Resolution parameter

TABLE 21.4 Peak Resolution Parameters Valley-to-Peak Ratios, v, and Peak Separation Parameters, P, for Batch 52 Gel... 

Secondly, although stable solutions covering the entire temporal range of interest are attainable, the spectra may not be well resolved that is, for a given dataset and noise, a limit exists on the smallest resolvable structure (or separation of structures) in the Laplace inversion spectrum [54]. Estimates can be made on this resolution parameter based on a singular-value decomposition analysis of K and the signal-to-noise ratio of the data [56], It is important to keep in mind the concept of the spectral resolution in order to interpret the LI results, such as DDIF, properly. 

The constants DT and a can usually be estimated on physicochemical grounds, as shown in Chapter 8. Thus zone width can be calculated and resolution parameters estimated [2]. 

From the theoretical point of view, the resolution parameters can be described as shown in Fig. 2.1. It follows that a relevant parameter is the valley existing between the two peaks. Usually, resolution data are related to 10% valley definition. 

Figure 2.1. Mass resolution parameters. (Full width at half-maximum = Fwhm.)...

It has been shown that the tendency for interfacial curvature can be reduced dramatically by a decreased fatty acid fraction in the lecithin/fatty acid mixtures rather than by an increase in pressure [93]. The marked differences between the effects of pressure and monolayer composition on the phase behavior of lecithin/fatty acid mixtures reflect the fact that compositional variations cause large changes in the lateral pressure between amphiphiles, whereas hydrostatic pressure does not. Hence, pressure provides an extremely fine resolution parameter for probing the stability and geometry of lyotropic lipid mesophases. 

Phase 1. Define neutron beam characteristics most sensitive to water distribution in fuel cells. Define spatial and temporal resolution parameters for visualization of water/vapor distribution. 

Fig. 1.2 Resolution parameter space as a function of wavelength/frequency for existing and inconstruction facilities. The FIRI expected angular resolution is compared to other current and future facilities. Dashed lines are to indicate ground-based facilities...

The sensitivity and resolution parameter were calculated from the sensitivity characteristic curve as Dp and y values. The Dp value denotes the dose at which the exposed area is fully developed to the substrate with minimal in the unexposed area.(75) The y value was calculated from the following equation. 

TABLE II. Retention, Selectivity, and Resolution Parameters for the LC Separation of Enantiomers upon the Beta-Cyclodextrin Column... 

The major issues to consider in the optimization of SEM operation for stable specimens are noise, depth of field and resolution. Parameters the operator can vary are the beam voltage, beam current, final aperture size and working distance. Standard conditions for maximum resolution are ... 

Nevertheless, one may wonder about the significance of the spatial resolution parameter for single cell analysis. Indeed, the sub-cellular components of a eukaryotic cell have sizes comparable to or smaller than the spatial resolution achievable by FTIR microscopy. For example the nucleus is 1-3 pm, the mitochondria 1 pm, the ribosomes, lisosomes and vesicules < 1 pm, etc. The size of the FTIR probe in the mid-IR is significantly larger than those for VUV, X-ray and NMR, which all work below a spatial resolution of 1 pm. However, with a spatial resolution of about 1 pm, FTIR microscopy provides molecular information on sub-cellular components of cells unavailable by other techniques. 

Fig. 13.7 Convergence study of the time evolution of the bubble sizes (in vertical and in the two identical perpendicular symmetry directions) and sphericity for Case 1 left) and Case 2 right), respectively. Line colors correspond to spatial resolution parameters as in Fig. 13.6...

No matter what type of spectrometer is used, a measured spectrum is always slightly different from the true spectrum because of the measurement process, and it is important to recognize that instrumental effects often determine how well Beer s law is obeyed for any chemical system. For example, when a monochromator is used to measure a spectrum, the true spectrum is convolved with the spectrometer s slit function. The effect of this convolution is to decrease the intensity and increase the width of all bands in the spectrum. The convolution of Lorentzian absorption bands with a triangular slit function was reported over 50 years ago in a classic paper by Ramsay [1]. Ramsay defined a resolution parameter, p, as the ratio of the full width at half-height (FWHH) of the slit function to the true FWHH of the band. He showed how the measured, or apparent, absorbance, A, at the peak of a Lorentzian band varied as a function of the true peak absorbance, peak> resolution parameter. Not surprisingly, Ramsay showed that as... 

If the peak absorbance of a band is too large, and the ratio of the numerical value of the resolution to the FWHH of the band (i.e., the resolution parameter, p) is not sufficiently low, the relationship between the measured value of absorbance and c, will become nonlinear. As shown in Section 8.3, some instrument lineshape... 

It is possible to purchase variable-pathlength liquid transmission cells, which commonly have a pathlength that can be varied between 5 pm and 5 mm. A suitable sample must be chosen, preferably a neat solvent that has relatively wide peaks, the resolution of the spectrometer must be set so that the resolution parameter, p, is no greater than 0.5, and a Norton-Beer medium apodization function should be applied. A series of measurements at increasing pathlengths should yield a linear Lambert plot if the instrument is functioning correctly. Some instruments will exhibit linear Lambert plots up to 4 AU however, this is unusual, and an acceptable... 

We will use uniform translates of the tensor product of cubic B-splines that are dilated according to a resolution parameter N. These translates constitute a basis for a finite dimensional subspace V of S. Since these basis functions have finite support the Gramian matrix B is sparse. Moreover, due to fundamental properties of cubic B-splines, V2 is included in V. 

Whenever we want to resolve small features, we have to increase the resolution parameter N. This increases the size of the system matrix (17). Limits to the resolution are set by the complexity of the system (17) which, in the... 

The following Figure 7 shows the convergence of the relative error between successive B-spline solutions when increasing the resolution parameter. 

For FTIR instrumentation, this absorbance limitation arises from the apodization process. For the common triangular (sinc ) apodization function, a linear relationship is found between the true absorbance and the apparent (observed) absorbance up to about 0.7 absorbance units. Above 0.7 absorbance units, the apparent absorbance becomes nonlinear, with the amount of decrease depending on the true absorbance and the resolution parameter, r, where r is the ratio of the instrument nominal resolution to the full width at half height. For absorbance values greater than 1, resolution parameters ofO. 1 or greater produce nonlinear behavior [12]. 

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