Cross-sections, comparison normalized

Normally a calibration curve—molar mass against the total retention volume—exists for every GPC column or column combination. As a measure of the separation efficiency of a given column (set) the difference in the retention of two molar masses can be determined from this calibration curve. The same eluent and the same type of calibration standards have to be used for the comparison of different columns or sets. However, this volume difference is not in itself sufficient. In a first approximation the cross section area does not contribute to the separation. Dividing the retention difference by the cross section area normalizes the retention volume for different diameters of columns. The ISO standard method (3) contains such an equation... 

Fig. 5.4. Comparison of the quantum mechanical and the classical absorption spectra for H2O in the second continuum. The quanta result is calculated by means of the time-independent close-coupling method and the classical curve is obtained in a Monte Carlo simulation. Both cross sections are normalized to the same area. The arrow indicates the threshold for H + OH(2E). Reproduced from Weide and Schinke (1989).

Ohta, H., I. Sugimoto, A. Masuda, S. Komukai, Y. Suda, K. Makita, K. Takamatsu, F. Horiguchi, and S. Nozawa. 1996. Decreased bone mineral density associated with early menopause progresses for at least ten years Cross-sectional comparisons between early and normal menopausal women. Bone 18(3) 227-231. 

In a controlled, cross-sectional comparison of 100 patients with mood disturbance who had taken lithium for at least 6 months and 100 psychiatrically normal controls, lithium did not increase the prevalence of thyroid autoimmunity a minimally larger number of control subjects had antithyroid peroxidase antibodies (11 controls versus 7 patients with mood disorders) and anti-thyroglo-bulin antibodies (15 versus 8) (259). 

The near-field intensity is calculated at a point, in the gap, 5 nm beyond the transmission side of the aperture. The cross sections are normalized with respect to the physical area of the aperture. For comparison with the near-field intensity, we normalize the cross sections such that the peak cross section is unity. To distinguish this from the area normalization, we call this the magnitude normalization. The cross sections and the near-field intensity are shown in Fig. 44. 

Fig. 25. Comparison between the experimental abstraction reaction H + H2O(00)(0) cross-section (solid point with error bars), and the 5D QM calculations (solid line). The 6D QM cross-sections with the CS approximation (dotted line), and the QCT data using normal (o) and Gaussian (A) binning procedures are shown.

Pressure effects on stopping cross sections have been recently addressed within the OLPA-FSGO scheme for molecular targets [25] and preliminary calculations have been reported for stopping and total path ranges of He and Li ions in compressed solid water and methane [68], where total path ranges were found to he predominantly decreased in comparison with those at normal pressure. 

Measurements of extinction by small particles are easier to interpret and to compare with theory if the particles are segregated somehow into a population with sufficiently small sizes. The reason for this will become clear, we hope, from inspection of Fig. 12.12, where normalized cross sections using Mie theory and bulk optical constants of MgO, Si02, and SiC are shown as functions of radius the normahzation factor is the cross section in the Rayleigh limit. It is the maximum infrared cross section, the position of which can shift appreciably with radius, that is shown. The most important conclusion to be drawn from these curves is that the mass attenuation coefficient (cross section per unit particle mass) is independent of size below a radius that depends on the material (between about 0.5 and 1.0 fim for the materials considered here). This provides a strong incentive for deahng only with small particles provided that the total particle mass is accurately measured, comparison between theory and experiment can be made without worrying about size distributions or arbitrary normalization. 

In the interests of standardisation it is desirable to limit as far as possible the variety of test piece sizes allowed. Success in this direction has not always been possible, as illustrated by the tensile test pieces detailed in ASTM D412. However, there would be no need to limit dimensions at all if it were not a fact that the size of test pieces can affect the magnitude of the result obtained, or at least the variability. In the case of tensile tests, the difference in level between results from rings and dumb-bells has already been mentioned. The variability of the two types of test pieces has been found to be similar. The measured tensile strength has a tendency to decrease with increasing cross-sectional area of the test piece and it is desirable to make comparisons only between groups of test pieces of nominally the same type and thickness. The difference between the results from type 1 and 2 dumb-bells is not normally significant but Bartenev and... 

These latter measurements led only to relative cross-section values. However, by comparison with absolute values of velocity-averaged cross sections, they can be put on an absolute scale. To do this, the absolute values obtained in FA measurements were used because here the velocity distribution is exactly known—a Maxwellian distribution /(t>, T) with the temperature of the buffer gas. Denoting the velocity-dependent relative total ionization cross section, obtained in the beam experiment, by oKl(v) and the absolute total ionization rate constant obtained in the FA experiment by R(T), then a normalization k may be determined by... 

