Region of influence

Topographic maps for the region of influence surrounding the site... 

As we saw in Section A, we can think of a field as a region of influence, like the gravitational field of the Earth. 

SYMBOL TYPE OP DIFFUSION REGION OF INFLUENCE COMMENTS... 

This technique makes use of the innate human cognition to perform clustering in multidimensional space (Osbourn and Martinez, 1995). It is unsupervised and model-free, therefore requires from the user only the data input. A special mask mathematically defines the visual region of influence. Its shape is based on human visual perception, taking advantage of the human brain to recognize and cluster objects (Fig. 10.10a). Its properties are as follows. Two points in space are clustered only if no other point lies within area of the mask which thus defines the exclusion region. In this way, an n-dimensional problem is reduced to set of n two-dimensional problems. 

Although the shape of the Visual-Empirical Region-of-Influence (VERI) mask is invariable, it size scales automatically according to the properties of the cluster (Fig. 10.10b). The VERI algorithm requires preprocessing of the data and for that purpose PCA or PCR preprocessing is routinely used. It is relatively immune to the presence of unknowns, and nonlinearity and nonadditivity of sensor responses (Osbourn et al., 1998). It has been used successfully to determine the optimum... 

Fig. 10.10 Rejection mask used in Visual Empirical Region of Influence (VERI). The shape of the mask is mathematically derived from the visual cognitive factors (a) geometrical scaling relationships used in the derivation of the shape (b) final mask which defines the exclusion region, that is, objects that do not belong to the group (Osbourn and Martinez, 1995)...

As seen in Fig. 7.3, the increase of O3 concentrations was up to 10%, whereas the NO2 concentrations showed a decrease of 25%. The red fine marks the region of influence of this specific emission reduction. 

Fig. 7.3 Traffic emission effect to O3 (a) and NO2 (b) concentrations at the nearby region of a highway during a 4 day period with strong north-easterly winds. The thick dotted black line indicates the region of influence...

We will now consider a second example which illustrates the electrostatic induction phenomenon. First of all, let us suppose that a conductive body of arbitrary shape is situated within the region of influence of an electric field Eq as shown in Fig. 1.9. Under the action of the field, the positive and negative charges residing inside the conductor move in opposite directions. As consequence of this movement, electric charges accumulate on both sides of the conductor. In so doing, they create a secondary electric field, which is directed in opposite direction to the primary field inside the conductor. The induced surface charges distribute themselves in such a way that the total electric field inside the conductor disappears, that is ... 

The effects of increasing the values of the parameters weight and region of influence are shown in Figure 7-49. The change of the shape is illustrated by the change of one of the border curves of a surface. The point P is on the sculpt curve. 

The qualitative argument is also simple. We know that each monomer enhances the structure of water in some sphere of influence around it. When two monomers form a dimer D, the two spheres of influence will overlap to a large extent (Fig. 4.31). Therefore, the enhancement of the structure of water in the combined regions of influence is expected to be less than twice the enhancement in one sphere of influence. The net effect is a breakdown of the structure of water in the HtpO process. 

Fig. 8.22. Schematic illustration of the change in the structure of water around the solutes when brought from infinite separation to a close distance. The stabilization of the structure of water induced by two separate solutes is expected to be larger than the corresponding effect for the same pair of solutes at close distance. The large circles surrounding the solute particles designate the regions of influence of the solute on the solvent.

Thus, a relaxation time t = rl/3rpD for the precipitation process can be given, c is the average concentration of the precipitating component in the region of influence 4/3-7rr, and is small compared to Furthermore, under the conditions of applicability of eq. (7-40) the following mass balance can be written ... 

Figure 159. Schematic representation of an indentation with the expected region of influence.

---