In motion Kinematics, it is well-known that the time derivative of a 3 × 3 rotation matrix equals a skew-symmetric matrix multiplied by the rotation matrix where the skew symmetric matrix is a linear (matrix-valued) function of the angular velocity and the rotation matrix represents the rotating motion of a frame with respect to a reference frame. The equation is widely used in engineering, e.g...

In this paper a parallel algorithm is presented for the numerical solution of the heat equation with derivative boundary conditions. The parallel algorithm is developed by approximating the second-order spatial partial derivative by third-order finite-difference approximations and a matrix exponential function by a rational approximation having distinct real poles. Problems are solved using the...

We apply the covariant derivative expansion of the Coleman-Weinberg potential to vector-like fermion models, matching the UV theory to the relevant dimension-6 operators in the standard model effective field theory. The γ matrix induced complication in the fermionic covariant derivative expansion is studied in detail, and all the contributing combinations are enumerated. From this analytical re...

Abstract. In this paper we propose a local spline method for the approximation of the derivative of a function f . It is based on an optimal spline quasi-interpolant operator Q2, introduced in [12]. Differentiating Q2 f , we construct the pseudo-spectral derivative at the quasi-interpolation knots and the corresponding differentiation matrix. An error analysis is proposed. Some numerical result...

This contribution is concerned with the robust stability analysis for linear systems with time-varying delay arising from networked control systems. The time-varying delay is supposed to be bounded and fast-varying. By constructing a new complete Lyapunov-Krasovskii functional, delay-dependent robust stability conditions are derived in terms of Linear Matrix Inequalities. The derivative of the ...