Intensity logarithmic

Figure 15. Evolution of the mean coordinate in the potential (v) = x4/4 for different values of noise intensity (logarithmic scale).

Typical SAXS curves, expressing the experimental intensity (logarithmic scale) versus the scattering vector S (logarithmic scale), are represented in Figure 3, for ail the samples. 

Multivariate data analysis usually starts with generating a set of spectra and the corresponding chemical structures as a result of a spectrum similarity search in a spectrum database. The peak data are transformed into a set of spectral features and the chemical structures are encoded into molecular descriptors [80]. A spectral feature is a property that can be automatically computed from a mass spectrum. Typical spectral features are the peak intensity at a particular mass/charge value, or logarithmic intensity ratios. The goal of transformation of peak data into spectral features is to obtain descriptors of spectral properties that are more suitable than the original peak list data. 

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. 

Noise. Technical differences exist between personal noise dosimeters and high accuracy sound level meters and these may alter the usual preference for personal monitors. But it is exposure to noise rather than general room noise that must be estimated for comparison with noise exposure criteria, the logarithmic expression and alternative means of summation (3 vs 5 db doubling) compHcate statistics. Exposure criteria for both dose and peak exposure must be evaluated, and space and time variabiUty of noise intensity can be immense. 

Fig. 13. Characteristics of a 50-)J.m long DFB laser, (a) Light-current properties, (b) spectral intensity plotted on a logarithmic scale to better illustrate...

The intensity of "umami" increases linearly with a logarithmic increase in the concentration of MSG. The synergistic effect of MSG with 5 -ribonucleotides is expressed by the following relation... 

Fig. 4.15. Angular dependence of the fluorescence radiation emitted from a Co-layered Si substrate. The Co-Ka intensity is plotted semi-logarithmically for layers of different thickness (mm). The maxima forthe ultra-thin Co-layers are located at the critical angle of Si (dashed vertical line). They are shifted to the critical angle of Co (dotted vertical line) ifthe layer is more than 10 mm thick ([4.21], after Ref [4.41]).

A weighting scale, dBA The unit of sound intensity expressed as a logarithmic scale, related to a reference level of 10 W m"-. The A weighting scale is the most commonly used scale, as it reduces the response of sound meters to very high and low frequencies and emphasize those within the range audible by the human ear. 

Fig. 14 Radiation characteristics of a high pressure Hg lamp (Osram HBO 100 continuous line) and of a xenon lamp (PEK 75 broken line) [4]. The intensity /is represented logarithmically in relative units.

Since rms pressure variations have to be measured in the range 20 x 10 N/M to 200 N/M (a range of 10 ) it can be seen that an inconveniently large scale would have to be used if linear measurements were adopted. Additionally, it has been found that the ear responds to the intensity of a sound (a P ) in a logarithmic way. The unit that has been adopted takes these factors into account and relates the measured sound to a reference level. For convenience, this is taken as the minimum audible sound (i.e. 20 x 10 N/M) at 1 K. 

For coherent sound waves addition of values is possible. It will be apparent that as the scale is logarithmic, values cannot merely be added to one another. Intensities can, however, be added and thus the equation becomes ... 

Absorbance (Section 14.7) In optical spectroscopy, the logarithm of the intensity of the incident light divided by the intensity of the light transmitted through a sample A=logT0/L... 

It should be noted that in atomic absorption spectroscopy, as with molecular absorption, the absorbance A is given by the logarithmic ratio of the intensity of the incident light signal I0 to that of the transmitted light / i.e. 

Fig. 6-4. Calculated curves showing relationship between intensity ratio and thickness for various values of exponent a. The abscissa scale is logarithmic. Circles = plated coatings squares = evaporated coatings. (Liebhafsky and Zemany, Anal. Chem., 28, 455.)...

In Figure 4 the logarithm of the observed ion intensities was plotted as a function of the logarithm of the pressure in the collision chamber. As the intensity of a product ion of a certain order increases proportionally to the same power of the pressure, the curves in the diagram corresponding to primary, secondary, and tertiary ions are represented by straight lines of slopes equal to 1, 2, and 3, respectively. Measurements were performed with 11 incident ions with different recombina-... 

