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 current research aims to construct a scale for the nine types of students’ personality according to Rob Fitzel model. To do this, (162) items were formed that present the nine types of personality with (18) items for each type. To test the validity of the scale, a sample of (584) students of Al-Mustansrya University were chosen. The data of their responses was analyzed by using factor analysis. The findings explored (9) factors as one factor for each type of personality with (12) items for each one. Then, the reliability of the scale was found by using the test-retest method and Alfa Cronbach method.
Inelastic longitudinal electron scattering form factors to 2+ and 4+ states in 65Cu nucleus has been calculated in the (2p3/2 1f 5/2 2p1/2) shell model space with the F5PVH effective interaction. The harmonic oscillator potential has been applied to calculate the wave functions of radial single-particle matrix elements. Two shell model codes, CP and NUSHELL are used to obtain results. The form factor of inelastic electron scattering to 1/21−, 1/22−, 3/22−, 3/23−, 5/21−, 5/22− and 7/2- states and finding the transition probabilities B (C2) (in units of e2 fm4) for these transitions and B (C4) (in units of e2 fm8) for the transition 7/2-, and comparing them with experimental data. Both the form factors and reduced transition pr
... Show MoreThis paper aims to make a historical review of jet grouting techniques and encountered problems at different sites in several countries. This review is a good guide to understanding the performance and limitations of improved soils or lands. The basic concept of jet grouting technology is to use cement as a binder to accelerate the hardening process of an admixture of material grout and soil. The different case history was conducted in both sand soil and clay soil in the horizontal and vertical direction. Other papers on field construction showed that the grout can be gelled within 5-10 minutes. Due to different cases and studies, these will help improve soil by supporting the foundation load with a minimal settlement.
... Show MoreThis study is due to insufficient development of the issues of initial training in tennis at youthful (student) age. Objective: development of a methodological and scientific-methodological base of students' tennis with current trends in tennis. Summing up the best practices of modern tennis, we came to the conclusion that the formation of the art of reflection backhands in teaching beginner students of sports specialization to achieve future success. In modern conditions in the development of Russian tennis student opens the possibility of using new technologies and programs. Using these approaches, we have developed a training program and tested students' tennis in the pedagogical experiment, which resulted in its effectiveness.
The study aimed to reveal the level of knowledge and tendencies of high- study students specializing in curriculum and teaching methods at King Khalid University towards harmonious strategies with brain-based learning (BBL). And Then, putting a proposed concept to develop knowledge and tendencies of high-study students specializing in curriculum and teaching methods at King Khalid University towards harmonious strategies with Brain-based learning (BBL). For achieving this goal, a cognitive test and a scale of tendency were prepared to apply harmonious strategies with brain-based learning. The descriptive approach was used because it suits the goals of the study. The study sample consisted of (70) male and female students of postgraduate
... Show MoreThe current research deals with short term forecasting of demand on Blood material, and its' problem represented by increasing of forecast' errors in The National Center for Blood Transfusion because using inappropriate method of forecasting by Centers' management, represented with Naive Model. The importance of research represented by the great affect for forecasts accuracy on operational performance for health care organizations, and necessity of providing blood material with desired quantity and in suitable time. The literatures deal with subject of short term forecasting of demand with using the time series models in order to getting of accuracy results, because depending these models on data of last demand, that is being sta
... Show MoreField of translation is sampled with many types of translation, such as the literary, scientific, medical, etc. The translation of grammatical aspects has always been with difficulties.
Political translation is the focus here. There are many general problems faced by translators when translating political texts from Arabic into Spanish. The aim here is to clarify the definition of functions or terms within the text, and to arrive at the correct from of translation of such texts from Spanish into Arabic. It is worth mentioning that the paper is of two parts: the first exemplifies what is meant by translation, the prerequisites of a translator, along with mentioning the methods followed&nbs
... Show MoreNanofluids, liquid suspensions of nanoparticles (NPs) dispersed in deionized (DI) water, brine, or surfactant micelles, have become a promising solution for many industrial applications including enhanced oil recovery (EOR) and carbon geostorage. At ambient conditions, nanoparticles can effectively alter the wettability of the strongly oil-wet rocks to water-wet. However, the reservoir conditions present the greatest challenge for the success of this application at the field scale. In this work, the performance of anionic surfactant-silica nanoparticle formulation on wettability alteration of oil-wet carbonate surface at reservoir conditions was investigated. A high-pressure temperature vessel was used to apply nano-modification of oil-wet
... Show MoreMonetary policy occupies a prominent role in achieving monetary stability by adjusting the growth rates of the number of available means of payment in line with changes in the size of the gross domestic product in the country and expressed by the monetary stability coefficient agreed upon by the International Monetary Fund, a term that hides the fact that there is a rate of change in the volume of commodity or real production which expresses the levels of aggregate supply in the economy, which corresponds to the quantities of cash in circulation, which represent a net purchasing power and stimulate aggregate demand, which completes the picture of the existence of the market mechanism, expressed by the monetary or economic stability
... Show MoreThis paper study two stratified quantile regression models of the marginal and the conditional varieties. We estimate the quantile functions of these models by using two nonparametric methods of smoothing spline (B-spline) and kernel regression (Nadaraya-Watson). The estimates can be obtained by solve nonparametric quantile regression problem which means minimizing the quantile regression objective functions and using the approach of varying coefficient models. The main goal is discussing the comparison between the estimators of the two nonparametric methods and adopting the best one between them