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 researcher studied transportation problem because it's great importance in the country's economy. This paper which ware studied several ways to find a solution closely to the optimization, has applied these methods to the practical reality by taking one oil derivatives which is benzene product, where the first purpose of this study is, how we can reduce the total costs of transportation for product of petrol from warehouses in the province of Baghdad, to some stations in the Karsh district and Rusafa in the same province. Secondly, how can we address the Domandes of each station by required quantity which is depending on absorptive capacity of the warehouses (quantities supply), And through r

Abstract:

Robust statistics Known as, resistance to errors caused by deviation from the stability hypotheses of the statistical operations (Reasonable, Approximately Met, Asymptotically Unbiased, Reasonably Small Bias, Efficient ) in the data selected in a wide range of probability distributions whether they follow a normal distribution or a mixture of other distributions deviations different standard .

power spectrum function lead to, President role in the analysis of Stationary random processes, form stable random variables organized according to time, may be discrete random variables or continuous. It can be described by measuring its total capacity as function in frequency.

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Seeds of the two rice genotypes namely Amber 33 (A33) and Amber Baghdad (AB) were divided into two groups; the first was presoaked in different concentrations of ethyl methane sulphonate (EMS) as chemical mutagen for different duration times (3, 6 and 12) hrs, and the other was exposed to different exposure times of ultra violate (UV-B) radiation (280-320 nm) as physical mutagen for different times (20, 40 and 60) min at room temperature. Treated and non-treated seeds were transferred into the callus induction medium containing 2.5 mg/L 2,4- dichlorophenoxy acetic acid (2,4-D) and 0.5 mg/L benzyl adenine (BA) under aseptic conditions. Calli were divided into two groups the first was treated with several EMS concentrations (0.0, 0.50. 1.0, 1

In earthquake engineering problems, uncertainty exists not only in the seismic excitations but also in the structure's parameters. This study investigates the influence of structural geometry, elastic modulus, mass density, and section dimension uncertainty on the stochastic earthquake response of a multi-story moment resisting frame subjected to random ground motion. The North-south component of the Ali Gharbi earthquake in 2012, Iraq, is selected as ground excitation. Using the power spectral density function (PSD), the two-dimensional finite element model of the moment resisting frame's base motion is modified to account for random ground motion. The probabilistic study of the moment resisting frame structure using stochastic fin

This paper studies the behavior of reinforced Reactive Powder Concrete (RPC) two-way slabs under static and repeated load. The experimental program included testing six simply supported RPC two-way slabs of 1000 mm length, 1000 mm width, and 70 mm thickness. All the tested specimens were identical in their material properties, and reinforcement details except their steel fibers content. They were cast in three pairs, each one had a different steel fibers ratio (0.5 %, 1 %, and 1.5 %) respectively. In each pair, one specimen was tested under static load and the other under five cycles of repeated load (loading-unloading). Static test results revealed that increasing steel fibres volume fraction from 0.5 % to 1 % and from 1% to 1.5%,

In this study, the effect of glass fiber reinforced polymer (GFRP) section and compressive strength of concrete in composite beams under static and low velocity impact loads was examined. Modeling was performed and the obtained results were compared with the test results and their compatibility was evaluated.‎ Experimental tests of four composite beams were carried out, where two of them are control specimen with 20 MPa compressive strength of concrete deck slab and 50 MPa for other. Bending characteristics were affected by the strength of concrete under impact loading case, as it increased maximum impact force and damping time at a ratio of 59% and reduced the damping ratio by 47% compared to the reference hybrid beam. Under stat