Section2.4SolidMechanicsPartIIIKelly2392.4MaterialTimeDerivativesThemotionisnowallowedtobeafunctionoftime, t,Xχx ,andattentionisgiventotimederivatives,boththematerialtimederivativeandthelocaltimederivative.2.4.1Velocity&AccelerationThevelocityofamovingparticleisthetimerateofchangeofthepositionoftheparticle.From2.1....
Central to the post Keynesian position is Hyman Minsky, whose financial instability hypothesis holds that crises are due to the structure of financial assets in complex economies and are thus endogenous. This article uses qualitative financial data to show how derivatives and other exotic instruments ...
The two-component vectors x and x0 describe the lateral position on the surface and within the investigated subsurface volume, respectively. As a result, in practice, the closed surface S in Eq. (A.2) is replaced by a finite surface aperture Sx and normal derivatives correspond to ...
Define the derivatives of position and velocity Assign the values of the position and velocity of the ball to the output variablesp_outandv_out Model Discrete Effects of the Bounce TheFallingstate has a self-loop transition that models the discontinuity of the bounce as an instantaneous mode cha...
Achieving accurate position tracking for robotics and industrial servo systems is an extremely challenging task, particularly when dealing with control saturation, parameter perturbation, and external disturbance. To address these challenges, a predefine
We derive two types of perturbative approximation for the response of collisionally broadened two-level atoms to a time-dependent field. The perturbative approximations for the inversion and polarization are valid to any desired order in the derivatives of the field. Comparison with a numerical soluti...
With the benzoic acids, 2:3-, 2:5- and 2:6-, disubstitution gave active compounds, the chloro-derivatives again being the more active. The 2:5-compound was the most active in the dichloro-series, all members of which were less active than the 2:3:6-trichloro- and 2:3:5:6-...
Starting from the differential form of the equations, both time- and space-derivatives are approximated with a finite differences scheme in a spatio-temporal grid. The standard grid, used in most implementations of the method, is generated from the so-called Yee cell, defined such that the elec...
The incorporation of unnatural amino acids with novel side chains into proteins introduces a new dimension to the study of protein structure and function. Previous research has involved the investigation of four derivatives of five amino acids using α-hemolysin nanopores48. To the best of our knowl...
High-gain observers have been used in non-linear control to estimate derivatives of the output. In this paper, we study discrete-time implementation of high-gain observers and their use as numerical differentiators, in noise-free as well as noisy measurements. We show that discretization using th...