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 use of Near-Surface Mounted (NSM) Carbon-Fiber-Reinforced Polymer (CFRP) strips is an efficient technology for increasing flexural and shear strength or for repairing damaged Reinforced Concrete (RC) members. This strengthening method is a promising technology. However, the thin layer of concrete covering the NSM-CFRP strips is not adequate to resist heat effect when directly exposed to a fire or at a high temperature. There is clear evidence that the strength and stiffness of CFRPs severely deteriorate at high temperatures. Therefore, in terms of fire resistance, the NSM technique has a significant defect. Thus, it is very important to develop a set of efficient fire protection systems to overcome these disadvantages. This pape

A numerical method is developed to obtain two-dimensional velocity and pressure distribution through a cylindrical pipe with cross jet flows. The method is based on solving partial differential equations for the conservation of mass and momentum by finite difference method to convert them into algebraic equations. This well-known problem is used to introduce the basic concepts of CFD including: the finite- difference mesh, the discrete nature of the numerical solution, and the dependence of the result on the mesh refinement. Staggered grid implementation of the numerical model is used. The set of algebraic equations is solved simultaneously by “SIMPLE” algorithm to obtain velocity and pressure distribution within a pipe. In order to

This paper deals with defining Burr-XII, and how to obtain its p.d.f., and CDF, since this distribution is one of failure distribution which is compound distribution from two failure models which are Gamma model and weibull model. Some equipment may have many important parts and the probability distributions representing which may be of different types, so found that Burr by its different compound formulas is the best model to be studied, and estimated its parameter to compute the mean time to failure rate. Here Burr-XII rather than other models is consider  because it is used to model a wide variety of phenomena including crop prices, household income, option market price distributions, risk and travel time. It has two shape-parame

The major of DDoS attacks use TCP protocol and the TCP SYN flooding attack is the most common one among them. The SYN Cookie mechanism is used to defend against the TCP SYN flooding attack. It is an effective defense, but it has a disadvantage of high calculations and it doesn’t differentiate spoofed packets from legitimate packets. Therefore, filtering the spoofed packet can effectively enhance the SYN Cookie activity. Hop Count Filtering (HCF) is another mechanism used at the server side to filter spoofed packets. This mechanism has a drawback of being not a perfect and final solution in defending against the TCP SYN flooding attack. An enhanced mechanism of Integrating and combining the SYN Cookie with Hop Count Filtering (HCF) mech

As the temperature of combustion gases is higher than the melting temperature of the turbine materials, cooling of turbine parts in a gas turbine engine is necessary for safe operation. Cooling methods investigated in this computational study included cooling flow losses. Film-cooling is one typically used cooling method whereby coolant is supplied through holes passage, in present study the holes placed along the camber line of the blade. The subject of this paper is to evaluate the heat transfer that occur on the holes of blade through different
blowing coolant rates. The cases of this study were performed in a low speed wind tunnel with two tip gap at small and large (0.03 and 0.09cm) and multiple coolant flow rates through the fil

The spray quality of two spraying agents with different physical properties was investigated under laboratory conditions to find whether the measurement of deposited drops could be affected by spraying those agents. The first spraying agent Moddus, which is a plant growth regulator, has a surface tension of 28 mN m-1 with almost half the value of the second spraying agent Kelpak (58 mN m-1). A mini boom sprayer containing three flat fan nozzles (XR 11003) was used in the test with three traveling speeds (4.74, 5.42 and 8.13 km. h-1). The test was performed to evaluate the quality of spray drops (spray coverage, spray density and stains diameter) after they were deposited on water sensitive papers (WSP). The results showed a higher ability o