Nonlinear differential equation stability is a very important feature of applied mathematics, as it has a wide variety of applications in both practical and physical life problems. The major object of the manuscript is to discuss and apply several techniques using modify the Krasovskii's method and the modify variable gradient method which are used to check the stability for some kinds of linear or nonlinear differential equations. Lyapunov function is constructed using the variable gradient method and Krasovskii’s method to estimate the stability of nonlinear systems. If the function of Lyapunov is positive, it implies that the nonlinear system is asymptotically stable. For the nonlinear systems, stability is still difficult even though

The current study examined the impact of using PowerPoint presentation on EFL student’s attendance, achievement and engagement. To achieve the aim of this study, three null hypotheses have been posed as follows: There is no statistically significant difference between the mean score of the experimental group attendance and that of the control one; there is no statistically significant difference between the mean score of the experimental group achievement and that of the control one, and there is no statistically significant difference between the mean score of the experimental group engagement and that of the control one. To verify a hypothesis, a sample of sixty students is chosen randomly from the third year, department of English,

Quadrotors are coming up as an attractive platform for unmanned aerial vehicle (UAV) research, due to the simplicity of their structure and maintenance, their ability to hover, and their vertical take-off and landing (VTOL) capability. With the vast advancements in small-size sensors, actuators, and processors, researchers are now focusing on developing mini UAV’s to be used in both research and commercial applications. This work presents a detailed mathematical nonlinear dynamic model of the quadrotor which is formulated using the Newton-Euler method. Although the quadrotor is a 6 DOF under-actuated system, the derived rotational subsystem is fully actuated, while the translational subsystem is under-actuated. The der

Developments are carried out to enhance the performance of vertical axis wind turbines (VAWT). This paper studies the performance of the ducted wind turbine with convergent duct (DAWT). Basically, the duct technique is utilized to provide the desired wind velocity facing the turbine. Methodology was developed to estimate the decisive performance parameter and to present the effect of the convergent duct with different inlet angles. The ducted wind turbine was analyzed and simulated using MATLAB software and numerically using ANSYS-Fluent 17.2. Result of both approaches were presented and showed good closeness for the two cases of covering angles 12  and 20 respectively. Results also showed that the convergent duct with an inlet angl

Four rapid, accurate and very simple derivative spectrophotometric techniques were developed for the quantitative determination of binary mixtures of estradiol (E2) and progesterone (PRG) formulated as a capsule. Method I is the first derivative zero-crossing technique, derivative amplitudes were detected at the zero-crossing wavelength of 239.27 and 292.51 nm for the quantification of estradiol and 249.19 nm for Progesterone. Method II is ratio subtraction, progesterone was determined at λmax 240 nm after subtraction of interference exerted by estradiol. Method III is modified amplitude subtraction, which was established using derivative spectroscopy and mathematical manipulations. Method IIII is the absorbance ratio technique, absorba

In this study water quality index (WQI) was calculated to classify the flowing water in the Tigris River in Baghdad city. GIS was used to develop colored water quality maps indicating the classification of the river for drinking water purposes. Water quality parameters including: Turbidity, pH, Alkalinity, Total hardness, Calcium, Magnesium, Iron, Chloride, Sulfate, Nitrite, Nitrate, Ammonia, Orthophosphate and Total dissolved solids were used for WQI determination. These parameters were recorded at the intakes of the WTPs in Baghdad for the period 2004 to 2011. The results from the annual average WQI analysis classified the Tigris River very poor to polluted at the north of Baghdad (Alkarkh WTP) while it was very poor to very polluted in t

Nowadays, the robotic arm is fast becoming the most popular robotic form used in the industry among others. Therefore, the issues regarding remote monitoring and controlling system are very important, which measures different environmental parameters at a distance away from the room and sets various condition for a desired environment through a wireless communication system operated from a central room. Thus, it is crucial to create a programming system which can control the movement of each part of the industrial robot in order to ensure it functions properly. EDARM ED-7100 is one of the simplest models of the robotic arm, which has a manual controller to control the movement of the robotic arm. In order to improve this control s

To damp the low-frequency oscillations which occurred due to the disturbances in the electrical power system, the generators are equipped with Power System Stabilizer (PSS) that provide supplementary feedback stabilizing signals. The low-frequency oscillations in power system are classified as local mode oscillations, intra-area mode oscillation, and interarea mode oscillations. Double input multiband Power system stabilizers (PSSs) were used to damp out low-frequency oscillations in power system. Among dual-input PSSs, PSS4B offers superior transient performance. Power system simulator for engineering (PSS/E) software was adopted to test and evaluate the dynamic performance of PSS4B model on Iraqi national grid. The res