The analysis of the conditions within a gas channel can also be assumed to be onedimensional given that the changes in properties in the direction transverse to the streamwise direction are relatively small in comparison to the changes in the stream-wise direction. In this section, we examine the transport in a fixed cross-sectional area gas channel. The principle conserved quantities needed in fuel cell performance modeling are energy and mass. A dynamic equation for the conservation of momentum is not often of interest given the relatively low pressure drops seen in fuel cell operation, and the relatively slow fluid dynamics employed. Hence, momentum, if of interest, is normally given by a quasi-steady model,... 

All the values of dae /dd described here so far have been relative, the absolute scale usually having been obtained by normalization to theory. Efforts have been made by the Detroit group to make direct absolute differential cross section measurements for positrons, where the only comparison was between the positron data and their own normalized electron data. Absolute values of dae /dO for positrons were reported by Dou et al. (1992a, b), but Kauppila et al. (1996) were subsequently unable to reproduce these data. Clearly, the unambiguous determination of absolute positron differential cross sections remains a task for the future. 

Figure 10.1. Comparison of normal (top) and surface-enhanced (bottom) Raman scattering. The top panel shows the conversion of incident laser light of intensity /(vl) into Stokes scattered light /NRS, which is proportional to the Raman cross section and the number of target molecules N in the probed volume. In the bottom panel

Figure 14.11 Site-specific experimental valence X-ray photoelectron spectrum of the rutile Ti02 single-crystal sample, obtained using the XRSW technique, in comparison with the calculated partial density of states (corrected for individual angular-momentum-dependent photoionization cross sections) [32]. (a) Ti, (b) O. The spectra are normalized to equal peak height.

Fig. 16a, b. Temperature dependence of the absorption spectrum of 10% Yb + Gs3Lu2Br9 a comparison of the 14 K and 42 K absorption spectra. The intensities of the F5/2(2 ) and 1 5/2(00 features increase markedly, while those of the F5/2(l ) and cold vibronic transitions stay the same or decrease slightly b scatter plot of the normalized 10,591 cm F7/2(0) -> F5/2(2 ) absorption cross section as a function of temperature, compared with the hysteresis data vs pump power for the same sample. The triangles indicate the widths of the power hys-tereses, which get larger as the temperature is lowered. The dashed lines in (b) are both obtained from the same arbitrary polynomial fit to the absorption data, which was inverted and superimposed on the hysteresis data as a guide to the eye. Adapted from [62]... 

The mechanical properties of a craze were first investigated by Kambour who measured the stress-strain curves of crazes in polycarbonate (Lexan, M = 35000) which had first been grown across the whole cross-section of the specimen in a liquid environment and subsequently dried. Figure 25 gives examples of the stress-strain curves of the craze determined after the 1st and 5th tensile loading cycle and in comparison the tensile behavior of the normal polymer. The craze becomes more and more elastic in character with increasing load cycles and its behavior has been characterized as similar to that of an opencell polymer foam. When completely elastic behavior is observed the apparent craze modulus is 25 % that of the normal poly-... 

Various SAPO-n zeolite-supported Pd catalysts were recently investigated and compared in CO hydrogenation reactions (365). Although the acidic narrow channel (chabazite type) Pd/SAPO-34 catalyst produces mainly normal Cl—Cs alkanes, the ratios of branched hydrocarbons to normal hydrocarbons are quite high (6.7 for C4 and 10.8 for C5) on less acidic Pd/ SAPO-5, which has wide, unidimensional channels of 7.3 A cross section diameter. The comparison of product distribution on Pd/SAPO-5 and Pd/SAPO-11 catalysts is particularly interesting because in TPD of NH3, these zeolites reveal similar acid profiles and their IR spectra are similar. SAPO-11 has narrower unidimensional channels (6.3 x 3.9 A) than SAPO-5, but it produces only methane and oxygenates. The lack of higher hydrocarbons with Pd/SAPO-11 in comparison to Pd/SAPO-5 has been ascribed to shape selectivity due to the smaller pore size (365). 

The normalization of the diffraction intensity pattern of a sample to an absolute cross section can be done through the comparison with another sample of known cross-section and volume with respect to the first. In our case, a vanadium solid cylinder was also measured in the experiments for this purpose. 

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