In this work, a weighted H lder function that approximates a Jacobi polynomial which solves the second order singular Sturm-Liouville equation is discussed. This is generally equivalent to the Jacobean translations and the moduli of smoothness. This paper aims to focus on improving methods of approximation and finding the upper and lower estimates for the degree of approximation in weighted H lder spaces by modifying the modulus of continuity and smoothness. Moreover, some properties for the moduli of smoothness with direct and inverse results are considered.

The discus throwing event is one of the complex events in athletics, and it is characterized by a performance method that depends on the principle of mechanical moments and requires high explosive capabilities of the thrower in addition to some physical specifications,which depends effectively and effectively on the biomechanical aspects in generating large moments during rotation. The importance of the research is highlighted by the interest in athletics, especially the effectiveness of the discus throw and the continuation of its development process, the importance of kinetic analysis in revealing the most important weaknesses and strengths of shooters, and the importance of explosive power And the moments generated in the rotation of the

The purpose of this paper is to study the instability of the zero solution of some type of nonlinear delay differential equations of fifth order with delay by using the Lyapunov-Krasovskii functional approach, we obtain some conditions of instability of solution of such equation.

The purpose of this paper is to study the instability of the zero solution of some type of nonlinear delay differential equations of fourth order by using the Lyapunov-Krasovskii functional approach; we obtain some conditions of instability of solution of such equation.

The loose sand is subject to large settlement when it is exposed to high stresses. This settlement is due to the nature of the high drainage of sand, which displays foundations and constructions to a large danger. The densification of loose sandy soils is required to provide sufficient bearing capacity for the structures. Thus soil stabilization is used to avoid failure in the facilities. Traditional methods of stabilized sandy soil such as fly ash, bituminous, and cement often require an extended curing period. The use of polymers to stabilize sandy soils is more extensive nowadays because it does not require a long curing time in addition to being chemically stable. In this study, the effect of adding different percent

Two unsupervised classifiers for optimum multithreshold are presented; fast Otsu and k-means. The unparametric methods produce an efficient procedure to separate the regions (classes) by select optimum levels, either on the gray levels of image histogram (as Otsu classifier), or on the gray levels of image intensities(as k-mean classifier), which are represent threshold values of the classes. In order to compare between the experimental results of these classifiers, the computation time is recorded and the needed iterations for k-means classifier to converge with optimum classes centers. The variation in the recorded computation time for k-means classifier is discussed.

The aim of this paper is to present method for solving ordinary differential equations of eighth order with two point boundary conditions. We propose two-point osculatory interpolation to construct polynomial solution.