In this paper, our purpose is to study the classical continuous optimal control (CCOC)  for quaternary nonlinear parabolic boundary value problems (QNLPBVPs). The existence and uniqueness theorem (EUTh) for the quaternary state vector solution (QSVS) of the weak form (WF) for the QNLPBVPs with a given quaternary classical continuous control vector (QCCCV) is stated and proved via the Galerkin Method (GM) and the first compactness theorem under suitable assumptions(ASSUMS). Furthermore, the continuity operator for the existence theorem of a QCCCV dominated by the QNLPBVPs is stated and proved under suitable conditions.

In this paper, three approximate methods namely the Bernoulli, the Bernstein, and the shifted Legendre polynomials operational matrices are presented to solve two important nonlinear ordinary differential equations that appeared in engineering and applied science. The Riccati and the Darcy-Brinkman-Forchheimer moment equations are solved and the approximate solutions are obtained. The methods are summarized by converting the nonlinear differential equations into a nonlinear system of algebraic equations that is solved using Mathematica®12. The efficiency of these methods was investigated by calculating the root mean square error (RMS) and the maximum error remainder (𝑀𝐸𝑅n) and it was found that the accuracy increases with increasi

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.

The penalized least square method is a popular method to deal with high dimensional data ,where  the number of explanatory variables is large than the sample size . The properties of  penalized least square method are given high prediction accuracy and making estimation and variables selection

 At once. The penalized least square method gives a sparse model ,that meaning a model with small variables so that can be interpreted easily .The penalized least square is not robust ,that means very sensitive to the presence of outlying observation , to deal with this problem, we can used a robust loss function to get the robust penalized least square method ,and get robust penalized estimator and

Abstract. This work presents a detailed design of a three-jointed tendon-driven robot finger with a cam/pulleys transmission and joint Variable Stiffness Actuator (VSA). The finger motion configuration is obtained by deriving the cam/pulleys transmission profile as a mathematical solution that is then implemented to achieve contact force isotropy on the phalanges. A VSA is proposed, in which three VSAs are designed to act as a muscle in joint space to provide firm grasping. As a mechatronic approach, a suitable type and number of force sensors and actuators are designed to sense the touch, actuate the finger, and tune the VSAs. The torque of the VSAs is controlled utilizing a designed Multi Input Multi Output (MIMO) fuzzy controll