Density-based methods

One density-based method is the Dry Tribo-Separation process where separation relies not only on density, but also on the difference in friction coefficients of various particle sizes and shapes (Eiderman et al. 2000). Dry material is fed onto the surface of a rotating conical bowl and a combination of centrifugal, frictional, and gravitational forces separates the ash into two products one that is enriched in carbon and one that is carbon-lean. This process is currently under development but has demonstrated the potential to separate particles by size as well as by shape. 

A density-based method clusters gene expression data based on the notion of density. It grows clusters either according to the density of neighborhood clusters or according to some estimated density functions.55... 

Clustering algorithms can be classified into four major approaches hierarchical methods, partitioning-based methods, density-based methods, and grid-based methods. Here, we will focus on the hierarchical cluster approach because it is often used in the context of structure-activity analysis. Recent research has suggested that hierarchical methods perform better than the more commonly used nonhierarchical methods in separating known actives and inactives [41]. 

Structure Optimization. - Independent of whether a wavefunction-based or a density-based method is applied, E of Eq. (3) is a function of all nuclear coordinates,... 

The differences between wave mechanics and density-based methods can be summarized as follows ... 

However, there is still interest in old-fashioned Thomas-Fermi-like OF-DFT. Part of this interest is practical in KS-DFT, one must determine the form of N three-dimensional functions (the occupied Kohn-Sham orbitals), but in OF-DFT, one needs to determine only one three-dimensional function (the electron density). Therefore, OF-DFT methods are computationally easier than KS-DFT. Some of the interest is certainly aesthetic density-based methods are appealing precisely... 

A density-based method has been introduced for polyethylene classification relying on ASTM-standards (Table 2.2). The density-based classification coincides to some extent with that based on the polymerisation processes. Consequently, polyethylene with low density (LDPE) is usually a polyethylene material produced by high-pressure polymerisation and polyethylene with high density (HDPE) is a polyethylene material manufactured by low-pressure polymerisation. Since the end of the 1970s co-... 

Density-based methods Wave function-based methods Some technical aspects Excitations in various systems Excitations in metal clusters Excitations in semiconductor nanoparticles Excitations in organic and biological systems Identification of structure Dynamics in excited states Conclusions... 

In addition, one may distinguish between density- and wavefunction-based methods. With the wavefunction-based methods one attempts to solve the electronic Schrodinger equation as accurately as possible, in some cases at high computational costs. The density-based methods are based on the density-functional theory and have, in practical applications, to invoke some more or less controllable approximations. On the other hand, in most cases they lead to accurate results at less computational costs as the wavefunction-based methods. In some of the earlier reports by the present author in this series, the performance of density-based methods has been studied and also compared with that of wavefunction-based methods. ... 

FIGURE 20 Density-based methods individual and cumulative potentials in the univariate case when (A) triangular or (B) Gaussian functions are used. 

Method Based on the Equivalent Determinant The second approach for estimating the critical limits of the cumulative potential to be used for class modelling was proposed by Forina et al. and is based on the concept of equivalent determinant [59,60]. By the term equivalent determinant, the authors indicate the determinant of the variance/covariance matrix of the multivariate normal distribution having the same value of the mean probability density as the one estimated by the density-based method. Without entering in the details of the procedure, it is possible to demonstrate... 

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