Continuous symmetry measure applications

These are but few examples which illustrate the need for a continuous scale of symmetry. A general approach which answers this need was layed out in refs. [7] and [2], Here we summarize its main features, show how the above mentioned examples are approached, and extend our theory of continuous symmetry measures (CSM) to three new applications ... 

TTie dissimilarity of A and Af i p p provides a symmetry deficiency measure analogous to the ZPA continuous symmetry measure of discrete point sets. As a dissimilarity measure, both the SNDSM metric and the Hausdorff metric, or any other dissimilarity measure suitable for continua, are applicable. 

In a sample containing a mixture of compounds, individual species may be resonance enhanced at different wavelengths. In some cases it may be possible to measure resonance Raman spectra from individual components in a mixture by selective excitation of specific absorption bands. Moreover, the assignment of resonance-enhanced vibrations provides detailed information about the local symmetry of the species. RRS has been used widely to characterize biological samples in which electronic transitions occur at visible excitation wavelengths, and commercial continuous wave lasers are readily available. Resonance Raman spectroscopic characterization of solid catalysts and adsorbed species has seen limited application. Many catalytic materials are white, but their electronic transitions often occur at ultraviolet wavelengths. With the availability of continuous wave and tunable, pulsed ultraviolet laser sources, we anticipate the application of RRS to catalysts will increase substantially. This expectation has motivated the present review. 

Computer Graphics and Molecular Modeling Conformational Analysis 1 Electrostatic Catalysis Molecular Docking and Structure-based Design Protein Structure Prediction in ID, 2D, and 3D Structural Chemistry Application of Mathematics Symmetry and Chirality Continuous Measures Symmetry in Chemistry. 

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