Shape domain partitioning

A shape domain partitioning in terms of relative local convexity of parameter b=0.005 leads to a simpler pattern. We obtain... 

The third shape domain partitioning shown has been calculated for the relative local convexity parameter b= - 0.008. We obtain... 

For the MIDCO surface G(a) of a given nuclear arrangement and for a selected shape domain partitioning relative to curvature parameter b, the shape matrix s(a,b) is defined [109,110,158,193] as follows ... 

If a different reference curvature value b is chosen, then the shape matrix may be different, although the matrix is invariant within small enough intervals of the b values. As examples, the three different shape matrices s(0.0l,0), s(0.01,0.005), and s(0.01,-0.008) of the three shape domain partitionings of the ally I alcohol MIDCO G(O.OI) shown in Figure 5.6 are given below. The index... 

A practical implementation of the above approach is the following a global shape property of the molecule is assigned to each point of the sphere S, followed by the determination of those domains of S where this shape property is invariant. A pair of examples is shown in Figure 5.9, where the shape globe invariance domains of a MIDCO surface for two relative convexity shape domain partitionings (P) with respect to two reference curvatures, b = 0, and b < 0, are given. As... 

As an example, the shape matrix s(0.0l,0) of the b=0 shape domain partitionings of the allyl alcohol MIDCO G(O.OI) shown in Figure 5.6 belongs to the (0.01,0) point of the parameter map (a,b). If the index ordering of the various D i domains follows the order of decreasing size of their surface area, then the shape matrix s(0.01,0) has the form given by Equation (5.12) ... 

As for the other partitionings mentioned above, these neighbor relations and graphs can be restricted to various subsets S, such as relaxed cross sections, and in particular, to individual catchment regions C(X,i) of the nuclear configuration space M. This approach leads to the local shape domain graphs g(S,x) and g(C(X,i),x), respectively. 

The crystalline PCL domain are rigid, and hold the matrix shape even when the drug begins to leach out (l ft)- This leaves voids into which water can diffuse (center). The remaining, hydrophilic drug preferentially partitions into the aqueous regions (right). 

These domains represent a partitioning of M, hence the union of these DD shape invariance domains is the entire nuclear configuration space M,... 

Domains of Common Three-Dimensional Shape Properties for the Partitioning of Nuclear Configuration Spaces... 

Several techniques have been developed over the last 15 years to visually probe the morphology of surfactant monolayers at the air-water interface. In fluorescence microscopy, a small amount of fluorescently labeled surfactant molecules is added to a monolayer due to steric effects these tagged molecules tend to partition into less-ordered phases, which results in a visual contrast between coexisting phases [25-29]. Fluorescence microscopy has been used to determine domain sizes and shapes during phase transitions [25,28,30]. Polarized fluorescence microscopy (PFM) provides additional information on the lipid hydrocarbon chain ordering within condensed monolayers, especially in areas where the lipid hydrocarbon chains are tilted with respect to the surface normal [31,32]. The interaction of the electric field vector of the polarized light with the absorption dipole moment of the... 

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