The high bounce activity according to the fosbery way is regarded as of the difficult sports concerning its way of training and perfection due to hard technique of its performance on one hand and because it depends on the player’s ability to overcome body weight resistance against the gravity. In addition to the strong ability to control the body posture when leaving the land and flying over the barrier. This activity needs to high plosion power at the moment of bouncing and this plosion depends on the period of bouncing, so the two researchers aimed to use a mechanical bouncing platform and an electronic one through several training by one foot and both feet in different directions and positions in order to reduce the time of bouncing an

The main work of this paper is devoted to a new technique of constructing approximated solutions for linear delay differential equations using the basis functions power series functions with the aid of Weighted residual methods (collocations method, Galerkin’s method and least square method).

This paper proposes a self organizing fuzzy controller as an enhancement level of the fuzzy controller. The adjustment mechanism provides explicit adaptation to tune and update the position of the output membership functions of the fuzzy controller. Simulation results show that this controller is capable of controlling a non-linear time varying system so that the performance of the system improves so as to reach the desired state in a less number of samples.

     In this article, we aim to define a universal set consisting of the subscripts of the fuzzy differential equation (5) except the two elements  and , subsets of that universal set are defined according to certain conditions. Then, we use the constructed universal set with its subsets for suggesting an analytical method which facilitates solving fuzzy initial value problems of any order by using the strongly generalized H-differentiability. Also, valid sets with graphs for solutions of fuzzy initial value problems of higher orders are found.

In this paper, Touchard polynomials (TPs) are presented for solving Linear Volterra integral equations of the second kind (LVIEs-2k) and the first kind (LVIEs-1k) besides, the singular kernel type of this equation. Illustrative examples show the efficiency of the presented method, and the approximate numerical (AN) solutions are compared with one another method in some examples. All calculations and graphs are performed by program MATLAB2018b.

A new method based on the Touchard polynomials (TPs) was presented for the numerical solution of the linear Fredholm integro-differential equation (FIDE) of the first order and second kind with condition. The derivative and integration of the (TPs) were simply obtained. The convergence analysis of the presented method was given and the applicability was proved by some numerical examples. The results obtained in this method are compared with other known results.

In this research, Haar wavelets method has been utilized to approximate a numerical solution for Linear state space systems. The solution technique is used Haar wavelet functions and Haar wavelet operational matrix with the operation to transform the state space system into a system of linear algebraic equations which can be resolved by MATLAB over an interval from 0 to . The exactness of the state variables can be enhanced by increasing the Haar wavelet resolution. The method has been applied for different examples and the simulation results have been illustrated in graphics and compared with the exact solution.

Objective: The aim of the research is to prepare skilled mental exercises according to spatial and temporal perceptions and the awareness of the strength of young pole-vaulters, and to recognize the impact of these exercises on improving the indicators of electrical activity of working muscles and some special physical abilities and accomplishing this effectiveness Research methodology: The researcher used the experimental curriculum (one experimental group), and included the sample of research on (5) two joint jumpers in the Iraqi club championship, all from the center of talent in athletics, the sample is trained on the same curriculum prepared by the coach himself but accompanied by a mental training approach that Prepared by the