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.
The Iraqi marshes are considered the most extensive wetland ecosystem in the Middle East and are located in the middle and lower basin of the Tigris and Euphrates Rivers which create a wetlands network and comprise some shallow freshwater lakes that seasonally swamped floodplains. Al-Hawizeh marsh is a major marsh located east of Tigris River south of Iraq. This study aims to assess water quality through water quality index (WQI) and predict Total Dissolved Solids (TDS) concentrations in Al-Hawizeh marsh based on artificial neural network (ANN). Results showed that the WQI was more than 300 for years 2013 and 2014 (Water is unsuitable for drinking) and decreased within the range 200-300 in years 2015 and 2016 (Very poor water). The
... Show MoreA long-span Prestressed Concrete Hunched Beam with Multi-Opening has been developed as an alternative to steel structural elements. The commercial finite element package ABAQUS/CAE version 2019 has been utilized. This article has presented the results of three-dimensional numerical simulations investigating the flexural behaviour of existing experimental work of supported Prestressed Concrete Hunched Beams with multiple openings of varying shapes under static monotonic loads. Insertion openings in such a beam lead to concentrate stresses at the corners of these openings; as a result, extensive cracking would appear. Correlation between numerical models and empirical work has also been discussed regarding load displacemen
... Show MoreThe growth curves of the children are the most commonly used tools to assess the general welfare of society. Particularity child being one of the pillars to develop society; through these tools, we can path a child's growth physiology. The Centile line is of the important tools to build these curves, which give an accurate interpretation of the information society, also respond with illustration variable age. To build standard growth curves for BMI, we use BMI as an index. LMSP method used for finding the Centile line which depends on four curves represents Median, Coefficient of Variation, Skews, and Kurtosis. These can be obtained by modeling four parameters as nonparametric Smoothing functions for the illustration variable. Ma
... Show MoreThe present article discusses innovative word-formation processes in Internet texts, the emergence of new derivative words, new affixes, word-formation models, and word-formation methods. Using several neologisms as an example, the article shows both the possibilities of Internet word-making process and the possibilities of studying a newly established work through Internet communication. The words selected for analysis can be attributed to the keywords of the current time. (In particular, the words included in the list of "Words of 2019") there are number of words formed by the suffix method, which is the traditional method of the Russian word formation. A negation of these words is usually made thro
... Show MoreThe biosorption of Pb (II), Cd (II), and Hg (II) from simulated aqueous solutions using baker’s yeast biomass was investigated. Batch type experiments were carried out to find the equilibrium isotherm data for each component (single, binary, and ternary), and the adsorption rate constants. Kinetics pseudo-first and second order rate models applied to the adsorption data to estimate the rate constant for each solute, the results showed that the Cd (II), Pb (II), and Hg (II) uptake process followed the pseudo-second order rate model with (R2) 0.963, 0.979, and 0.960 respectively. The equilibrium isotherm data were fitted with five theoretical models. Langmuir model provides the best fitting for the experimental results with (R2) 0.992, 0
... Show MoreIn the beta decay process, a neutron converts into a proton, or vice versa, so the atom in this process changes to a more stable isobar. Bethe-Weizsäcker used a quasi-experimental formula in the present study to find the most stable isobar for isobaric groups of mass nuclides (A=165-175). In a group of isobars, there are two methods of calculating the most stable isobar. The most stable isobar represents the lowest parabola value by calculating the binding energy value (B.E) for each nuclide in this family, and then drawing these binding energy values as a function of the atomic number (Z) in order to obtain the mass parabolas, the second method is by calculating the atomic number value of the most stable isobar (ZA). The results show
... Show MoreAbstract Infinitives and gerunds are non-finite verb forms which cannot be indicated by tense, number, or person. The construction of non-finite verbs is intricate because of their nature of meanings, forms, and functions. The major problem is that both infinitival and gerundial complements have identical functions and occupy identical positions in the sentences. Thus, there is a confusion in using an infinitival and gerundial forms after aspectual verbs. The selection of either one of these two forms as complements is controlled syntactically or semantically. Moreover, both forms can be used usually with similar predicate but with neat difference in meaning. In addition, there are problems with controlling the use of aspect, since aspectua
... Show MoreThe elastic transverse electron scattering form factors have been studied for the 11Li nucleus using the Two- Frequency Shell Model (TFSM) approach. The single-particle wave functions of harmonic-oscillator (HO) potential are used with two different oscillator parameters bcore and bhalo. According to this model, the core nucleons of 9Li nucleus are assumed to move in the model space of spsdpf. The outer halo (2-neutron) in 11Li is assumed to move in the pure 1p1/2, 1d5/2, 2s1/2 orbit. The shell model calculations are carried ou
... Show MoreKnowing the distribution of the mechanical rock properties and the far field stresses for the field of interest is an important task for many applications concerning reservoir geomechanics, including wellbore instability analysis, hydraulic fracturing, sand production, reservoir compaction, and subsidence. A major challenge with determining the rock's mechanical properties is that they cannot be directly measured at the borehole. Furthermore, the recovered carbonate core samples for performing measurements are limited and they provide discrete data for specific depths.
The purpose of this study is to build 2D and 3D geomechanical models of the Khasib reservoir in the East Baghdad oil field/ Central area. TECHLOG.2015.3 softwa
... Show MoreThis paper develops a fuzzy multi-objective model for solving aggregate production planning problems that contain multiple products and multiple periods in uncertain environments. We seek to minimize total production cost and total labor cost. We adopted a new method that utilizes a Zimmermans approach to determine the tolerance and aspiration levels. The actual performance of an industrial company was used to prove the feasibility of the proposed model. The proposed model shows that the method is useful, generalizable, and can be applied to APP problems with other parameters.