Localization Properties

Simultaneous time and frequency localization properties give to wavelets the... 

These chain models are well suited to investigate the dependence of tire phase behaviour on the molecular architecture and to explore the local properties (e.g., enriclnnent of amphiphiles at interfaces, molecular confonnations at interfaces). In order to investigate the effect of fluctuations on large length scales or the shapes of vesicles, more coarse-grained descriptions have to be explored. 

The optimization of the backtracking algorithm usually consists of an application of several heuristics which reduce the number of candidate atoms for mapping from Gq to Gj. These heuristics are based on local properties of the atoms such as atom types, number of bonds, bond orders, and ring membership. According to these properties the atoms in Gq and Gj are separated into different classes. This step is known in the literature as partitioning [13]. Table 6.1 illustrates the process of partitioning. 

Table 6.1. Application of partitioning approach for substructure search optimization. According to their local properties, the atoms of the graphs in Figure 6-2 are separated into several classes.

By a variation of chemistry and/or chain length the different time regimes can be shifted. From a simulation point of view we are again faced by the decision what kind of information we want to get out of the simulation. If one wants to look at very local properties, depending on the local chemistry of the individual monomers, there is no way around a simulation with all chemical details. However, one should keep in mind that by such a technique it is impossible to equilibrate the system near the glass transition temperature. 

The surface dividing the components of the mixture formed by a layer of surfactant characterizes the structure of the mixture on a mesoscopic length scale. This interface is described by its global properties such as the surface area, the Euler characteristic or genus, distribution of normal vectors, or in more detail by its local properties such as the mean and Gaussian curvatures. 

The division of the molecular volume into atomic basins follows from a deeper analysis based on the principle of stationary action. The shapes of the atomic basins, and the associated electron densities, in a functional group are very similar in different molecules. The local properties of the wave function are therefore transferable to a very good approximation, which rationalizes the basis for organic chemistry, that functional groups react similarly in different molecules. It may be shown that any observable... 

Tax-free holidays periods of possibly 3 to 15 years of no tax liability on profits (this also can apply to local, property or any other tax normally imposed on a firm) ... 

Once wells have been drilled into the formation, the local properties of the reservoir rocks and fluids can be determined. To constmct a realistic model of the reservoir, its properties over its total extent— not just at the well sites—must be known. One way of estimating these properties is to match production histories at the wells with those predicted by the reservoir model. This is a classic ill-posed inverse problem that is very difficult to solve. 

Usefulness From Energy Decomposition to Local Properties... 

Reinhardt P, Piquemal J-P, Savin A (2008) Fragment-localized Kohn-Sham orbitals via a Singles-CI procedure and application to local properties and intermolecular energy decomposition analysis. J Chem Theory Comput 4 2020... 

Serizawa, A., I. Kataoka, and I. Michiyoshi, 1975, Turbulence Structure of Air-Water Bubbly Flow— II, Local Properties, Int. J. Multiphase Flow 2 235 246. (3)... 

Frohlich, S., Lotz, M., Larson, B., Lilbbert, A., Schilgerl, K., Seekamp, M., Characterization of a Pilot Plant Airlift Tower Loop Bioreactor III. Evaluation of Local Properties of the Dispersed Gas Phase During Yeast Cultivation and in a Model Media, Biotechnol. Bioeng., 38 56 (1991b)... 

To date, the use of radiolabeled metalloporphyrins as imaging agents has focused on the intrinsic tumor localizing properties of porphyrins with variation in the porphyrin peripheral substructure... 

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