Down-going curve

You will very often need to find a rate constant or a half-life from real data. In the old days (before Microsoft), it was difficult to plot these data as a curved line as shown in Figure 2.2 and to fit a curved line to it such that one could read off the rate constant, k. Thus, it was handy to convert these data into a linear form and to fit a straight line. We can do this easily by taking the natural logarithm of the down-going equation and getting... 

We conclude that the probability for ET is given by the total probability to switch to the down-going curve. This probability is the electronic factor k, given by the following series ... 

While the F-N curve is a cumulative illustration, the risk profile shows the expected frequency of accidents of a particular category or level of consequence. The diagonal line is a line of constant risk defined such that the product of expected frequency and consequence is a constant at each point along the line. " As the consequences of accidents go up, the expected frequency should go down in order for the risk to remain constant. As the example illustrates, if a portion of the histogram sticks its head up above the line (i.e., a particular type of accident contributes more than its fair share of the risk), then that risk is inconsistent with the risk presented by other accident types. (Note There is no requirement that you use a line of constant risk other more appropriate risk criteria for your application can be easily defined and displayed on the graph.)... 

Systematizing these results, we see that both in Fig. 72 and in Fig. 73, if we follow tho succession of curves from top to bottom, we go from ions of dissimilar character to ions of similar character in Fig. 73 we go down to Li+ and (Oil)", both strong order-producing ions, while in Fig. 72 we go down to Cs+ and Br", both strong order-destroying ions. If the same rule—from dissimilar character downward to similar character— is to be applied to the rubidium and cesium halides, the order I, Br, Cl, F, will clearly have to be reversed, in order that Rbl and Csl shall be the lowest in each case. It has been known for several years that such an inversion exists. Table 40, compiled by Robinson and Harned, shows the order observed in the whole set of iodides, bromides, and chlorides. It will be seen that, for RbCl, RbBr, and Rbl, and likewise for CsCl, CsBr, and Rbl, the observed order is opposite to that found for the other alkali halides. Hitherto this inversion has been regarded as mysterious. But it falls in line with the facts depicted in Fig. 72,... 

Now that we have some of the ground rules down, let s just have a quick review of curved arrows, and the different types of arrows that you can draw. Every curved arrow has a head and a tail. It is essential that the head and tail of every arrow be drawn in precisely the proper place. The tail shows where the electrons are coming from, and the head shows where the electrons are going ... 

As a result of the adsorption of a donor gas, we are transferred up the curve go = go(er) in Fig. 8a. The adsorption of an acceptor gas, on the contrary, transfers one down this curve. If one remains on the acceptor branch of the curve, this will mean that the catalytic activity must increase when a donor gas is adsorbed and fall upon adsorption of an acceptor gas. This is in accord with much experimental data (see Section III.A). 

The kinetic curve of the accumulation and consumption of o-DNB anion-radicals is S-shaped and that of the accumulation of o-nitrophenolate is parabolic. The anion-radical accumulation curve starts to go down when the o-nitrophenolate accumulation curve reaches its maximum (Abe and Ikegame 1978). 

Beginning vertical strokes on the lower case t that go down and curve to the right (no beginning upstroke). This person wants people to stop beating around the bush and get to the point. Direct people don t like to be slowed down. 

Figure 6.55 presents the pressure profiles within the material for various melt flow front locations. First of all, we can see that the shear thinning behavior of the polymer has caused the pressure requirement to go down significantly (by a factor of 30). The curves presented in Fig. 6.55 also reveal that the shape of the curves was also affected when compared to the Newtonian profiles. 

This formula is valid for the modulus of elasticity, while v is the Poisson ratio of the matrix material. It is only valid up to cp 0,7 (near the tightest packing of spheres). For higher values, from cp = 1 going down to tp 0,3 (or lower) the structure can be reversed the roles of the components are exchanged. We can use the same formula, but now with 1 -

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