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.
Abstract
The changes that happened in the environment of business have great effects upon organizations with different activities specially the banks which requires the existence of an able opinion resources can adapt with the changes . Accordingly importance put upon intellectual capital which become one of the basic resources for organizations and one of success and growth elements with the availability of expertise , skills and capability of making essential changes in different process due to the presentation of innovations and creations of the to support banks activities .Therefore the intellectual capital represents the more r
... Show MoreThe study aimed to identify the treatment of the press image of the Great Return Marches in the French international news agency AFP by knowing the most important issues, their direction and the degree of interest in them. The study belongs to the descriptive research, and used the survey method, within the context of the content analysis method, and the researcher relied on the content analysis form tool and the interview tool to collect data. The study population is represented in the photos published by the French News Agency about the Great Return Marches during the period (end of March / 2018 until the end of November / 2019. The researcher chose an intentional sample using the Complete Census method. The study material represented
... Show MoreThe research aims to measure the extent of the impact of Earnings quality in the continuity of the company for a sample of private commercial banks listed on the Iraq Stock Exchange. The research sample included (15) of the listed commercial banks that continue to issue their financial statements for the period from (2009-2018).The research relied on three main models of measurement and on four steps. The first step is to measure the Persistence (Earnings Quality) by Depending the sustainability model. While the second step included measuring the Predictability of accounting profits by deriving the square root of the disparity of the estimation error from the first model Persistence (Earnings Quality), and the third step included
... Show MoreNo country in the world has an ancient heritage of its own. It represents the product of the civilizations left behind by previous eras. It represents the development of urban life and its capital of the interest of its people in the field of construction and reconstruction. The urban heritage and its associated arts may seem to be a material heritage at first glance, but it is not free from the spiritual side. Therefore, the nations in different parts of the earth cherish it and care for it with all due diligence, because it mixes with its history, memories and emotions.
This research discusses the use of local environment materials in the production of urban fabric constituents. I
Self-repairing technology based on micro-capsules is an efficient solution for repairing cracked cementitious composites. Self-repairing based on microcapsules begins with the occurrence of cracks and develops by releasing self-repairing factors in the cracks located in concrete. Based on previous comprehensive studies, this paper provides an overview of various repairing factors and investigative methodologies. There has recently been a lack of consensus on the most efficient criteria for assessing self-repairing based on microcapsules and the smart solutions for improving capsule survival ratios during mixing. The most commonly utilized self-repairing efficiency assessment indicators are mechanical resistance and durab
... Show MoreNowadays, internet security is a critical concern; the One of the most difficult study issues in network security is "intrusion detection". Fight against external threats. Intrusion detection is a novel method of securing computers and data networks that are already in use. To boost the efficacy of intrusion detection systems, machine learning and deep learning are widely deployed. While work on intrusion detection systems is already underway, based on data mining and machine learning is effective, it requires to detect intrusions by training static batch classifiers regardless considering the time-varying features of a regular data stream. Real-world problems, on the other hand, rarely fit into models that have such constraints. Furthermor
... Show MoreAn experiment was conducted to study how SAE 50 engine oil contaminated with diesel fuel affects engine performance. The engine oil was contaminated with diesel fuel at concentrations of 0%, 1%, and 3%. The following performance characteristics were studied: brake-specific fuel consumption, brake thermal efficiency, friction power, and exhaust gas temperature. Each treatment was tested three times. The three treatments (0%, 1%, and 3%) were analyzed statistically with a one-way ANOVA model at the 5% probability level to determine if the three treatments produced significant differences in engine performance. The statistical results showed that there were significant differences in engine performance metrics among the three treatments. The 3
... Show MoreA freshwater bivalve plays a crucial function in aquatic habitats as the filtered water and burrowing mussels mix the sediment, thus increasing oxygen content and making the ecosystem healthier. The aim of the study is to see how chlorpyrifos affects biochemical markers in freshwater mussel Unio tigridis. About 180 individuals per taxon and water samples were collected from the Qandil water resource on the Greater Zab River, Erbil Province, Iraq. Once arrived at the lab, the individuals were kept in aquaria with river water and an air-conditioned room Temperature: 25±2 and Light: 12h/12h and acclimatized to laboratory conditions for seven days in aged tap water. The mussel's identification molecularly and the DNA sequence of t
... Show MoreBackground: Odontogenisis is a complex process controlled by dynamic and reciprocal interactions that regulated by various molecules. Thymosin β4 is a small bioactive peptide with wide spectrum biological effects on much cell types. The present study was designed to highlight the effect of synthetic exogenous Tβ4 on developing dental tissue of the upper central teeth of rats, by histological examination and immunohistochemical evaluation of TGFβ1. Materials and method: Thirty six Albino Wister pregnant rat 18control group received intraperitoneal injection of normal saline and the others are experimental group received 50µg/300µl of Tβ4 injection. The animals were sacrificed at periods 16th and 18th day I.U.L and one day p
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