Centroids of distributions

A recommended method of characterizing the RTD in flow systems is by using their moments. These are known as the mean, variance, and skewness. The mean value or the centroid of distribution for a concentration versus time curve is... 

Most structural determinations are X-ray diffractions of single crystals which refer to the solid state. These geometries may be influenced by crystal packing forces and various disorders, and the atomic positions derived by X-ray diffraction analysis do not correspond to equilibrium positions but rather to centroids of distributions obtained by... 

Centroid of Distribution Hard- ness Elon- gation Tensile Strength (tons/... 

The residence time distribution curve (RTD) can be inscribed by its statistical moments, of which the centroid of distribution T and spread of distribution a are the most important numerical values. Thus, for a C curve, the zeroth moment is... 

A particularly difficult aspect of the problem of diffusion of atmospheric pollution is the determination of the height to which a buoyant plume with an initial exit velocity will rise. Plume rise, which is defined as the distance between the top of the stack and the axis of the centroid of the pollutant distribution, has been found to depend on ... 

These weights depend on several characteristics of the data. To understand which ones, let us first consider the univariate case (Fig. 33.7). Two classes, K and L, have to be distinguished using a single variable, Jt,. It is clear that the discrimination will be better when the distance between and (i.e. the mean values, or centroids, of 3 , for classes K and L) is large and the width of the distributions is small or, in other words, when the ratio of the squared difference between means to the variance of the distributions is large. Analytical chemists would be tempted to say that the resolution should be as large as possible. 

Here we assume 0(oo) = 0 and choose Sa > 0. It is now clear that differential capacitance becomes negative at some value of a if the centroid of the ionic distribution induced by a small variation Sa becomes negative. Given that ions do not penetrate the region x < 0, this can only happen if Sn x) is a nonmonotonic function of variable polarity. 

Here, the centroids of the charge distributions of phases A and B have been introduced ... 

The first two PCs account for 85% of the total variance of the data set. The PCA highlights that the sample is placed in the area of the mastic resin cluster. This confirmed the hypothesis made on the basis of a qualitative examination of the mass spectra, even though the sample is clearly shifted at lower values of PC2 with respect to the centroid of the mastic cluster. This was attributed to the presence of other substances mixed with the resin, and/or to a different quantitative distribution of the triterpenoids present in the censer with respect to the reference raw mastic resin. 

The reason for F is not too far to seek. In the general context of charge distributions, the role of an atom caimot be described solely by reference to the number of electrons it contributes to the molecular fabric. The centroid of its integrated charge density is equally important. 

Table 15.7. The centroids of charge implied by the second moment of the charge distribution of the nuclear and a framework. The C and H nuclear positions are those of the 6-3IG SCF equilibrium geometry.

A possible approach that we have presented in detail elsewhere C6, 7) is to consider the centroids of these globular segments to be distributed as the centres of randomly close-packed spheres. 

The centroid of each clinometer distribution of an integrated spectrum gives the the crystal (Ob) and detector (2Ob) angles. The dispersion function is determined by a bi-variate nonlinear least squares fit to the function... 

The spectrometer provides two series of data as a function of time the number of detected ions and, simultaneously, a physical value indicating the mass of these ions. This can be, for example, the value of the magnetic field measured by a Hall probe in the case of a magnetic instrument. The ions of every mass appear with a certain distribution over a time period, as shown in the sketch. The surface under the curve is proportional to the number of detected ions, while the value of the magnetic field at the centroid of the peak is an indicator of the ion mass. This centroid and mass must therefore be determined. In order to achieve... 

As indicated in Fig. 5, the signal is spread out over several elements of the read-out electrode. The role of a position sensitive read-out system is to determine the centroid of the signal distribution. 

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