Generalized LS

Case HI Generalized LS estimation will yield ML estimates whenever the errors are distributed with variances that change from experiment to experiment. Therefore, in this case our choice for Q, should be [CGFfs,)] 1 for r l.N. 

The converged parameter values represent the Least Squares (LS), Weighted LS or Generalized LS estimates depending on the choice of the weighting matrices Q,. Furthermore, if certain assumptions regarding the statistical distribution of the residuals hold, these parameter values could also be the Maximum Likelihood (ML) estimates. 

Least squares (LS) estimation minimizes the sum of squared deviations, comparing observed values to values predicted by a curve with particular parameter values. Weighted LS (WLS) can take into account differences in the variances of residuals generalized LS (GLS) can take into account covariances of residuals as well as differences in weights. Cases of LS estimation include the following ... 

IGLS = Flag to use Generalized LS (IGLS=1) or Weighted LS (IGLS=0)... 

V n der W ls Interactions. Van der Waals iateractions result from the asymmetric distribution of electronic charge surrounding an atom, which induces a complementary dipole in a neighboring atom, resulting in an attractive force. In general, the attractive force of van der Waals interactions is very weak (<4.2 kJ/mol (1 kcal/mol)) but may become significant if steric complementarity creates an opportunity to form a large number of van der Waals attractions. 

Moderately Volatile Ma.teria.ls, For moderately volatile materials, such as the amines commonly used in feedwater and boiler water chemical treatment, the distribution ratios vary from 0.1 to 30 for gases, the ratios are much higher. The distribution ratios of amines and organic acids are generally temperature-dependent. The distribution ratios for ammonia [7664-41-7] morpholine [110-91-8] and acetic acid [64-19-7] are shown in Figure 16 as examples. 

Specific Conductance. The specific conductance depends on the total concentration of the dissolved ioni2ed substances, ie, the ionic strength of a water sample. It is an expression of the abiUty of the water to conduct an electric current. Freshly distilled water has a conductance of 0.5—2 ]lS/cm, whereas that of potable water generally is 50—1500 ]lS/cm. The conductivity of a water sample is measured by means of an a-c Wheatstone-bridge circuit with a null indicator and a conductance cell. Each cell has an associated constant which, when multiphed by the conductance, yields the specific conductance. 

GPF = general purpose furnace SRF = semireinforcing furnace MT = medium thermal HS = high structure LS = low structure LM = low modulus. Dibutyl phthalate [84-74-2] absorption. 

Underwood minimum reflux constant XjF = Mol fraction of component i in the feed XjD = Mol fraction of component i in the distillate q = Thermal condition of the feed Bubble point liquid q =1.0 Dew point vapor q =0 General feed q = (Ls - Lr)/F... 

For greater details on the techniques of LS counting in general, including the specialized nuclear instrumentation required and sample handling and preparation, see Refs 5, 6 7... 

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