Gauss distribution

Often forgotten is the fact that there may be a clinically significant drug response difference between two populations even if the average response differences are small, perhaps not even statistically significant (39). If population data are represented by a normal distribution (Gauss) curve, the persons with abnormal responses may be represented by one of the edges of the curve. 

At the same time it is worth to notice that in modern numerical methods of a solution of boundary value problems, based on replacement of differential equations by finite difference, these steps are performed simultaneously. In accordance with the theorem of uniqueness, the field inside the volume V is defined by a distribution of masses inside this volume and boundary conditions, and correspondingly it is natural to derive an equation establishing this link. With this purpose in mind we will again proceed from Gauss s theorem,... 

FIGURE 6.10 Three characteristic structures of pressure-treated casein micelles representative AFM images together with the associated size-histograms are shown. The solid lines are fit to Gauss distributions. (A) Intact micelles, P < SO MPa (B) compact reconstituted micelles, 120 MPa < P < 240 MPa (C) mini-micelles, P > 280 MPa. Reprinted with permission from Gebhardt et al. (2006). 

When the Gauss-Newton method is used to estimate the unknown parameters, we linearize the model equations and at each iteration we solve the corresponding linear least squares problem. As a result, the estimated parameter values have linear least squares properties. Namely, the parameter estimates are normally distributed, unbiased (i.e., (k )=k) and their covariance matrix is given by... 

For spherically symmetric nuclear charge distribution (Gaussian, Fermi, or point nucleus), the electric field at a point r outside the nucleus can be evaluated from Gauss law as... 

Tor instance, Gauss distributions, Lorentz distributions or their combinations... 

For the transformation of the macrocomposite model to a molecular composite model for the ultimate strength of the fibre the following assumptions are made (1) the rods in the macrocomposite are replaced by the parallel-oriented polymer chains or by larger entities like bundles of chains forming fibrils and (2) the function of the matrix in the composite, in particular the rod-matrix interface, is taken over by the intermolecular bonds between the chains or fibrils. In order to evaluate the effect of the chain length distribution on the ultimate strength the monodisperse distribution, the Flory distribution, the half-Gauss and the uniform distribution are considered. 

Fig. 44 Flory distribution, half-Gauss and uniform chain length distribution for an average DP of 100 monomeric units (m.u.)...

As an example of a distribution with a smaller number of long chains than the Flory distribution, a half-Gauss distribution is chosen,... 

Fig. 47 Ultimate strength of PpPTA fibres versus the degree of polymerisation applying a half-Gauss distribution of chain lengths for various values of the diameter 2r... 

Fig. 54 Ultimate strength of PpPTA versus the degree of polymerisation for a rod diameter of 0.5 nm. Comparison of the results calculated for the Flory, the half-Gauss and the uniform distributions...

The same result is obtained fiom the Gauss distribution, equation 19.4-56, but we haven t given the basis here fa- using the closed-closed and closed-open conditions. 

In this problem the Gram-Charlier will be compared with the Gamma Gauss distributions for an impulse response curve with the equation... 

Figure 4 Distribution of Lanczos eigenvalues in the H02 system (adapted with permission from Ref. 40) and Gauss-Chebyshev quadrature points.

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