Logarithms, proportional

An external standardisation method is employed to perform quantitative analysis. In the cited study, calibration curves for each compound are obtained by injecting amounts ranging from 0.08 to 10 nmol. The amount of injected standards is logarithmically proportional to the peak area. 

The amounts of injected compounds are logarithmically proportional to the peak area. Calibration curves in the range from 0.08 to 10 nmol showed a regression coefficient from 0.991 to 0.998. Sensitivity was in the subnanomolar range. This method results in a versatile and cost-effective procedure for the detection and quantification of BAs. 

Fig. 9. Schematic design of a carbon dioxide partial pressure (pC02) electrode. C02 diffuses through the membrane into or out of the electrolyte where it equilibrates with HCO, thus generating or consuming protons. The respective pH change of the electrolyte is sensed with a pH electrode and is logarithmically proportional to the pC02 in the measuring solution. Since the electrolyte may become exhausted, one can replace it through in/out lines. These can also be used to re-calibrate the pH electrode. Therefore, the electrode is retractable by means of a mechanical positioner...

The volatile components of both wasabi and horseradish formed by the hydrolysis of thioglucosides with myrosinase are known to possess a strong pungency. The difference between wasabi and horseradish is a green odor. The ratio of the concentration to the odor threshold, C/T, is called the aroma value. Sensory response is logarithmically proportional to the amount of stimulus. In this study, the log of the aroma values, log(C/T), for 14 isothiocyanates have been used instead of their conventional aroma values. co-Alkenyl isothiocyanates, which possessed higher log(C/T) values than those of horseradish, contributed to the green odor of wasabi. Furthermore, the yields and the values of log(C/T) of the isothiocyanates catalyzed by myrosinase were affected by pH and temperature. 

The concentration divided by the odor threshold value, C/T is called the aroma value (22). Odorants with high aroma values are important contributors to the characteristic flavors. In general, the estimated feel of the stimulus is logarithmically proportional to the objectively measured strength of the stimulus... 

This model suggests that //> is linearly proportional to pi, kj, Cb, and and logarithmically proportional to K. Furthermore, it increases with a decreasing po, which is an intrinsic advantage of facilitated transport membranes, as observed experimentally. The linear increase in / F relative to Cb and 2 represents the importance of both the carrier concentration and the releasing-reaction rate between the carrier and the small molecule. Note that pd can be empirically obtained from the slope of a plot of /F-1 versus (l/poX2 k, CC Xln(l+/i p )/po) [48,49]. 

A typical detector system in FIA usually records the signal against time in a continuous flow and must be sensible to variations of sample concentration. The most frequently used detector systems are potentiometric and spectrophotometric ones (Table 30.1) due to ease of assembly and their specificity, once the potential is proportional to concentration as well as to absorbance. Potentiometric detection was used by Shpigun et al. (2006) to assess antioxidant activity by iron reduction. The potential of the [Fe(CN)g] was measured against time, when an antioxidant sample was injected, the potential decreased due to iron reduction to [Fe(CN)g] a negative peak height (H) (measured in mV) has a logarithmic proportion to antioxidant concentration. 

An interesting detail is that in logarithmic proportions the middle, rising part of the dependence is practically linear, meaning that there is a certain range of bias currents where specific detectivily increases exponentially. In real situations this is significantly impaired by the existence of 1/f noise. 

The associated logarithmic function touches another inquisitive sphere -psychology - where an almost anonymous Czech priest Simerka [66] in the year 1882 made an experimental record and analysis of confrontation and quarrels based on his confession practice. He proposed that the strength of conviction, P, and number of reasons, D, are logarithmically proportional as P = log (1 + D) showing the table of D versus P pairs 0-0, 1 - 0.7, 2 - 1.1, 3 - 1.4, 10 - 2.4, 20 - 3.0 and 50 - 3.9. It follows that the most confident belief is for just one motive regardless if it is certainty or insinuation, defamation, journalese, publicity or politics while the cause multiplication does not improve the... 

In the simplest case, for a pressure drawdown survey, the radial inflow equation indicates that the bottom hole flowing pressure is proportional to the logarithm of time. From the straight line plot ot pressure against the log (time), the reservoir permeability can be determined, and subsequently the total skin of the well. For a build-up survey, a similar plot (the so-called Horner plot) may be used to determine the same parameters, whose values act as an independent quality check on those derived from the drawdown survey. 

Odors are characterized by quaUty and intensity. Descriptive quaUties such as sour, sweet, pungent, fishy, and spicy are commonly used. Intensity is deterrnined by how much the concentration of the odoriferous substance exceeds its detection threshold (the concentration at which most people can detect an odor). Odor intensity is approximately proportional to the logarithm of the concentration. However, several factors affect the abiUty of an individual to detect an odor the sensitivity of a subject s olfactory system, the presence of other masking odors, and olfactory fatigue (ie, reduced olfactory sensitivity during continued exposure to the odorous substance). In addition, the average person s sensitivity to odor decreases with age. 

H2O/100 kg of adsorbent. At equilibrium and at a given adsorbed water content, the dew point that can be obtained in the treated fluid is a function only of the adsorbent temperature. The slopes of the isosteres indicate that the capacity of molecular sieves is less temperature sensitive than that of siUca gel or activated alumina. In another type of isostere plot, the natural logarithm of the vapor pressure of water in equiUbrium with the desiccant is plotted against the reciprocal of absolute temperature. The slopes of these isosteres are proportional to the isosteric heats of adsorption of water on the desiccant (see... 

To reduce the work of compression in this cycle a two-stage or dualpressure process may be usedwhereby the pressure is reduced by two successive isenthalpic expansions. Since the isothermal work of compression is approximately proportional to the logarithm of the pressure ratio, and the Joule-Tnomson cooling is roughly proportional to... 

Deciview a unit of visibility proportional to the logarithm of the atmospheric extinction. Under many circumstances a change in one deciview will be perceived to be the same on clear and hazy days. 

Usually, only the Arrhenius energy of activation, E, is given in these papers it differs from the heat of activation,JH, by RT (about 0.6 kcal at ordinary temperatures). Only a few entropies of activa-tion, JS, were calculated the frequency factor, whose logarithm is tabulated, is proportional to this reaction parameter. It is clear that the rate, E, and JS determined for an 8jfAr2 reaction are for the overall, two-stage process. Both stages will contribute to the overall results when their free energies of activation are similar. 

A common error is to confuse the GPC distribution with the weight distribution. The response of a refractive index detector is proportional to the mass of polymer. The GPC elution volume (V) typically scales according to the logarithm of the degree of polymerization (or the logarithm of the molecular... 

IS we assume that np is constant or that it is sufficiently large so that np(r) is negligible (since (r) < 1) then in either case the total sum of money to be invested is proportional to A(ft)/[1 — n(r)]. Minimizing this function with respect to ft is achieved through its logarithm since d/dxlogf(x) =/ ( )//( ) is equal to zero if f (x) vanishes, which is precisely the desired condition. Applying these ideas leads to the equation... 

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