Interval methods for verified integration of initial value problems (IVPs) for ODEs have been used for more than 40 years. For many classes of IVPs, these methods have the ability to compute guaranteed error bounds for the flow of an ODE, where traditional methods provide only approximations to a solution. Overestimation, however, is a potential drawback of verified methods. For some problems, the computed error bounds become overly pessimistic, or integration even breaks down. The dependency problem and the wrapping effect are particular sources of overestimations in interval computations. Berz (see [1]) and his co-workers have developed Taylor model methods, which extend interval arithmetic with symbolic computations. The latter is an effective tool for reducing both the dependency problem and the wrapping effect. By construction, Taylor model methods appear particularly suitable for integrating nonlinear ODEs. In this paper, we analyze Taylor model based integration of ODEs and compare Taylor model with traditional enclosure methods for IVPs for ODEs. More advanced Taylor model integration methods are discussed in the algorithm (1). For clarity, we summarize the major steps of the naive Taylor model method as algorithm 1.
six specimens of the Hg0.5Pb0.5Ba2Ca2Cu3-y
The study aimed to reveal the extent of the first intermediate grade science curriculum focus on the national values, health, environmental, economic values, in the light of the education policy in the Kingdom of Saudi Arabia, in addition to present a proposed vision to strengthen it in the science curriculum for the first intermediate grade. The study was applied to the two books student and the two books of activity on the first-second semesters for the academic year 1441 AH. To analyze the curriculum content, the study used a verified card prepared by the researchers and a criterion for interpreting percentages. The study reached the following results: environmental values ranked first with a concentration of (43%), i.e. with an avera
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Abstract
Indeed, being busy with the understanding of religion is the best sort of worship that the almighty God has given each period of time a number of scholars and wise men. They receive what has been passed down to them from their great ancestors, and those who are willing to learn will learn, their students preserve their knowledge through teaching and writing. Thus, the scholars were pioneers in this field due to the value and importance of their knowledge. They have strived in learning, explaining, and writing new subjects.
One of those scholars is sheikh (Abdulrahman Al-Penjweni) who passed away 1319 AH in one of the villages of the city of Sulaimani in Iraq. He was one of the wisest scholars, a br
... Show MoreThe research seeks to identify the contemporary events that face the use of electronic payment methods to localize the salaries of state employees and its impact in enhancing the mental image of customers, and to achieve this purpose from the fact that a questionnaire was designed and distributed to an optional sample of (31) individual customers (employees) dealing With the researched private banks, it has been analyzed and reached a number of conclusions and recommendations, the most prominent of which is the lack of modernity of electronic payment methods by customers, which is reflected in the mental image of customers and the achievement of their satisfaction, in the Emiratization project for salaries needs an advanced leade
... Show MoreIn this article four samples of HgBa2Ca2Cu2.4Ag0.6O8+δ were prepared and irradiated with different doses of gamma radiation 6, 8 and 10 Mrad. The effects of gamma irradiation on structure of HgBa2Ca2Cu2.4Ag0.6O8+δ samples were characterized using X-ray diffraction. It was concluded that there effect on structure by gamma irradiation. Scherrer, crystallization, and Williamson equations were applied based on the X-ray diffraction diagram and for all gamma doses, to calculate crystal size, strain, and degree of crystallinity. I
... Show MoreThese researches have shown the magnitude of the influence that culture exerts on all human extensions and spaces. Rather, the conviction of many thinkers, researchers and specialists in the comprehensiveness of this influence is such that it is used as a starting point and perspective to explain the various aspects, manifestations, problems and practices. According to these perceptions, a man carries a cultural mind that is slowly formed throughout the young years of a man’s life and is completed upon reaching the age of maturity. Therefore, it has become evident in the behavioral, social and human sciences to acknowledge the multiplicity of human thought patterns as a natural result of the different cultures of peoples and societies.
... Show MorePublic spending represents the government’s financial leverage and has a significant impact on real and monetary economic variables, and one of these effects is the effect of public spending on the exchange rate as an important monetary variable for monetary policy, As we know that public spending in Iraq is financed from oil revenues sold in US dollars, and the Ministry of Finance converts the US dollar into Iraqi dinars to finance the government's need to spend within the requirements and obligations of the state's general budget, And converting the US dollar into Iraqi dinars has an impact on the parallel exchange market, even if there is a contractual exchange rate between the Ministry of Finance and the Central Bank of Iraq to
... Show MoreIn our research, we dealt with one of the most important issues of linguistic studies of the Holy Qur’an, which is the words that are close in meaning, which some believe are synonyms, but in the Arabic language they are not considered synonyms because there are subtle differences between them. Synonyms in the Arabic language are very few, rather rare, and in the Holy Qur’an they are completely non-existent. And how were these words, close in meaning, translated in the translation of the Holy Qur’an by Almir Kuliev into the Russian language.
The Taylor series is defined by the f and g series. The solution to the satellite's equation of motion is expanding to generate Taylor series through the coefficients f and g. In this study, the orbit equation in a perifocal system is solved using the Taylor series, which is based on time changing. A program in matlab is designed to apply the results for a geocentric satellite in low orbit (height from perigee, hp= 622 km). The input parameters were the initial distance from perigee, the initial time, eccentricity, true anomaly, position, and finally the velocity. The output parameters were the final distance from perigee and the final time values. The results of radial distance as opposed to time were plotted for dissimilar times in
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