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An Introduction to Error-Correcting Codes
Published in Erozan M. Kurtas, Bane Vasic, Advanced Error Control Techniques for Data Storage Systems, 2018
GF(8), if f(x)=α+α3x+α4x2, then f'(x)=α3 (since 2=0 over GF(2) ). The formal derivative has several properties similar to the traditional derivative, like the derivative of a product, (fg)'=f'g+fg'. Back to the error locator and error evaluator polynomials, we have the following relationship between the two:
Inverse random source problem for the Helium production-diffusion equation
Published in Applicable Analysis, 2022
Jing Li, Hao Cheng, Xiaoxiao Geng
The noise added in the above researches is the classical white noise , which is the formal derivative of Brownian motion . Actually in the more general case, the increments of the noise are not independent of each other, the source term is driven by a more general stochastic process. In [16], Li considered the random source problems for the time-harmonic acoustic and elastic wave equations in two and three dimensions, where the source term was assumed to be a microlocally isotropic generalized Gaussian random function. Li and Feng discussed the inverse random source problem for wave equation and time fractional diffusion equation, where the source was driven by a fractional Brownian motion in [8,9].
Global trajectory tracking of a class of manipulators without velocity measurements in random surroundings
Published in International Journal of Control, 2022
Mingyue Cui, Cun Yang, Zhaojing Wu
When there is no noise (i.e. ), model (1) can reduce to the manipulator model in the determined case (see Lewis et al., 1993; Spong et al., 2006). When is a white noise, by regarding as the formal derivative of a Wiener process, model (1) can be transformed to the stochastic model described by Itô SDEs (see Cui, Wu, et al., 2013; Cui, Xie, et al., 2013). Due to the mildness of actual noises and the absence of white noises in engineering practice tasks, it is more reasonable to established the random model (1) described by RDEs where noises are regarded as stationary processes.
Stochastic failure process of railway vehicle dampers and the effects on suspension and vehicle dynamics
Published in Vehicle System Dynamics, 2021
Y. C. Zeng, D. L. Song, W. H. Zhang, Z. Y. Hu, Z. C. Chang
As a non-Gaussian and strong stationary delta correlated process, Poisson white noise is the formal derivative of the following homogeneous compound Poisson process C(t), i.e. [5]. where U(·) is unit step function. Besides, the r-order moment of dC(t) can be calculated by .