Weighing factors

An estimate for the G value for ethylene removal by ionic reactions can be made from the ion intensities of the 5-torr spectrum. First, the total intensity of accounted ions is set equal to unity. Then we multiply the intensities of the given ions by the number of ethylene molecules used up in their formation. Some of the weighing factors used were ... 

The overall cost optimization criterion (5.4-137) to be minimized is composed of two terms. The first, which is called proportional, is related to the yield of both C and E one needs to maximize the yield of C, Yc, while minimising the ratio of yields, Y c. Yc and Kg are nc.f/nB.o and nE./nBA, respectively, n is number of moles, and y is a factor expressing the relative weight of the two terms (y was assumed to be one). The second term, called the non-proportional or fixed cost of operation, is the reciprocal of the ratio of yield of C per batch time, s, and as such it should be minimized, p is the weighing factor (equal to 174 in the process under consideration) in this term. 

Cost-weighing factor applied to film heat transfer coefficients to allow for mixed materials of construction, pressure rating, and equipment types in heat exchanger networks (-), or fugacity coefficient (-)... 

With a proper balancing of C and Ci this turned out to be a valid strategy, which of course is very sensitive to changes in the weighing factors of other terms in the objective function components. The makespan can be simply obtained by introducing an additional inequality that describes that the makespan should be greater than the end-time of casting for the last - or all - batches. 

It can be concluded that, with regard to aquatic toxicities, in the Environment Agency (UK) assessment, the longer chain ethox-ylates (nEo = 4-15) were attributed higher relative potencies than in the Environment Canada assessment. This may be due to several reasons the UK assessment considered only acute toxicities, whereas the Canadian considered both acute and chronic ones. Moreover, in the Canadian assessment many more data (i.e. more than 200) were considered than in the UK assessment, and weighing factors were applied related to the confidence in the studies. 

The relative SAA s of the surface atoms that may later be used as weighing factors in estimations of the surface-solvent interactions. 

In caring for an individual, a treatment based on broad analytical thinking about the cause and nature of the pain has the best chance of success. However, the ladder may serve as an educational and, to some extent, practical guide in weighing factors such as analgesic potency, mechanism of action and risk of adverse reactions. 

To control the relation between M(x) and V(x) in L(x), which is in equation (17) still completely dependent on t, a weighing factor /L is introduced, which results in ... 

Fig. 4. ESC—European Stationary Cycle, weighing factors are given for the individual points...

The architecture of a common NN is shown in Fig. 10.8. The design depends on the types of sensor responses, on their dynamic range, drift, and so on. In short, it depends on all the complexities of the transfer functions of different types of sensors. Once again there is an input layer containing m input elements. It is massively interconnected to the n nodes of the next hidden layer %n at which the weighing factors Wn operate on the signal. There can be more than one hidden layer, if necessary. The connection to the output layer 0O has the form of nonlinear transfer function /hid for example,... 

This is useful for pattern recognition. The parameter / influences the nonlinearity of the hidden layer transfer function. The training of the NN is then based on the feedforward and backpropagation algorithm, in which the weighing factors Wn are adjusted during the NN learning in order to minimize the difference between the desired output D and the actual output Y. 

In principle, weighing factors w, can be based upon the information of the measurement error of y at position x,-. If the error has been estimated from n[ measurements at each calibration position x ... 

For a given size distribution, various averaged diameters can be calculated, depending on the forms of weighing factors. The selection of an appropriate averaged diameter of a particle system depends on the specific needs of the application. For instance, in a pulverized coal combustion process, the surface area per unit volume may be important. In this case, Sauter s averaged diameter should be chosen. 

We might say that if Pv is used as the elemental criterion, a weighing factor is automatically built into the (sum or product) criterion for the entire chromatogram, which puts the emphasis either on the major or on the minor components in the sample. 

Weighted Regression Heteroskedasticity can be solved by introducing weighing factors (Wj) in the regression model. The weighing factors are inversely related to the variance Wt = 1 /S t. 

The above equations have already been described in the literature [8]. It is not the evaluation of heteroskedasticity, nor the application of the above equations, that causes problems in analytical chemistry, but the choice of the weighing factors. If you have a large number of replicates at each concentration level, the weighing factors are easily estimated by calculating the variance of the replicates at each concentration level. However, the number of data points available during a calibration experiment is limited (i.e., six concentration levels with two or three replicates at each level). 

Ignoring heteroskedasticity in an ordinary calibration experiment will not lead to major errors when measuring in the middle of the calibration line since the estimated regression parameters are unbiased (it should be recalled that the regression estimators are inefficient, but unbiased). However, the uncertainty of the results is much larger in the lower part of the calibration line when incorrect or no weighing factors have been applied to correct for heteroskedasticity. It should be stressed that extreme errors are introduced by using the calibration line for the estimation of the detection capability, if heteroskedasticity is not corrected. 

Here Wj is the weighing factor associated with component i. Altena and Smolders (1982) propose Wj be set equal to the reciprocal of mf to account for the large differences in molar volumes between solvents and polymers. pjkl is the experimental volume fraction of... 

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