Figure 4. Logarithmic ion intensity-pressure graph of ethylene obtained by bombarding with H2S + of low kinetic energy...

Figure 5. Semi-logarithm plots of the fractional intensities of C2Hi+, C2H2+, and C2H + ions as functions of the pressure of C2Ht...

The temperature-factor parameter B and the scale factor k were determined by a least-squares procedure/ with observational equations set up in logarithmic form and with weights obtained from those in equation (9) by multiplying by (G (obs.))2. Since a semi-logarithmic plot of G2 (obs.)/Gf (calc.) against B showed a pronounced deviation from linearity for the last five lines, these lines were omitted from the subsequent treatments. They were much broader than the others, and apparently their intensities were underestimated. The temperature-factor parameter B was found by this treatment to have the value 1-47 A2. 

Basic Interferometer Properties (1.6-9) Although the relationship between element aperture diameter, baseline, and wavelength is quite simple, it is instructive to visualise the influence of each of these characteristics. To this end, we consider a Young s interferometer with element diameters D = Im, a baseline B = 10m at a wavelength A = 1/nm in the animations. The intensity profile across the fringe pattern on the detector (screen) is shown with linear and logarithmic intensity scales in the lower two panels. The blue line represents the intensity pattern produced without interference by a single element. 

Here B is the world average burden of anthropogenic sulfate aerosol in a column of air, in grams per square meter. The optical depth is then used in the Beer Law (which describes the transmission of light through the entire vertical column of the atmosphere). The law yields I/Iq = where I is the intensity of transmitted radiation, Iq is the incident intensity outside the atmosphere and e is the base of natural logarithms. In the simplest case, where the optical depth is much less than 1, (5 is the fraction of light lost from the solar beam because of... 

Binding assays for the saxitoxins were conducted with homogenized rabbit brain and saxitoxin exchange-labelled with tritium at C-11 (92, 93). If the various saxitoxins were available with suitably intense radiolabels, then the equilibrium dissociation constant, K, could be measured directly for each. Since only saxitoxin is currently available with the necessary label, the binding experiments instead measure the ability of a compound to compete with radiolabelled saxitoxin for the binding site. The value obtained, Kj, corresponds to the uilibrium dissociation constant, K, that would be observed for the compound if it were measured directly. Affinity is defined for this assay as the reciprocal of Kj. The affinities of several of the saxitoxins (94) are summarized in Figure 11, expressed relative to saxitoxin and plotted on a logarithmic scale. 

Fig. 5. a Total emission intensity, b Linewidth, both as functions of excitation intensity for DCM/dendrimer solution in cuvette. DCM concentration was 4.0 mmol/1. Inset in a shows plot in logarithmic scale at moderate excitation intensity... 

Figure 8.2e shows the dependence of the fluorescence intensity on the excitation power of the NIR light for the microcrystals measured with a 20x objective. In this plot, both axes are given in logarithmic scales. The slope of the dependence for the perylene crystal is 2.8, indicating that three-photon absorption is responsible for the florescence. On the other hand, slopes for the perylene and anthracene crystals are 3.9 for anthracene and 4.3 for pyrene, respectively. In these cases, four-photon absorption resulted in the formation of emissive excited states in the crystals. These orders of the multiphoton absorption are consistent with the absorption-band edges for each crystal. The four-photon absorption cross section for the anthracene crystal was estimated to be 4.0 x 10 cm s photons by comparing the four-photon induced fluorescence intensity of the crystal with the two-photon induced fluorescence intensity of the reference system (see ref. [3] for more detailed information). 

Fig. 1.15 Left propagator for unrestricted self- tained in an experiment, 5(q), plotted semi-diffusion. The propagator P(R, A) is shown for logarithmically over q2. In this representation, increasing encoding times A and becomes the slope of the decaying function is equal to broader with increasing A, while its intensity at (4 jt)2AD, so that the diffusion coefficient D zero displacement is reduced due to the re- can be obtained directly by comparing at least quirement that the area remains normalized to two measurements taken at different values unity. Right signal function as would be ob- of q.

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