Results distribution

The resulting distribution of compounds having different modes of action in the output layer after training the network is shown in figure 10.1-10. 

In using the table for pore size calculations, it is necessary to read off the values of the uptake from the experimental isotherm for the values of p/p° corresponding to the different r values given in the table. Unfortunately, these values of relative pressure do not correspond to division marks on the scale of abscissae, so that care is needed if inaccuracy is to be avoided. This difficulty can be circumvented by basing the standard table on even intervals of relative pressure rather than of r but this then leads to uneven spacings of r . Table 3.6 illustrates the application of the standard table to a specific example—the desorption branch of the silica isotherm already referred to. The resultant distribution curve appears as Curve C in Fig. 3.18. 

The same approach can be used to derive an equation for the distribution ratio when the solute is a molecular weak base, B, (Figure 7.24). The resulting distribution ratio is... 

Since the t distribution relies on the sample standard deviation. s, the resultant distribution will differ according to the sample size n. To designate this difference, the respec tive distributions are classified according to what are called the degrees of freedom and abbreviated as df. In simple problems, the df are just the sample size minus I. In more complicated applications the df can be different. In general, degrees of freedom are the number of quantities minus the number of constraints. For example, four numbers in a square which must have row and column sums equal to zero have only one df, i.e., four numbers minus three constraints (the fourth constraint is redundant). 

The resultant distribution of the parameter estimates are also unknown. 

The Central Limit Theorem gives an a priori reason for why things tend to be normally distributed. It says the sum of a large number of independent random distributions having finite means and variances is normally distributed. Furthermore, the mean of the resulting distribution the sum of the individual means the combined variance is the sum of the individual variance.. ... 

The above considerations give us a technique for estimating the required jet momentum and outlet flow rates. Other important parameters are the heights of the inlet and outlet apertures. The choice of these parameters will not, in general, have a significant effect on the overall fluid flow pattern and the resulting distribution of the contaminant, and these should be chosen to optimize the performance of the inlet and exhaust pumps. 

In pressing, the threshold concentration of the filler amounts to about 0.5% of volume. The resulting distribution of the filler corresponds, apparently, to the model of mixing of spherical particles of the polymer (with radius Rp) and filler (with radius Rm) for Rp > Rm as the size of carbon black particles is usually about 1000 A [19]. During this mixing, the filler, because of electrostatical interaction, is distributed mainly on the surface of polymer particles which facilitates the forming of conducting chains and entails low values of the percolation threshold. 

Pulsed deuteron NMR is described, which has recently been developed to become a powerftd tool for studying molectdar order and dynamics in solid polymers. In drawn fibres the complete orientational distribution function for the polymer chains can be determined from the analysis of deuteron NMR line shapes. By analyzing the line shapes of 2H absorption spectra and spectra obtained via solid echo and spin alignment, respectively, both type and timescale of rotational motions can be determined over an extraordinary wide range of characteristic frequencies, approximately 10 MHz to 1 Hz. In addition, motional heterogeneities can be detected and the resulting distribution of correlation times can directly be determined. 

Assume that we have a program we will run on np processors and that this program has a serial portion and a parallel portion. For example, the serial portion of the code might read in input and calculate certain global parameters. It does not make any difference if this work is done on one processor and the results distributed, or if each processor performs identical tasks independently this is essentially serial work. Then the time t it takes the program to run in serial on one processor is the sum of the time spent in the serial portion of the code and the time spent in the parallel portion (i.e., the portion of the code that can be parallelized) is t = tg + tp. Amdahl s law defines a parallel efficiency, Pe, of the code as the ratio of total wall clock time to run on one processor to the total wall clock time to run on np processors. We give a formulation of Amdahl s law due to Meijer [42] ... 

This distinction is meaningful if the resultant distribution function is of the type shown in Figure 4.7 (Szwarc, 1965). This figure shows that there is a high probability that the cation and anion are either in contact, separated by a solvent molecule or far apart (Szwarc, 1965). Intermediate positions are improbable. The structure of solvated ion-pairs has been studied by Grunwald (1979) using dipole measurements. 

The response from the water and hydrocarbon can be distinguished by measuring the distributions of the diffusion coefficients simultaneously with the distributions of the relaxation times. The resulting distributions are displayed on a two-dimensional diffusion coefficient-relaxation time map and the distributions for... 

In the previous section it was assumed that quantities of (he order of Unp and 1 tnpq were negligible. In that case the mean value of np is a large number. However, in many applications the quantity p is small and the product np remains finite. In this case the distribution is spread out, although the mean value remains small. The resulting distribution is no longer symmetrical. This behavior is illustrated in Fig. 1. 

