.5cm spacing between the electrodes. First and second order rate equation were applied to study adsorp
... Show MoreThis paper proposes a new method to tune a fractional order PID controller. This method utilizes both the analytic and numeric approach to determine the controller parameters. The control design specifications that must be achieved by the control system are gain crossover frequency, phase margin, and peak magnitude at the resonant frequency, where the latter is a new design specification suggested by this paper. These specifications results in three equations in five unknown variables. Assuming that certain relations exist between two variables and discretizing one of them, a performance index can be evaluated and the optimal controller parameters that minimize this performance index are selected. As a case study, a third order linear time
... Show MoreIn this work, PAni nanofibers (NFs) are successfully synthesized via hydrothermal method. The structural, surface morphological, optical, electrical and H2S gas sensing properties have been investigated for PAni thin films deposited by spin coating technique. The XRD pattern reveals crystalline nature of PAni NFs with crystallite size of 9.2 nm. The SEM image of Polyaniline clearly indicates that the polymer possesses nanofiber like structure. The optical properties show that the optical energy gap follows allowed direct electronic transition calculated using Tauc’s equation. Intense hotoluminescence (PL) peaks at 309, 340 and 605 nm are observed. The electrical properties such as D.C. conductivity and Hall effect have been studied wher
... Show MoreAbstract :- In this paper, silver nanoparticles had been prepared by chemical reduction method. Many tests had been done to it such as UV-Visible spectrophotometer, XRD, AFM&SEM test. finally an attempt had been done to get the optimum condition to control the grain size of silver Nanoparticles by variation the heating period and other parameters which has an effect in silver Nanoparticles synthesis process. in this method we can get a silver nanoparticles in the size range from 52 to 97 nm.
This research include building mathematical models for aggregating planning and shorting planning by using integer programming technique for planning master production scheduling in order to control on the operating production for manufacturing companies to achieve their objectives of increasing the efficiency of utilizing resources and reduce storage and improving customers service through deliver in the actual dates and reducing delays.
Diyala River is a tributary of Tigris River, it is one of the important rivers in Iraq. It covers a total distance of 445 km (275 miles). 32600 km2is the area that drains by Diyala River between Iraqi-Iranian borders. This research aims to evaluate the water quality index WQI of Diyala River, where three stations were chosen along the river. These stations are D12 at Jalawlaa City at the beginning of Diyala River, the second station is D15 at Baaquba City at the mid distance of the river, and the third station is D17 which is the last station before the confluence of Diyala River with Tigris River at Baghdad city. Bhargava method was used in order to evaluate the water quality index for both irrigation and drink
... Show MoreIn this paper the method of singular value decomposition is used to estimate the ridge parameter of ridge regression estimator which is an alternative to ordinary least squares estimator when the general linear regression model suffer from near multicollinearity.
This paper proposes a new method to tune a fractional order PID controller. This method utilizes both the analytic and numeric approach to determine the controller parameters. The control design specifications that must be achieved by the control system are gain crossover frequency, phase margin, and peak magnitude at the resonant frequency, where the latter is a new design specification suggested by this paper. These specifications results in three equations in five unknown variables. Assuming that certain relations exist between two variables and discretizing one of them, a performance index can be evaluated and the optimal controller parameters that minimize this performance index are selected. As a case study, a thir
... Show MoreConstruction projects have become a changing dramatically in recent decades and that the goal of the beneficiaries of the implementation of structural project is to complete the work with less time and within the cost of the specific and the best possible quality may sometimes happen that highlights the importance of time on the rest of the items at the implementation of projects for various reasons, including the need to use the project as soon as possible possible change rapidly to customer's requests, but the high cost of the project represents the biggest obstacle for entrepreneurs with its effects on the quality and the time workers, and is a measure of those elements in monetary terms is the key to integration between them, so the
... Show MoreThe aim of the present research is to investigate the effecting of pH parameter on the feasibility of lead removal from simulated wastewater using an electrochemical system. Electrocoagulation method is one of electrochemical technology which is used widely to treat industrial wastewater. Parameters affecting this operation, such as initial metal concentration, applied current, stirrer speed, and contact time of electroprocessing were taken as 155ppm, 1.5 Ampere, 150 rpm, 60 minutes respectively. While pH of the simulated wastewater was in the range of 2 to 12 in the experiments. It was found from the results that pH is an important parameter affecting lead removal operation. The best value of pH parameter is appro
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