Gaussian assumption

The Gaussian assumption yields the first equality. Assumption (25) is used in the second expression on the right-hand side. Thus the line shape function /(co) can also be written as... 

If one y/ were sufficiently far away from the others, every one of us would find some reason for removing it from the calculation. The pull exerted by a very discrepant observation needs to be very small-con-veniently, zero. (To recognize that this is so is to recognize the inadequacy of any Gaussian assumption for the distribution of the 6/.)... 

Under the Gaussian assumption, the probability of the end-to-end distance vector being R is... 

This Gaussian assumption is used so frequently in the interpretation of light scattering that it has become a traditional assumption. However it is not generally valid. We show this in the ensuing sections. 

LDA assumes normal distribution of the explanatory variables, while logistic regression does not. If the Gaussian assumptions are met, then LDA is a more powerful and efficient model than logistic regression. 

This, in principle, invalidates all theoretical predictions like the Rouse result for the intermediate dynamic structure factor, because they all rely on the dynamic Gaussian assumption... 

An obvious extension of the Marcus approach consists of departing from the Gaussian assumption of eqn (18.7) and eqn (18.8), and postulating from the beginning a non-harmonic form for the Landau free energy in the reactant... 

We have also given attention to the fact that this straight Gaussian assumption can be violated. This is the case when solvation has a quite different character in the reactant and product states, so that the solvent fluctuations are different. Such effect was recently evidenced by FPMD simulations for the elementary oxidation reaction Cu Cu -I- e, and we found it amplified in... 

Probe spectra interpreted with the Gaussian assumption... 

The expected ctoss over from a to a law has been recently observed by NSE spectroscopy. Experiments were performed on PE samples at 509 K. The observed spectra were converted via eqn [63] toward mean square displacement. Thereby the Gaussian assumption is implied (Figure 37). 

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