Local maxima in

As mentioned in the text, the local maxima in p at the positions of nuclei are not true (3, — 3) critical points because the gradient vector of the charge density is discontinuous at the nuclear cusp that is present in both the state function and the density (Kato 1957). However, there always exists a function homeomorphic to p(r X) which coincides with p almost everywhere and for which the nuclear positions are (3, — 3) critical points. In this sense, the nuclear positions behave topologically as do (3, — 3) critical points in the charge distribution. 

Another change in the usual topology of p can occur when two nuclei with disparate charges approach very close to one another. Under these conditions the charge density will continue to exhibit the required cusp at the position of each nucleus but, at some small separation, the local maximum at 

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Thus, the user can input the minimum site boundary distance as the minimum distance for calculation and obtain a concentration estimate at the site boundary and beyond, while ignoring distances less than the site boundary. If the automated distance array is used, then the SCREEN model will use an iteration routine to determine the maximum value and associated distance to the nearest meter. If the minimum and maximum distances entered do not encompass the true maximum concentration, then the maximum value calculated by SCREEN may not be the true maximum. Therefore, it is recommended that the maximum distance be set sufficiently large initially to ensure that the maximum concentration is found. This distance will depend on the source, and some trial and error may be necessary however, the user can input a distance of 50,000 m to examine the entire array. The iteration routine stops after 50 iterations and prints out a message if the maximum is not found. Also, since there may be several local maxima in the concentration distribution associated with different wind speeds, it is possible that SCREEN will not identify the overall maximum in its iteration. This is not likely to be a frequent occurrence, but will be more likely for stability classes C and D due to the larger number of wind speeds examined. 

In regions I, II, and III shown in Fig. 7.3. this spectrum consists of one, two and three lines, correspondingly. The numbers of lines, like in [18], is supposed to be equal to the number of local maxima. In this reference system the regions are separated by two semicircles... 

The data are dominated by a few low molecular weight components. Figure 15.11 presents an image that has been amplified by a factor of 30 many more components are visible. Figure 15.12 presents the same data amplified by another factor of 30 for a total amplification of 1000, and a sea of peaks is visible. An unsupervised routine was used to isolate all local maxima in the data 190 components were resolved with amplitude greater than 10 times the standard deviation of the background signal. 

Locate the three local minima in Figure 2.7. Which is the global minimum Locate the four local maxima in Figure 2.8. Which is the global maximum ... 

Moreover, because the nuclei are effectively point charges, it should be obvious that their positions correspond to local maxima in tlie election density (and these maxima are also cusps), so the only issue left to completely specify the Hamiltonian is die assignment of nuclear atomic numbers. It can be shown diat diis information too is available from the density, since for each nucleus A located at an electron density maximum Fa... 

Fourier representation of electron density suggests the possibility of direct structure analysis. If all structure factors, F(hkl), are known, p(xyz) can be computed at a large number of points in the unit cell and local maxima in the electron-density function are interpreted to occur at the atomic sites. A typical single-crystal diffraction pattern of the type used for measuring structure factor amplitudes is shown in Figure 6.12. 

The local maxima in a charge distribution are illustrated in Fig. 2.1. The charge density in the ethylene molecule, C2H4, is displayed in two ways for each of three planes as a projection in the third dimension above the geometric plane and as a contour map, in which each contour represents a... 

VSEPR model maximize the interpair separations or, equivalently, maximize the separations between the local maxima in the VSCC of the central atom. 

Chemometric optimization of the chromatographic system consists, in fact, in predicting local maxima in multiparametric space and, then, in further deciding which of these parameters is global with regard to the overall efficiency of a given chromatographic system. 

The correlation implicit in Eq. (21) is quantitatively best for clusters of iron and vanadium consisting of more than eight atoms. For the case of niobium clusters, the correlation is more qualitative, but a distinct one-to-one correspondence of local minima in reactivity with local maxima in IP is indeed observed for clusters containing eight or more atoms. 

Shoulders cannot be recognized as separate reflections by this method, but only peaks with individual local maxima in the pattern (roots of the 1st derivative). 

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