Copula modeling is widely used in modern statistics. The boundary bias problem is one of the problems faced when estimating by nonparametric methods, as kernel estimators are the most common in nonparametric estimation. In this paper, the copula density function was estimated using the probit transformation nonparametric method in order to get rid of the boundary bias problem that the kernel estimators suffer from. Using simulation for three nonparametric methods to estimate the copula density function and we proposed a new method that is better than the rest of the methods by five types of copulas with different sample sizes and different levels of correlation between the copula variables and the different parameters for the function. The

The flexible joint robot (FJR) typically experiences parametric variations, nonlinearities, underactuation, noise propagation, and external disturbances which seriously degrade the FJR tracking. This article proposes an adaptive integral sliding mode controller (AISMC) based on a singular perturbation method and two state observers for the FJR to achieve high performance. First, the underactuated FJR is modeled into two simple second-order fast and slow subsystems by using Olfati transformation and singular perturbation method, which handles underactuation while reducing noise amplification. Then, the AISMC is proposed to effectively accomplish the desired tracking performance, in which the integral sliding surface is designed to reduce cha

In this work, an analytical approximation solution is presented, as well as a comparison of the Variational Iteration Adomian Decomposition Method (VIADM) and the Modified Sumudu Transform Adomian Decomposition Method (M STADM), both of which are capable of solving nonlinear partial differential equations (NPDEs) such as nonhomogeneous Kertewege-de Vries (kdv) problems and the nonlinear Klein-Gordon. The results demonstrate the solution’s dependability and excellent accuracy.

The state and partial level densities were calculated using the corresponding formulas that are obtained in the frame work of the exciton model with equidistant spacing model (ESM) and non-ESM (NESM). Different corrections have been considered, which are obtained from other nuclear principles or models. These corrections are Pauli Exclusion Principle, surface effect, pairing effect, back shift due to shell effect and bound state effect . They are combined together in a composite formula with the intention to reach the final formula. One-component system at energies less than 100 MeV and mass number range (50-200) is assumed in the present work. It was found that Williams, plus spin formula is the most effective approach to the composite

Lagrange series and the Bessel function are two classical methods that were created by series expanding from Taylor series. In this paper, the purpose of those two methods was to find the values of the eccentric anomaly for one period (0–360)°. The Matlab program is used to apply the results, the input parameters were eccentricity (0–1), mean anomaly (0–360)°, and finally the parameter W (1–13). The program does not need a tolerance to obtain a precise value for eccentric anomaly like other iterative and non-iterative methods to stop the program; it will stop after completing the required period from 0° to 360° for a body that is determined by the solver. The output will be the final value of the eccentric anomaly. Furthermore,