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.
Vapor-liquid equilibrium data are presented for the binary systems n-hexane - 1-propanol, benzene - 1-propanol and n-hexane – benzene at 760 mm of mercury pressure. In addition ternary data are presented at selected compositions with respect to the 1-propanol in the 1-propanol, benzene, n-hexane system at 760 mmHg. The results indicate the relative volatility of n-hexane relative to benzene increases appreciably with addition of 1-propanol.
The photocatalyst process is considered the most promising method for the removal of water contamination. For excellent chemical and structural properties of Co3O4 nanoparticles, various Co3O4-based nanostructures can be applied as a photocatalyst. In this work, carbon quantum dots is prepared via an eco-friendly process and linked to Co3O4 effectively. X-ray diffraction pattern (XRD), scanning electron microscopy (SEM), transmission electron microscopy (TEM), UV-visible absorption spectroscopy and Fourier transform infrared spectroscopy (FT-IR). The photocatalyst process reveals that prepared nanocomposites can be degraded methylene blue under solar irradiation strongly. Results showed that methylene blue and methyl orange are degraded via
... Show MoreAtmospheric residue fluid catalytic cracking was selected as a probe reaction to test the catalytic performance of modified NaY zeolites and prepared NaY zeolites. Modified NaY zeolites have been synthesized by simple ion exchange methods. Three samples of modified zeolite Y have been obtained by replacing the sodium ions in the original sample with lanthanum and the weight percent added are 0.28, 0.53, and 1.02 respectively. The effects of addition of lanthanum to zeolite Y in different weight percent on the cracking catalysts were investigated using an experimental laboratory plant scale of fluidized bed reactor.
The experiments have been performed with weight hourly space velocity (WHSV) range of 6 to 24 h
... Show MoreIraqi EFL college instructors, who supervise the teaching practice of EFL student teachers, commonly experience the inefficient teaching performance of prospective teachers. This inefficiency is usually due to their inability to make connections between the practical experience and the theoretical knowledge of TEFL. One of the reasons behind this inability may be the employment of traditional ways of training and instructing student teachers. Moreover, it is usually noticed that many Iraqi EFL student teachers have a negative attitude toward the teaching profession. They explicitly state that they would join the teaching force only if they fail to work in any other field.
... Show MoreGypseous soil covers approximately 30% of Iraqi lands and is widely used in geotechnical and construction engineering as it is. The demand for residential complexes has increased, so one of the significant challenges in studying gypsum soil due to its unique behavior is understanding its interaction with foundations, such as strip and square footing. This is because there is a lack of experiments that provide total displacement diagrams or failure envelopes, which are well-considered for non-problematic soil. The aim is to address a comprehensive understanding of the micromechanical properties of dry, saturated, and treated gypseous sandy soils and to analyze the interaction of strip base with this type of soil using particle image
... Show MoreBackground: One of the unique prosthesis for tooth or teeth replacement is the dental implant. Our attempt is using a biomaterial system that is easily obtained and applicable and has the ability to provoke osteoinductive growth factor to enhance bone formation at the site of application. One of these natural polymers is hyaluronic acid. Material and methods: Sixty machined surface implants from commercially pure titanium rod inserted in thirty NewZealand rabbits. Two implants placed in both tibia of each rabbit. The animals scarified at 1, 2 and 4 weeks after implantation (10 rabbits for each interval). For all of animals the right tibia’s implant was control (uncoated) and the left one was experimental (coated with 0.1ml Hyaluro
... Show MoreIn this work, the performance of the receiver in a quantum cryptography system based on BB84 protocol is scaled by calculating the Quantum Bit Error Rate (QBER) of the receiver. To apply this performance test, an optical setup was arranged and a circuit was designed and implemented to calculate the QBER. This electronic circuit is used to calculate the number of counts per second generated by the avalanche photodiodes set in the receiver. The calculated counts per second are used to calculate the QBER for the receiver that gives an indication for the performance of the receiver. Minimum QBER, 6%, was obtained with avalanche photodiode excess voltage equals to 2V and laser diode power of 3.16 nW at avalanche photodiode temperature of -10
... Show MoreThe research aims to design a narrow-band frequency drive amplifier (1.5GHz -1.6GHz), which is used to boost the transmitter amplifier's input signal or amplify the GPS, GlONASS signals at the L1 band.
The Power Amplifier printed circuit board (PCB) prototype was designed using InGaP HBT homogeneous technology transistor and GaAs Heterojunction Bipolar Transistor (HBT) transistor. Two models have been compared; one of the models gave 16dB gain, and the other gave 23dB when using an input power signal (-15dBm). The PCB consumes 2.4W of power and has a physical dimension of 11 x 4 cm.
Car drivers hear many kinds of noise inside their vehicles' cabins, and the most annoying ones are the noise generated by tires, engines, and outside winds. Noise affects the comfort of the passengers inside the cabin, and it’s sad to say that modern cars are noisier in many kinds of noise signals due to using a lot of plastic materials in new budget cars. For expensive and luxury cars, the problem is solved by using better sound insulation materials, but for the budget ones, the approach used here is effective. It is called Active Noise Cancellation and can be done using analog or digital electronics. An operational amplifier and filters are used for the analog one, and in the digital one, signal processor chips are used. In engineeri
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