Using the previous equations and the calculated P/t- ratios, we can determine the angular shapes of the /detection( d) distribution for m J = 0, 1, or 2. The resulting distributions are shown in Fig. 4. Note that since the ratios of V k were used, the absolute scale is arbitrary only the relative shapes and magnitudes are important. We then fit the angular distribution data to a sum of these functions multiplied by the /dissociation term to obtain the relative m,j populations and the / value ... 

A total of 10,000 iterations or calculations of dose were performed as part of this simulation, and Figure 4 shows the resulting distribution of average daily doses of chlorpyrifos as determined by the Monte Carlo simulation. Common practice in exposure and risk assessment is to characterize the 50th percentile as a "typical" exposure and the 95th percentile as the "reasonable maximum" exposure.4 The distributional analysis for these calculated doses... 

Data on surface radium concentrations has been compiled for 394 of the 474 quadrangles covering the conterminous 48 states. The resulting distribution is illustrated in Figure 2, where the parameters shown for the distribution are calculated from the binned data. This distribution has a GM of 25 Bq kg and geometric standard deviation (GSD) of 1.75. Based on this distribution, approximately 20% of the surface radium concentration data are above 40 Bq kg and 0.7% are above 100 Bq kg... 

Adsorption and ion exchange share so many common features in regard to application in batch and fixed-bed processes that they can be grouped together as sorption for a unified treatment. These processes involve the transfer and resulting distribution of one or more solutes between a fluid phase and particles. The partitioning of a single solute between fluid and sorbed phases or the selectivity of a sorbent toward multiple solutes makes it possible to separate solutes from a bulk fluid phase or from one another. 

A special case of the gamma distribution is obtained by replacing a. by n+1, where n is an integer, and x by fix (this can be easily achieved using the change of variable technique discussed below). The resulting distribution f(x) is... 

The pore size distribution (PSD) for mesopores and micropores were calculated using DFT (Density Funetional Theory) method and the resulting distribution curves are given in Fig. 21.3. Total mesopore volume (V ) was determined as 0.022 cm g and total mieropore volume (V. ) was determined as 0.709 em g from the eorresponding method. The ACC consists of pores mainly in micro character (<20 A) as seen both from Fig. 21.3. The pH value of ACC used in this study had been previously found to be 7.4 [4]. 

The first method chosen to express the coal-mineral association results is in terms of the weight fraction of mineral matter in the individual particles, as determined from their cross section. The resulting distribution is comparable to the so-called "grade distributions" used in the mineral industry [8,9]. Such a distribution is included in Table II for the Upper Freeport coal. The data in the table indicate that pyrite is preferentially liberated as compared to quartz or kaolinite. About 78% of the pyrite is in particles containing more than 80% mineral matter, which should be easily removed by density-based separations. 

The non-equivalence of the statistical and kinetic methods Is given by the fact that the statistical generation Is always a Markovian process yielding a Markovian distribution, e.g. In case of a blfunc-tlonal monomer the most probable or pseudo-most probable distributions. The kinetic generation Is described by deterministic differential equations. Although the Individual addition steps can be Markovian, the resulting distribution can be non-Markovian. An Initiated step polyaddltlon can be taken as an example the distribution Is determined by the memory characterized by the relative rate of the Initiation step ( ). ... 

The nature of soil-phenolic acid interaction adsorption-desorption. Adsorption of a solute from solution onto a solid matrix results in a higher solute concentration at the fluid-solid interface than in the solution. Huang and coworkers (27) observed a high sorption capacity of the mineral fraction of four latosols for phenolic acids. On the basis of their results, distribution coefficients,... 

When distributions are combined, for example, in joint probability curves, it is important to ensure that the resulting distribution is meaningful, again in terms of what is distributed and with respect to what variable (Suter 1998, p 129). 

The 2nd limitation is that maintaining the optimality of answers may be hard when there are repeated variables or when there is a lot of empirical information about complex dependencies among the variables. Although the individual arithmetic operations yield best possible results at each step in the calculation, when these operations are chained together to compute the full risk expression, this optimality may be lost when variables appear multiple times in the expression, or when there are subtle intervariable dependencies present. Repeated variables are a problem essentially because they introduce their uncertainty more than once into the calculation. For this reason, the resulting bounds may not be as narrow as they should be. It is always possible to guarantee that the results will enclose the true result distribution,... 

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