Estimated density

Keywords, protein folding, tertiary structure, potential energy surface, global optimization, empirical potential, residue potential, surface potential, parameter estimation, density estimation, cluster analysis, quadratic programming... 

One therefore needs a smooth density estimation techniques that is more reliable than the histogram estimates. The automatic estimation poses additional problems in that the traditional statistical techniques for estimating densities usually require the interactive selection of some smoothing parameter (such as the bin size). Some publicly available density estimators are available, but these tended to oversmooth the densities. So we tried a number of ideas based on numerical differentiation of the empirical cdf to devise a better density estimator. 

We can estimate densities of solids from the information in Figure 10-1. Radium has Z = 88 and an approximate atomic volume of 40 cm3 /mol. Then we use the molar mass of radium to determine its density ... 

Figure 8.16 (a) IR and (b) Raman spectra for the mineral calcite, CaC03. The estimated density of vibrational states is given in (c) while the deconvolution of the total heat capacity into contributions from the acoustic and internal optic modes as well as from the optic continuum is given in (d). 

Light hydrocarbon is a field term referring to color and estimated density, and is used where no NAPL samples have been analyzed. b LNAPL pool borders site boundary or lacks sufficient wells for good control, resulting in minimum area estimates. c Only one LNAPL sample was analyzed. 

For a system of fused rings, a 7.5% increase has been recommended for each ring. Based on 166 test liquids, the correlation between observed and estimated densities has been analyzed by a least square fit (p0bS = 1.01/9est - 0.006 r2 = 0.982). For only two compounds (acetonitrile and dibromochloromethane) does the error exceed 0.1 gem-3. Girolami has demonstrated this method for dimethylethylphosphine,... 

Application of the LOGIC method is demonstrated in Figure 3.4.1 with 3,8-diethyldecane. The estimated density is 0.7740gem-3. Experimental values of 0.7770 and 0.7340gem-3 are known at 20 and 80°C, respectively [34], Interpolation yields a value of 0.7732gem-3 at 25°C, which compares favorably with the estimated value. 

Similarly, if the effect of rare earth is modeled as if rare earth were present as RE203, the estimated density change for a 0.5% change in RE content is... 

The study by TC with the surface X-ray scattering also suggested that at high electric fields the density of the water next to the metal surface is unexpectedly high. At a equal to —10 and + 25 juC/cm2, the ratios of the estimated density in the inner layer to that expected from the bulk density of water were 1.3 and 2.3, respectively. 

Using this simplified approach the estimated density is 531.8 kg/m3. 

The density of a substance is the mass per unit volume of the substance (kg/m, g/cm Ibm/ft, etc.) The specific volume of a substance is the volume occupied by a unit mass of the substance it is the inverse of density. Densities of pure solids and liquids are essentially independent of pressure and vary relatively slightly with temperature. Hie temperature variation may be in either direction the density of liquid water, for example, increases from 0.999868 g/cm at 0°C to 1.00000 g/cm at 3.98°C, and then decreases to 0.95838 g/cm at 100°C. Densities of many pure compounds, solutions, and mixtures may be found in standard references (such as Perry s Chemical Engineers Handbook pp. 2-7 through 2-47 and 2-91 through 2-120). Methods of estimating densities of gases and mixtures of liquids are given in Chapter 5 of this book. 

High pressure equipment is generally cumbersome to handle, and only in rare instances is it possible to make meaningful visual observations on a reacting system. It is almost always better to rely on indirect measurements. It is also unfortunate that P-V-T relations are known for only the most common monomers at high pressures, and in most cases it is necessary to estimate densities. Due largely to the work of Bridgman (4) some excellent P-V-T data are available for most common solvents. 

Adjust the Percoll gradients, placing the solution with the estimated density of apoptotic cells at the bottom of the tube. 

The gravimetric density of the crystals was not measured hut the content of the unit cell may be established by using Eq. 6.5 and the expectation that the reasonable value of p should be between 4 and 5 g/cm. The estimated density assuming NiMnOs composition has a reasonable value of 4.86 g/cm when Z = 4. The two closest numbers of formula units (Z = 3 or 5) are impossible due to the restrictions imposed by symmetry in a base-centered lattice, sites with odd multiplicities are impossible. The next two closest numbers (Z = 2 or 6) result in unrealistically low and high densities, respectively. Thus, we assume that there are 4 Mn, 4 Ni and 12 O atoms in the unit cell. 

To estimate the statistical errors in the estimated density of states, 7 independent simulations are conducted, with exactly the same code, but with different random-number generator seeds. The calculated density of states always contains an arbitrary multiplier the estimated densities of states from these 7 runs are matched by shifting each In f2 E) in such a way as to minimize the total variance. 

A number of models which can estimate density at atmospheric pressure have recently been reported. For example, Rebelo et al. [63, 64] defined the effective molar volumes of ions at 298.15 K and used the assumption of ideal behavior for the determination of the molar volume of ionic liquids. Yang et al. [65] used a theory based on the interstice model which correlated the density and the surface tension of the ionic liquid. Group contribution models have been reported by Kim et al. [66, 67] for the calculation of the density and C02 gas solubility for 1-alkyl-3-methylimidazolium based ionic liquids as a function of the temperature and C02 gas pressure with reasonable accuracy over a 50 K temperature range however, the... 

Palomar et al. have carried out continuum model calculations on B3LYP/6-31++G optimized geometries of the following cations [Cmim]+ with n = 1, 2,4, 6, 8 and the following anions [Cl]-, [BFJ-, [FeClJ-, [PF6] , [NTf2]", [MeSOJ-, [EtSOJ", [TfO]" in order to estimate density and molar volume [158], A satisfactory prediction of the data is found with the exception of the ion pairs containing [PF6]- and [BFJ- anions. 

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... 

In the second phase of the development, the ability of property estimation of the network is examined with the data samples which are measured from the experimental process but never used in the training session. Based on the experimental data which were available for the trial, we trained and tested the ANN network to predict densities of FGM. Table 1 shows the comparison of measured and the network estimated densities of as-synthesized TiB2-Cu FGM using the Self-propagating High-temperature Synthesis (SHS) technique. The result indicates that the ANN network can give quite good estimations to the FGM properties. 

Prior to 1960, chemists had few tools with which to answer these questions. In some cases, it was possible to make reasonably good estimates of a planet s density, for example, based on its mass and volume. Both characteristics can be determined relatively easily from the planet s orbital path. Once a planet s density had been estimated, scientists could develop models that would fit the estimated density. 

Figure 4 shows results when the reference state uses data on another system. The P — x behavior for hydrogen and tetralin (12) is obtained using estimated densities, pure component and binary parameters, and Henry s constant for hydrogen in quinoline. The last was found from correlating the high-pressure data of Chao (12). 

An analytical relation for estimating density-driven fluid overturning was dealt with in detail by England et al. (1995). The relation they used was (symbols as in Table 1)... 

The small decrease or practically no change in density observed for material B in all exposures and for material A in exposures without water is as expected the density of cristobalite is 2.33 g/cm whereas the estimated density of the amorphous phase is 2.45 g/cm thus crystallization of Si02 should lead to a decrease in density. The most extensive crystallization was observed in material B after the bulk exposures in water vapour. Also the oxidation leads to the decrease in density, density of SiC is 3,17 g/cm and of amorphous Si02 2.2 g/cm. A thin oxidation layer formed on cut and plain SiC grain surfaces in all exposures. Despite that the oxidation was minor in material A and again the most effective in material B after the bulk exposures with water vapour. 

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