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 Cu(II) was found using a quick and uncomplicated procedure that involved reacting it with a freshly synthesized ligand to create an orange complex that had an absorbance peak of 481.5 nm in an acidic solution. The best conditions for the formation of the complex were studied from the concentration of the ligand, medium, the eff ect of the addition sequence, the eff ect of temperature, and the time of complex formation. The results obtained are scatter plot extending from 0.1–9 ppm and a linear range from 0.1–7 ppm. Relative standard deviation (RSD%) for n = 8 is less than 0.5, recovery % (R%) within acceptable values, correlation coeffi cient (r) equal 0.9986, coeffi cient of determination (r2) equal to 0.9973, and percentage capita

The catalytic activity of faujasite type NaY catalysts prepared from local clay (kaolin) with different Si/Al ratio was studied using cumene cracking as a model for catalytic cracking process in the temperature range of 450-525° C, weight hourly space velocity (WHSV) of 5-20 h1, particle size ≤75μm and atmospheric pressure. The catalytic activity was investigated using experimental laboratory plant scale of fluidized bed reactor.
It was found that the cumene conversion increases with increasing temperature and decreasing WHSV. At 525° C and WHSV 5 h-1, the conversion was 42.36 and 35.43 mol% for catalyst with 3.54 Si/Al ratio and Catalyst with 5.75 Si/Al ratio, respectively, while at 450° C and at the same WHSV, the conversion w

Bendable concrete, also known as Engineered Cementitious Composite (ECC) is a type of ultra-ductile cementitious composites reinforced with fibres to control the width of cracks. It has the ability to enhance concrete flexibility by withstanding strains of 3% and higher. The properties of bendable concrete mixes (compressive strength, flexural strength, and drying shrinkage) are here assessed after the incorporation of supplementary cementitious materials, silica fume, polymer fibres, and the use of ordinary Portland cement (O.P.C) and Portland limestone cement (IL). Mixes with Portland limestone cement show lower drying shrinkage and lower compressive and flexural strength than mixes with ordinary Portland cement, due to the ratio o

Smear zone is usually formed around the prefabricated vertical drains (PVD’s) due to mandrel driving. The geotechnical properties of the soil in this zone exhibit significant changes that affect the performance of the PVD’s. The most relevant property in this respect is the coefficient of permeability. So far, no serious attention is paid to investigate the effects of shearing under large shear strains on the geotechnical properties of the soft soil in Fao region. In this study, an extensive laboratory testing program was conducted to assess the characteristics of the smear zone with an emphasis on the permeability coefficient of Fao soft soil. The results show that the permeability of the smear zone is about 70% of

Two dimensional meso-scale concrete modeling was used in finite element analysis of plain concrete beam subjected to bending. The plane stress 4-noded quadrilateral elements were utilized to model coarse aggregate, cement mortar. The effect of aggregate fraction distribution, and pores percent of the total area – resulting from air voids entrapped in concrete during placement on the behavior of plain concrete beam in flexural was detected. Aggregate size fractions were randomly distributed across the profile area of the beam. Extended Finite Element Method (XFEM) was employed to treat the discontinuities problems result from double phases of concrete and cracking that faced during the finite element analysis of concrete beam. Crac

       Canonical correlation analysis is one of the common methods for analyzing data and know the relationship between two sets of variables under study, as it depends on the process of analyzing the variance matrix or the correlation matrix. Researchers resort to the use of many methods to estimate canonical correlation (CC); some are biased for outliers, and others are resistant to those values; in addition, there are standards that check the efficiency of estimation methods.

In our research, we dealt with robust estimation methods that depend on the correlation matrix in the analysis process to obtain a robust canonical correlation coefficient, which is the method of Biwe

Static Synchronous Series Compensator (SSSC) is a well known device for effectively regulating the active power flow in a power system. In this paper, the SSSC linearized power flow equations are incorporated into Newton-Raphson algorithm in a MATLAB written program to investigate the control of active poweer flow and the transient stability of a five bus and a thirty bus IEEE test systems, during abnormal conduction (three phase fault near buses). A comparison of the results obtained for the base case without SSSC and with it to investigate the effectiveness of the device on both of the active power flow and the transient stability.