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.
To test the effect of 4 levels of nitrogen (i.e. 0, 45, 90 and 135 Kg N ha-1) as urea (46% N) and 3 levels of phosphorus (i.e. 0, 17.5 and 35 Kg P ha-1) as triple superphosphate (21.8% P) on yield and concentration of dill (Anethum graveolens L. local cultivar) seed oil this experiment was carried out during winter season of 1999 - 2000 at the experimental field of Agriculture College, Abu-Ghraib.
Both fertilizers were applied in two equal splits, first at seeds sowing and the second was added one month after emergence. Dried and ground seed samples were subjected to water distillation for extraction of volatile oils
Result indicated that fertilization of dill plants with 90 Kg N
... Show MoreBackground: disruptive behavioral disorders among primary school children is oone of the most popular, which has negative social, psychological, educational, and physical repercussions on children and families. Objective: This study sought to determine effect disruptive behavioral disorders quality of learning among school chil dren. Methods: A descriptive cross-sectional design study was conducted at Baquba primary schools in Diyala Governorate, and the study period was extended from October 6th, 2024, to January 15th, 2025. A nonprobability purposive sample was used to include 275 teachers working at selected Baquba primary schools, Iraq. Data were collected using a self-admin istered questionnaire, two components of the st
... Show MoreThe research aims to find out the effect of PEDODE Strategy on the acquisition of historical concepts of First Intermediate Grade. To achieve this goal, the researcher has put forward this zero hypothesis: There is no statistically significant difference at the level of (05,0) between the mean of the students' marks in the experimental group who study the history subject using PEDODE strategy and that of the students' marks in the control group who study the subject according to the traditional method in the post-testing on the acquisition of historical concepts. The sample of the study consists of (62 female-students) of First Intermediate Grade in the Directorate of Baghdad Education/ Karkh2nd for the academic year 2016-2017. The sampl
... Show MoreBackground: Laparoscopic cholecystectomy has many difficulties which include port Insertion, Dissectionof the Calot’s Triangle , Grasping of the Gallbladder , Wall thickness, Adhesion and extraction of theGallbladder. Aim of the Study: To predict how difficult cholecystectomy will be from assessing the patientpreoperatively which, in turn, help in decreasing the risks on the patients and preventing post-operativecomplications. Patients and Methods: A prospective study conducted in the department of General Surgeryat Al-Ramadi Teaching Hospital for the period of nine months from 15th of May 2018 till the 15th of February2019. It included 60 patients, all of them were undergone laparoscopic cholecystectomy for Gallstone. Patientswit
... Show MoreBackground: Laser is a novel physical therapy technique used to treat various conditions, including wound healing, inhibition of bacterial growth, and postoperative wounds. High-power pulsed alexandrite laser therapy is one of the most prevalent forms of laser therapy, which is a noninvasive method for treating various pathological conditions, thereby enhancing functional capacities and quality of life. It is a modern medical and physiotherapeutic technology. Generally, the Alexandrite laser emits infrared light with a wavelength of 755 nm, allowing it to propagate and penetrate tissues. Objective: This study focused on the application of a high-power pulsed alexandrite laser in vitro to evaluate the effect of a pulsed alexandrite l
... Show MoreObjectives: A cross sectional analytic study was carried out to identify the maternal risk factors which
contribute to occurrence of low birth weight, and to determine the statistical significant differences between low
birth weight and maternal risk factors.
Methodology: A purposive sample of (400) woman was selected from AL-Elwyia Maternity Teaching Hospital
and Fatima Al-Zaharia Maternity and Pediatric Teaching Hospital. Data was collected through the interview of
mothers. Questionnaire format was designed and consisted seven parts, demographic variables, and reproductive
variables , Reproductive health variables, complications during the current pregnancy, the mother newborn
variables nutritional status for the m
The trade war, of course, leads to a sharp tension in international relations because the economy is the lifeblood of the states. In the world of trade and economy, countries began to lean towards cooperation. Economic relations after World War II were more liberal, trade barriers were removed and global trade became more flexible and smooth
Objective(s): This study aims at determining the effectiveness of an educational program on knowledge of high school students' knowledge about substance abuse and its health consequences, and to find out the association between students’ knowledge about substance abuse and its health consequences and their demographic data of age, socioeconomic status, and educational level of parents.
Methodology: A quasi-experimental study is conducted for the period of October 28th, 2019 to March 30th, 2020. The study sample included a nonprobability “purposive” sample of (124) male students (62) students for the control group and (62) students for the study group, aged (14-19) years who are selected from Al-Hikma High School for Boys in Kirk
Length of plasma generated by dc gas discharge under different vacuum pressures was studied experimentally. The cylindrical discharge tube of length 2m was evacuated under vacuum pressure range (0.1-0.5) mbar at constant external working dc voltage 1500V. It was found that the plasma length (L) increased exponentially with increasing of background vacuum air pressure. Empirical equation has been obtained between plasma length and gas pressure by using Logistic model of curve fitting. As vacuum pressure increases the plasma length increases due to collisions, ionizations, and diffusions of electrons and ions.