The Wang-Ball polynomials operational matrices of the derivatives are used in this study to solve singular perturbed second-order differential equations (SPSODEs) with boundary conditions. Using the matrix of Wang-Ball polynomials, the main singular perturbation problem is converted into linear algebraic equation systems. The coefficients of the required approximate solution are obtained from the solution of this system. The residual correction approach was also used to improve an error, and the results were compared to other reported numerical methods. Several examples are used to illustrate both the reliability and usefulness of the Wang-Ball operational matrices. The Wang Ball approach has the ability to improve the outcomes by minimizing the degree of error between approximate and exact solutions. The Wang-Ball series has shown its usefulness in solving any real-life scenario model as first- or second-order differential equations (DEs).
In this work, a series of new maleimides linked to substituted benzothiazole moiety were synthesized. Synthesis of these new cyclic imides were performed via three steps, the first one involved preparation of a series of 2-aminobenzothiazole substituted with different substituents via reaction of different primary aromatic amines with ammonium thiocyanate and bromine in glacial acetic acid. The prepared 2- amino benzothiozoles were introduced in the second step in reaction with maleic anhydride producing a series of N-(substituted benzothiazole-2-yl) maleamic acids.The resulted maleamic acids were dehydrated in the third step via treatment with acetic anhydride and anhydrous sodium acetate to afford a series of the desirable N-(substitu
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In light of the development in the banking environment and the increasing reliance on electronic systems in providing banking services and due to the intense competition witnessed by the banking sector, the need has emerged to apply the comprehensive electronic banking system, which works on the Internet in providing new and diverse banking services regardless of time and place by linking all branches to one central database, and despite the advantages achieved from the application of the comprehensive system, there is a set of risks that accompany the use of that system, What requires the auditors to develop the audit method in line with the size of the development in the
... Show Moreconversation is an oral skill in which two persons can exchange their ideas, thoughts and opinions to communicate with each other. Learners can work in pairs or groups to practice dialogues chosen by the teacher from their textbook materials or from additional resources. Nowadays, because of Corona virus infection, our college students are taught all the subjects including conversation course either via google classroom platform or any other platforms. Google meet is one of online meetings between the teacher and students, i.e., a video meet in which students and the teacher join the online meetings in a specified time to communicate, express their ideas, thoughts and feelings about what is mentioned above. In this study, the resea
... Show MoreBuzurgan oil field suffers from the phenomenon of asphaltene precipitation. The serious negatives of this phenomenon are the decrease in production caused by clogging of the pores and decrease in permeability and wettability of the reservoir rocks, in addition to the blockages that occur in the pipeline transporting crude oil. The presence of laboratories in the Iraqi oil companies helped to conduct the necessary experiments, such as gas chromatography (GC) test to identify the components of crude oil and the percentages of each component, These laboratory results consider the main elements in deriving a new equation called modified colloidal instability index (MCII) equation based on a well-known global equation called colloidal in
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השירה החילונית זו מיזגה בין התרבות היהודית והתרבות הערבית השלטת. התרבות הערבית השלטת השפיעה על היהודים בשירה, בספרי פילוסופייה ועיון, בהגות דתית, ביצירה של פרשנות המקרא, במחקר בדקדוק עברי, ברפואה ועוד. ספרי המדע המחקר והעיון נכתבו כולם בערבית. זו היתה שפת הדיבור בקהילות היהודיות. אבל השירה שהתפתחה, שירה אשר קבלה את יסודותיה מן השירה הערבית, שהגיעה לשיא בתקופה זאת – נכתבה כולה בעב
... Show MoreDiesel engine oil was subjected to thermal oxidization (TO) for six periods of time (0 h, 24 h, 48 h, 72 h, 96 h, and 120 h) and was subsequently characterized by terahertz time domain spectroscopy (THz-TDS). The THz refractive index generally increased with oxidation time. The measurement method illustrated the potential of THz-TDS when a fixed setup with a single cuvette is used. A future miniaturized setup installed in an engine would be an example of a fixed setup. For the refractive index, there were highly significant differences among the oxidation times across most of the 0.3–1.7 THz range.
The amicus curiae is one of the judicial procedures adopted in many judicial and legal systems around the world, under which a person who is not a party to the case, and without having a personal and direct interest in it, intervenes to draw the court’s attention to many factual and legal aspects
the research goal is preparing a list of standard criteria and quality controls for information technology applications to serve the Holy Quran.
To achieve this goal, the researcher has built a list of criteria according to the following steps:
First - identify the key areas covered by the whole list which are:
1 – Standards of system building and implementing with the operating screens.
2 – Standards of display forms including audio and video presentation.
3 – Standards which are related to the program philosophy.
4 - Standards which are related to the program objectives.
... Show MoreBackground: The vertical distance between the upper and lower incisal edge of the central incisors when the mouth is opened as wide as possible is called maximum mouth opening (MMO). Any pathological change in the masticatory system had a direct effect on the maximal mouth opening. The aim of this study was to evaluate the relationship between the maximum bite force and the maximum mouth opening among group of children. Materials and methods: Four hundred children of both genders were included in this study, their age ranged from eight to ten years. Anterior and posterior (right, left) bite force were measured using bite force sensor. Maximum mouth opening was evaluated by electronic digital caliper. Data was statistically analyzed by de
... Show MoreThe current study was designed to remove Lead, Copper and Zinc from industrial wastewater using Lettuce leaves (Lactuca sativa) within three forms (fresh, dried and powdered) under some environmental factors such as pH, temperature and contact time. Current data show that Lettuce leaves are capable of removing Lead, Copper and Zinc ions at significant capacity. Furthermore, the powder of Lettuce leaves had highest capability in removing all metal ions. The highest capacity was for Lead then Copper and finally Zinc. However, some examined factors were found to have significant impacts upon bioremoval capacity of studied ions, where best biosorption capacity was found at pH 4, at temperature 50º C and contact time of 1 hour.