Directly proportionality

For the straight line in Fig. 2.5 where m = 1.0, this equation expresses direct proportionality between and y, the condition of Newtonian behavior. In the non-Newtonian region where m < 1, Eq. (2.11) may describe the data over an order of magnitude or so. Next we consider the relationship between the constant K and viscosity. If Eq. (2.11) is solved for K and the resulting expression multiplied and divided by 7 ", we obtain... 

According to some recent results (Sect. 5.5), the dependence of K on e and qs is more involved than suggested by Eq. (94). The dependence of K on ris is much weaker than a direct proportionality and the correct flow parameter to be used in Eq. (94) should be the local fluid kinetic energy ( v2) rather than the strain rate (e). For a constant flow geometry, however, the two variables v and e are interchangeable. At the present stage and in order not to complicate unduly the kinetic scheme, it will be assumed that the rate constant K varies with the MW and strain rate as ... 

Obviously, if the step in which T reacts is rate-controlling, then the overall reaction rate depends in some way upon the concentration and identity of T. This dependence may take the form of a direct proportionality to [T], but more complex forms have been given in the preceding paragraphs. If the reaction of an intermediate with a trap is faster than the step generating the intermediate, on the other hand, then the rate may not depend on either the concentration or the identity of the trap. If, for example, an organometal (RM) undergoes a slow, homolytic decomposition,... 

Thus, there is a direct proportionality between the momentum transfer and that portion of the mass transfer which is not attributable to bulk flow. 

The frequency with which molecules colHde is directly proportionate to their concentrations. For two different molecules A and B, the frequency with which they collide will double if the concentration of either A or B is doubled. If the concentrations of both A and B are doubled, the probability of collision will increase fourfold. 

Figure 41-11. A comparison of the kinetics of carrier-mediated (facilitated) diffusion with passive diffusion. The rate of movement in the latter is directly proportionate to solute concentration, whereas the process is saturable when carriers are involved. The concentration at half-maximal velocity is equal to the binding constant (KJ of the carrier for the solute. maximal rate.)...

Similarly, the condition dE/dV)T = 0 for an ideal gas demands direct proportionality between P and T, for according to Eq. (14) we then have... 

Expressions (1.45) and (1.46) which are valid in case of applicability of above assumptions indicate on availability of direct proportionality between the value of the change of the surface-adjacent conductivity of semiconductor adsorbent and concentration of chemisorbed particles on its surface, the latter being in charged form. This results in the fact that when the surface is covered by adsorbed particles at degrees lower... 

The key factor in voltammetry (and polarography) is that the applied potential is varied over the course of the measurement. The voltammogram, which is a current-applied potential curve, / = /( ), corresponds to a voltage scan over a range that induces oxidation or reduction of the analytes. This plot allows identification and measurement of the concentration of each species. Several metals can be determined. The limiting currents in the redox processes can be used for quantitative analysis this is the basis of voltammetric analysis [489]. The methods are based on the direct proportionality between the current and the concentration of the electroactive species, and exploit the ease and precision of measuring electric currents. Voltammetry is suitable for concentrations at or above ppm level. The sensitivity is often much higher than can be obtained with classical titrations. The sensitivity of voltammetric... 

Because of the interionic forces, the conductivity is directly proportional to the concentration only at low concentrations. At higher concentrations, the conductivity is lower than expected from direct proportionality. This decelerated growth of the conductivity corresponds to a decrease of the molar conductivity. Figure 2.4 gives some examples of the dependence of... 

This is the second of the two questions identified at the start of Section 1.2, where it was noted that the earliest pharmacologists had no choice but to use indirect methods in their attempts to account for the relationship between the concentration of a drug and the tissue response that it elicits. In the absence at that time of any means of obtaining direct evidence on the point, A. V. Hill and A. J. Clark explored the consequences of assuming (1) that the law of mass action applies, so that Eq. (1.2), derived above, holds and (2) that the response of the tissue is linearly related to receptor occupancy. Clark went further and made the tentative assumption that the relationship might be one of direct proportionality (though he was well aware that this was almost certainly an oversimplification, as we now know it usually is). 

Should there be direct proportionality, and using y to denote the response of a tissue (expressed as a percentage of the maximum response attainable with a large concentration of the agonist), the relationship between occupancy and response becomes ... 

An important difference from Ariens s concept of intrinsic activity is that efficacy, unlike intrinsic activity, has no upper limit it is always possible that an agonist with a greater efficacy than any existing compound may be discovered. Also, Stephenson s proposal was not finked to any specific assumption about the relationship between receptor occupancy and the response of the tissue. (Ariens, like A. J. Clark, had initially supposed direct proportionality, an assumption later to be abandoned.) According to Stephenson,... 

Assuming, hnally, that we are fortunate enough to be dealing with a simple response that is directly proportional to the fraction of receptors in the active condition, we can go on to predict the EC50. This is the concentration of L that causes the response to rise from its value ymn in the absence of L to vmm plus 50% of the maximum increase (ymax - vlmn) that L can induce. More formally, and assuming direct proportionality between y and pactive, we can write ... 

Table 5 shows that the ratio of the excretion rate under hydrous condition to that under anhydrous condition decreases with the decreasing water solubility of the salicylate or with the oil/water distribution coefficient. It can be said that the more water soluble compound is aided to a greater degree by the presence of moisture than those of lesser solubility. This trend is, however, not a direct proportionality due to the influence of other physical phenomena such as viscosity, molecular size, and intermolecular bonding. 

On a graph, what criteria represent direct proportionality ... 

It is important, however, to remove the protein layer from the surface over which the air/liquid meniscus is displaced during the measurement so as to assure that the conditions of flow with and without the layer in the capillary are totally comparable. Using this method we find that in the case of bovine serum albumin very thick layers are formed layers whose thickness grows in direct proportionality to albumin concentration up to 15% w/v, at least. We also find a reversible doubling of layer size as temperature is raised from 7.7 to 15°C in the case of triple helical soluble collagen adsorbed end on to glass. 

The set of energy levels associated with a particular substance is a unique characteristic of that substance and determines the frequencies at which electromagnetic radiation can be absorbed or emitted. Qualitative information regarding the composition and structure of a sample is obtained through a study of the positions and relative intensities of spectral lines or bands. Quantitative analysis is possible because of the direct proportionality between the intensity of a particular line or band and the number of atoms or molecules undergoing the transition. The various spectrometric techniques commonly used for analytical purposes and the type of information they provide are given in Table 7.1. 

Only arc/spark, plasma emission, plasma mass spectrometry and X-ray emission spectrometry are suitable techniques for qualitative analysis as in each case the relevant spectral ranges can be scanned and studied simply and quickly. Quantitative methods based on the emission of electromagnetic radiation rely on the direct proportionality between emitted intensity and the concentration of the analyte. The exact nature of the relation is complex and varies with the technique it will be discussed more fully in the appropriate sections. Quantitative measurements by atomic absorption spectrometry depend upon a relation which closely resembles the Beer-Lambert law relating to molecular absorption in solution (p. 357 etal.). 

We see a direct proportionality between the charge passed and the amount of material formed during electrolysis, as predicted by Faraday s first law. 

The lack of direct proportionality between the MIC values and the gyrase inhibition values is suggested reasonably to be related to varying relative cell-penetrating properties of the different agents. Thus, enoxacin would appear... 

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