In this paper Heun method has been used to find numerical solution for first order nonlinear functional differential equation. Moreover, this method has been modified in order to treat system of nonlinear functional differential equations .two numerical examples are given for conciliated the results of this method.

أن الطرق اللامعلمية هي نوع من الطرق الاحصائية الاستدلالية التي يمكن استخدامها للتوصل إلى أستنتاجات لذا كان حرص المؤلف على أصدار هذا الكتاب والذي يعمل على توضيح ( لماذا ؟ ومتى ؟ وكيف ؟ ) تستخدم كل طريقة إحصائية . وبإمكان القاريء سواء أكان أستاذا ً جامعيا ً أو باحثا ً أو طالبا ً في الدراسات العليا ( الماجستير والدكتوراه ) أو طالبا ً في الدراسات الأولية أن يتتبع جميع الخطوات لحساب كل قانون إحصائي وبدءا ً من عملية إدخ

 In this paper, the human robotic leg which can be represented mathematically by single input-single output (SISO) nonlinear differential model with one degree of freedom, is analyzed and then a simple hybrid neural fuzzy controller is designed to improve the performance of this human robotic leg model. This controller consists from SISO fuzzy proportional derivative (FPD) controller with nine rules summing with single node neural integral derivative (NID) controller with nonlinear function. The Matlab simulation results for nonlinear robotic leg model with the suggested controller showed that the efficiency of this controller when compared with the results of the leg model that is controlled by PI+2D, PD+NID, and F

In this study, nanocomposites have been prepared by adding
multiwall carbon nanotubes (MWCNTs) with weight ratios (0, 2, 3,
4, 5) wt% to epoxy resin. The samples were prepared by hand lay-up
method. Influence of an applied load before and after immersion in
sodium hydroxide (NaOH) of normality (0.3N) for (15 days) at
laboratory temperature on wear rate of Ep/MWCNTs
nanocomposites was studied. The results showed that wear rate
increases with increasing the applied load for the as prepared and
immersed samples and after immersion. It was also found that epoxy
resin reinforced with MWCNTs has wear rate less than neat epoxy.
The sample (Ep + 5wt% of MWCNTs) has lower wear rate. The
immersion effect in base so

The study aims to evaluate the removal of sulfur content from Iraqi light naphtha produced in Al-Dora refinery by adsorption desulfurization DS technique using modified activated carbon MAC loaded with nickel Ni and copper Cu as single binary metals. The experiments were carried in a batch unit with various operating parameters;  MAC dosage, agitation speed, and a contact time of 300 min at constant initial sulfur concentration 155 ppm and temperature. The results showed higher DS% by AC/Ni-Cu (66.45)% at 500 rpm and 1 g dosage than DS (29.03)% by activated carbon AC, increasing MAC dosage, agitation speed, and contact time led to increasing DS% values.  The adsorption capacity of MAC results was recorded (16,

This paper is devoted to investigate the effect of burning by fire flame on the behavior and load carrying capacity of rectangular reinforced concrete rigid beams. Reduced scale beam models (which are believed to resemble as much as possible field conditions) were suggested. Five end restrained beam specimens were cast and tested. The specimens were subjected to fire flame temperatures ranging from (25-750) ºC at age of 60 days, two temperature levels of 400ºC and 750ºC were chosen with exposure duration of 1.5 hour. The cast rectangular reinforced concretebeam (2250×375×375 mm) (length× width× height respectively) were subjected to fire. Results indicate remarkable reduction in the ultrasonic pulse velocity and rebound number of

The present investigation is concerned for the purification of impure zinc oxide (80-85 wt %) by using petroleum coke
(carbon content is 76 wt %) as reducing agent for the impure zinc oxide to provide pure zinc vapor, which will be
oxidized later by air to the pure zinc oxide.
The operating conditions of the reaction were studied in detail which are, reaction time within the range (10 to 30 min),
reaction temperature (900 to 1100 oC), air flow rate (0.2 to 1 l/min) and weight percentage of the reducing agent
(petroleum coke) in the feed (14 to 30 wt %).
The best operating conditions were (30 min) for the reaction time, (1100 oC) for the reaction temperature, (1 l/min) for
the air flow rate, and (30 wt %) of reducing

An investigation was conducted effect of addition co- solvent on solvent extraction process for two types of a lubricating oil fraction (spindle) and (SAE-30) obtained from vacuum distillation unit of lube oil plant of Daura Refinery. In this study two types of co-solvents ( formamide and N-methyl, 2, pyrrolidone) were blended with furfural to extract aromatic hydrocarbons which are the undesirable materials in raw lubricating oil, in order to improve the viscosity index, viscosity and yield of produced lubricating oil. The studied operating condition are extraction temperature range from 70 to 110 °C for formamide and 80 to 120 °C for N-methyl, 2, pyrrolidone, solvent to oil ratio range from 1:1 to 2:1 (wt./wt.) for furfural with form

A variety of oxides were examined as additives to a V2O5/Al2O3 catalyst in order to enhance the catalytic performance for the vapor phase oxidation of toluene to benzoic acid. It was found that the modification with MoO3 greatly promoted the little reaction leading to improve catalyst performance in terms of toluene conversion and benzoic acid selectivity. The effect of catalyst surface area, catalyst promoters, reaction temperature, O2/toluene, steam/toluene, space velocity, and catalyst composition to catalyst performance were examined in order to increase the benzoic acid selectivity and yield.