In classical Cartesian space position control, KD, the end-effector follows set-point trajectory with a stiffness expressed in directions of external coordinates through matrix, K, and damping proportional to first-order derivatives errors D. This work deals fractional-order extension KDHD, which is characterized by an additional term, half-order second HD. The proposed control scheme applied S...

For axisymmetric evolution of isolated systems, we prove that there exists a gauge such that the total mass can be written as a positive definite integral on the spacelike hypersurfaces of the foliation and the integral is constant along the evolution. The conserved mass integral controls the square of the extrinsic curvature and the square of first derivatives of the intrinsic metric. We also ...

‎the subject of this paper is the solution of the fredholm integral equation with toeplitz, hankel and the toeplitz plus hankel kernel. the mean value theorem for integrals is applied and then extended for solving high dimensional problems and finally, some example and graph of error function are presented to show the ability and simplicity of the ‎method.