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.
Each era has advantages in terms of innovation and development in form, technology, style, and design in ceramic vessels, both at the level of functional and aesthetic performance, so this study aimed to demonstrate the importance of geometrical foundations in the design structure of contemporary ceramic vessels, and also to reveal the constructive skills in The structure of the ceramic figure.
The researchers used the descriptive analytical approach to suit the nature of the study, and they described and analyzed the ceramic works in terms of geometric shape systems, elements and foundations of design in construction, formal diversity in the general design of ceramic vessels, and references and sources of artwork. In addition to th
The TV has the ability to combine sound and picture, which makes it of a direct impact on the recipient as it is a rich communicative tool with various artistic forms that display through this small screen programs and films, so that the TV has become superior over many other means of communication.
This research is concerned with the technical and artistic ability in the production of programs owned by the TV as a means of attraction of educated children aged between 5-12 years old, which makes it an educational supplement for the school that helps them in providing knowledge, acquiring skills and being informed about the different sciences through educational programs. It is known that the child at this stage enjoys when wa
The musical sign was associated with the first appearances of acting that are based on human gestures and expressive and silent movements, and they contributed in accentuating and clarifying these gestures and explain their meanings and indications, and they remained with them until these gestures turned into artistic theatrical shows so that the musical sign would have many functions and constitute the main pillars for this kind of show.
The musical sign is a language not much different than the human language in the semiotic analysis. There has been an increased interest in it and its use in the mime shows by the graduates who realized its necessity and significance in the pantomime show intellectually, artistically and aesthetical
Albizia lebbeck biomass was used as an adsorbent material in the present study to remove methyl red dye from an aqueous solution. A central composite rotatable design model was used to predict the dye removal efficiency. The optimization was accomplished under a temperature and mixing control system (37?C) with different particle size of 300 and 600 ?m. Highest adsorption efficiencies were obtained at lower dye concentrations and lower weight of adsorbent. The adsorption time, more than 48 h, was found to have a negative effect on the removal efficiency due to secondary metabolites compounds. However, the adsorption time was found to have a positive effect at high dye concentrations and high adsorbent weight. The colour removal effi
... Show MoreThis study is concerned with making comparison in using different geostatistical methods for porosity distribution of upper shale member - Zubair formation in Luhais oil field which was chosen to study.
Kriging, Gaussian random function simulation and sequential Gaussian simulation geostatistical methods were adopted in this study. After preparing all needed data which are contour map, well heads of 12 wells, well tops and porosity from CPI log. Petrel software 2009 was used for porosity distribution of mentioned formation in methods that are showed above. Comparisons were made among these three methods in order to choose the best one, the comparing cri
Estimation the unknown parameters of a two-dimensional sinusoidal signal model is an important and a difficult problem , The importance of this model in modeling Symmetric gray- scale texture image . In this paper, we propose employment Deferential Evaluation algorithm and the use of Sequential approach to estimate the unknown frequencies and amplitudes of the 2-D sinusoidal components when the signal is affected by noise. Numerical simulation are performed for different sample size, and various level of standard deviation to observe the performance of this method in estimate the parameters of 2-D sinusoidal signal model , This model was used for modeling the Symmetric gray scale texture image and estimating by using
... Show MoreThis research mainly aims to analyze local development strategy in Baghdad Governance, build the Strategic Model based on the study area's spatial interaction, and achieve the Trinity of Excellence based on the global model of excellence.
This research applied SWOT strategic analysis for the strengths and weaknesses of the internal environment and opportunities and threats of the external environment for the provincial council. In conclusion, the research specifies appropriate alternatives and choosing the best in line with the reality of the Baghdad Provincial Council. Also, the strategic goals in the national plan and the spatial interaction of the development goals,
... Show MoreThe aim of this study is to provide an overview of various models to study drug diffusion for a sustained period into and within the human body. Emphasized the mathematical compartment models using fractional derivative (Caputo model) approach to investigate the change in sustained drug concentration in different compartments of the human body system through the oral route or the intravenous route. Law of mass action, first-order kinetics, and Fick's perfusion principle were used to develop mathematical compartment models representing sustained drug diffusion throughout the human body. To adequately predict the sustained drug diffusion into various compartments of the human body, consider fractional derivative (Caputo model) to investiga
... Show MoreThe current research aims to examine the effect of the rapid learning method in developing creative thinking among second-grade female students in the subject of history. Thus, the researcher has adopted an experimental design of two groups to suit the nature of the research. The sample of the study consists of (36) randomly selected students from Al-Shafaq Secondary School for Women, which are divided randomly into two groups. The first group represents the experimental; it includes (31) students who studied the subject of history using the quick learning method. The second group, on the other hand, is the control group, which consists of (32) students, who studied the same subject using the traditional way. Before starting with the exp
... Show MoreA (k,n)-arc is a set of k points of PG(2,q) for some n, but not n + 1 of them, are collinear. A (k,n)-arc is complete if it is not contained in a (k + 1,n)-arc. In this paper we construct complete (kn,n)-arcs in PG(2,5), n = 2,3,4,5, by geometric method, with the related blocking sets and projective codes.