Log scales

Figure Bl.11.1. Resonance frequencies for different nuclei in a field of 14.1 T. Widths indicate the quoted range of shifts for each nucleus, and heights mdicate relative sensitivities at the natural isotopic abundance, on a log scale covering approximately six orders of magnitude. Nuclei resonatmg below 140 MHz are not shown.

Figure Cl. 1.3. Relative reactivity of transition-metal clusters with H2 (full curves, log scale) and tire promotion...

Figure 6.3 shows some data which constitute a test of Eq. (6.26). In Fig. 6.3a, Rp and [M] are plotted on a log-log scale for a constant level of redox initiator. The slope of this line, which indicates the order of the polymerization with respect to monomer, is unity, showing that the polymerization of methyl methacrylate is first order in monomer. Figure 6.3b is a similar plot of the initial rate of polymerization—which essentially maintains the monomer at constant con-centration—versus initiator concentration for several different monomer-initiator combinations. Each of the lines has a slope of indicating a half-order dependence on [I] as predicted by Eq. (6.26).

Fig. 24. Generalized method using log scales for estimating packed column flooding and pressure drop, AP, in kPa/m g = gravitational constant, 9.81 m/s t = kinematic viscosity in mm /s (= cSt) E, G have units of kg/(m s) are in kg/m and the packing factor, F, in can be found in...

The above information is conveniently summarised in the modulus diagram for a polymer. Figure 23.7 shows an example it is a modulus diagram for PMMA, and is typical of linear-amorphous polymers (PS, for example, has a very similar diagram). The modulus E is plotted, on a log scale, on the vertical axis it runs from 0.01 MPa to... 

Mathcad Plus 6, of MathSoft, Inc. was used) Independent Variables on log scale... 

All dimensions and tolerances are in millimetres and both axis have log scales. 

It can be observed from the previous expression that when rigid support), then Lu t = lu or the natural frequency of the rigid system. For a system with a finite stiffness at the supports, or K/, = Kr, then lu is less than Lu t. Hence, flexibility causes the natural frequency of the system to be lowered. Plotting the natural frequency as a function of bearing stiffness on a log scale provides a graph as shown in Figure 5-15. 

This equation implies that the relative reactivity is independent of the specific nucleophile and that relative reactivity is insensitive to changes in position of the transition state. Table 8.4 lists the B values for some representative ketones. The parameter B indicates relative reactivity on a log scale. Cyclohexanone is seen to be a particularly reactive ketone, being almost as reactive as cyclobutanone and more than 10 times as reactive as acetone. 

The creep modulus will vary with time, i.e. decrease as time increases, in a manner similar to that shown for the relaxation modulus. The classical variation of these moduli is illustrated in Fig. 2.9. On log-log scales it is observed that there is a high value of creep or relaxation modulus at short times. This is referred to as the Unrelaxed Modulus and is independent of time. Similarly at long times there is a low value Relaxed Modulus which is also independent of time. 

Quite often isochronous data is presented on log-log scales. One of the reasons for this is that on linear scales any slight, but possibly important, non-linearity between stress and strain may go unnoticed whereas the use of log-log scales will usually give a straight-line graph, the slope of which is an indication of the linearity of the material. If it is perfectly linear the slope will be 45°. If the material is non-linear the slope will be less than this. 

Formation constants K for complexes of dicyclohexyl-18-crown-6 ether with various cations. Note that, although the radii of Ca ", Na" and Hg + are very similar, the ratio of the formation constants is 1 6.3 225. Again, K" and Ba " have similar radii but the ratio of K is 1 35 in the reverse direction (note log scale). 

With the lithology matching the log scale, and assuming the formation fully invaded by mud filtrate, a neutron porosity and a density porosity can be determined. 

Fig. 14.3 Relationship between the resistance of an / him (log scale) and the concentration of the solute (courtesy Official Digest, 34 No. 452, 972-990, Sept. (1970))...

FIGURE 2.19 Potentiation and modulation of response through control of cellular processes, (a) Potentiation of inotropic response to isoproterenol in guinea pig papillary muscle by the phosphodiesterase inhibitor isobutylmethylxanthine (IBMX). Ordinates percent of maximal response to isoproterenol. Abscissa percent receptor occupancy by isoproterenol (log scale). Responses shown in absence (open circles) and presence (filled circles) of IBMX. Data redrawn from [7], (b) Effect of reduction in calcium ion concentration on carbachol contraction of guinea pig ileum. Responses in the presence of 2.5 mM (filled circles) and l.5mM (open circles) calcium ion in physiological media bathing the tissue. Data redrawn from [8],... 

FIGURE 2.21 Effects of desensitization on inotropic responses of guinea pig atria to isoproterenol (panel a) and prenalterol (panel b). Ordinates response as a percent of the maximal reaponse to isoproterenol. Abscissae logarithms of molar concentrations of agonist (log scale). Responses shown after peak response attained (within 5 minutes, filled circles) and after 90 minutes of incubation with the agonist (open triangles). Data redrawn from [6]. 

FIGURE 3.11 Constitutive activity in melanophores expressing hCTR2 receptor, (a) Basal melanophore activity, (b) Effect of transfection with human cDNA for human calcitonin receptors (16 j-ig/ml). (c) Concentration response curve for cDNA for human calcitonin receptors (abscissae as log scale) and constitutive activity. Data redrawn from [27]. 

FIGURE 11.13 A collection of 10 responses (ordinates) to a compound resulting from exposure of a biological preparation to 10 concentrations of the compound (abscissae, log scale). The dotted line indicates the mean total response of all of the concentrations. The sigmoidal curve indicates the best fit of a four-parameter logistic function to the data points. The data were fit to Emax = 5.2, n = 1, EC5o = 0.4 pM, and basal = 0.3. The value for F is 9.1, df=6, 10. This shows that the fit to the complex model is statistically preferred (the fit to the sigmoidal curve is indicated). 

The variation of the absolute surface charge as a function of surface potential (in linear-log scale) is shown in Figure 14-5. 

Plot the observed e.m.f. values against the concentrations of the standard solutions, using a semi-log graph paper which covers four cycles (i.e. spans four decades on the log scale) use the log axis for the concentrations, which should be in terms of fluoride ion concentration. A straight line plot (calibration curve) will be obtained. With increasing dilution of the solutions there tends to be a departure from the straight line with the electrode combination and measuring system referred to above, this becomes apparent when the fluoride ion concentration is reduced to ca 0.2 mg L-1. 

Fig. 2-39 Tensile-creep behavior of PP top on semilog scale and bottom on log-log scale.

Number of layers (plotted on a log scale) of 0.3-mil aluminum foil... 

Figure 6.5. 5 0 of tooth enamel phosphate versus body size (log scale) for Kenyan fauna analyzed in this study. With the exception of the dikdik, there is a general association between the two variables. In contrast to tbe body-size model (Bryant and Froelicb 1995) wbicb predicts a range of values close to l%o, however, the measured range in 8 0 values for species averages is 5%a. This and the anomalous values for the dikdik reflect physiological and behavioral adaptations by these desert adapted species. 

Levels of Exposure concentrations or doses for each health effect in the LSE tables are graphically displayed in the LSE figures. Exposure concentration or dose is measured on the log scale "y" axis. Inhalation exposure is reported in mg/m or ppm and oral exposure is reported in mg/kg/day. 

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