Stumpff functions are an infinite series that depends on the value of z. This value results from multiplying the reciprocal semi-major axis with a universal anomaly. The purpose from those functions is to calculate the variation of the universal parameter (variable) using Kepler's equation for different orbits. In this paper, each range for the reciprocal of the semi-major axis, universal anomaly, and z is calculated in order to study the behavior of Stumpff functions C(z) and S(z). The results showed that when z grew, Stumpff functions for hyperbola, parabola, and elliptical orbits were also growing. They intersected and had a tendency towards zero for both hyperbola and parabola orbits, but for elliptical orbits, Stumpff functions

   In this work, a novel technique to obtain an accurate solutions to nonlinear form by multi-step combination with Laplace-variational approach (MSLVIM) is introduced. Compared with the  traditional approach for variational it overcome all difficulties and enable to provide us more an accurate solutions with extended of the convergence region as well as covering to larger intervals which providing us a continuous representation of approximate analytic solution and it give more better information of the solution over the whole time interval. This technique is more easier for obtaining the general Lagrange multiplier with reduces the time and calculations. It converges rapidly to exact formula with simply computable terms wit

يعد العلاج الحركي من الوسائل العلاجية التأهيلية من الوسائل المهمة الامنة  لأنها تؤمن على حياة الانسان بكافة شؤونه وتعد التمرينات التأهيلية اسلوبا فعالاً وطبيعياً لا تعرض المريض الى مضاعفات على وظائف الجسم الاخرى لأنها خالية من اي دواء كيمياوي ضار ، كما استخدمت تقنيات حديثة في العلاج الطبيعي بشكل واسع معد حسب اسس علمية منها تمرينات (Core)  التي تساعد في تخفيف الالام بالانزلاق الغضروفي للفقرة الرابعة والخا

Objective: preparing exercises for the third intensity zone for strength and speed for the legs, and identifying their effect on some physiological and biochemical indicators for (the level of lactic acid concentration, the concentration of sodium bicarbonate, the concentration level of (potassium K+) and (sodium Na+) in the blood, and the number of breathing times (RF) Research methodology: the experimental research method was adopted by designing the experimental and control groups on a sample of Army Sports Club players amounting to (16) players, deliberately selected (100%) from their community using a comprehensive enumeration method, and then divided into two groups of equal number, After determining the tests for physiologica

The research dealt with a comparative study between some semi-parametric estimation methods to the Partial linear Single Index Model using simulation. There are two approaches to model estimation two-stage procedure and MADE to estimate this model. Simulations were used to study the finite sample performance of estimating methods based on different Single Index models, error variances, and different sample sizes , and the mean average squared errors were used as a comparison criterion between the methods were used. The results showed a preference for the two-stage procedure depending on all the cases that were used

This paper presents a comparative study of two learning algorithms for the nonlinear PID neural trajectory tracking controller for mobile robot in order to follow a pre-defined path. As simple and fast tuning technique, genetic and particle swarm optimization algorithms are used to tune the nonlinear PID neural controller's parameters to find the best velocities control actions of the right wheel and left wheel for the real mobile robot. Polywog wavelet activation function is used in the structure of the nonlinear PID neural controller. Simulation results (Matlab) and experimental work (LabVIEW) show that the proposed nonlinear PID controller with PSO
learning algorithm is more effective and robust than genetic learning algorithm; thi