Density of data points

Preparation of data for deconvolution must begin prior to the acquisition of the first data point. Once the resolution of the system is set (in a dispersive spectrometer this is equivalent to setting the slit width), the density of data points per resolution element must be chosen as discussed in Sections III.D and III.E. There are some subtle factors that must be taken into account. For example, for continuous scanning, approximately 10 data points per resolution element are recommended (Blass, 1976a) to capture all of the information required by the data and the noise. On the other hand, the data-point density must be great enough to characterize the spectral lines after... 

The spatial distribution of these mineral constituents was assessed by contouring and by trend surface analysis. One problem that must be addressed in a study such as this, is whether the density of data points is sufficient to justify the description of trends across the basin, or is local variability in the constituents too great. Application of trend surface analysis permitted a statistical assessment of basinal trends, and indicated the extent of local variation. In this paper, contour maps are presented to show important basinal trends trend surface analysis indicated that these trends were statistically significant. Details of the trend surface technique and complete data are described in Rimmer (12). 

A greater density of data points taken from a continuous signal gives correspondingly more information and a more precise signal. The same holds true, though, for the noise (Fig. 3-50). On the other hand, a higher number n of points used in polynomials (set of... 

Density or Mode-Seeking Techniques. Clusters are identified and formed by locating regions in a graphic representation which contains concentrations of data points. 

The same data collection and reduction techniques are commonly used by the same workers for many different polymers. Therefore, data for these other polymers may contain errors on a similar scale, but that the errors have usually, but not always, gone undetected (8). If more than 500 reflections are observed, from single crystals of simple molecules, recognizable electron-density distributions have been derived from visually estimated data classified only a "weak", "medium" or "strong". The calculation of the structure becomes more sensitive to the accuracy of the intensity data as the number of data points approaches the number of variables in the structure. One problem encountered in crystal structure analyses of fibrous polymers is that of a very limited number of reflections (low data to parameter ratio). In addition, fibrous polymers usually scatter x-rays too weakly to be accurately measured by ionization or scintillation counter techniques. Therefore, the need for a critical study of the photographic techniques of obtaining accurate diffraction intensities is paramount. 

Digitizing the waveforms at 5 ns increments over nearly 6 decades yields in excess of 260,000 data points. This has two drawbacks. One is that it is simply inconvenient the excessive number of data points is cumbersome and impedes data analysis and display. The second drawback has a more important consequence. Digitizing a long time span in small intervals leads to unnecessary point density at longer times. For example, at t — 25 ns, the... 

Theoretical chemistry is informed by the observation of charge density distributions in crystals and molecules, and these do not appear as sets of discrete points. Conventional wisdom implicates the time scale of diffraction experiments for building up, what appears to be diffuse charge densities, by the statistical accumulation of data points. However, not only does quantum theory deny the existence of electronic positions and paths, but until it has been shown experimentally that the data points appear sequentially, the statistical argument is no more persuasive than the wave-mechanical. 

Planning of a hydrochemical study should include the question, will the data be expressed in contour maps If so, data have to be obtained with an adequate geographical coverage and adequate density of measured points. These requirements are necessary to ensure adequate resolution and to avoid white holes in the maps. 

Anodes and cathodes need not be separate electrodes but can be areas on the same piece of metal. O Halloran et al. [4] have developed a technique in which isopotential contours on the corroding electrode may be mapped (see Fig. 1). As the technique involves gathering a large number of data points, a microprocessor is used. A small reference electrode is passed across a corroding specimen close to its surface and the potential differences relative to another fixed reference electrode are recorded. The potential profile reflects the ion current density in the vicinity of the corroding surface and... 

Figure 4. Pictorial representation of 3D-QSAR models. The color code is as follows sterically favourable and unfavourable interactions, green and red regions, respectively favourable and unfavourable influence of high electron density, cyan and yellow zones respectively. To aid interpretation the template 26, idazoxan compounds 35 and 40 have been added to the electrostatic map, whereas clonidine, compounds 5, 8 and 34 are shown in the steric map. n, number of data points q and r, cross-validated and non-cross-validated correlation coefficient, respectively s, standard deviation one, optimal number of components.

Figure 1 compares the time dependence of the density in undoped and Ti-doped aluminas fired in air at 1400°C. Under these conditions, Ti should be in the 4+ state. Pairs of data points for both the undoped and 500 ppm Ti-doped material represent measurements taken on different samples, not measurement error. It is evident that both the undoped and doped alumina sinter to... 

The obvious starting point would be to compute the data (the angle and the length of the latus rectum) for the Condon locus of the band systems of each fixed-period diatomic molecule (e.g., both atoms from period 2). This procedure suffers from a severe lack of such data. The density of data is greater among isoeiectronic series. Table 8.1 shows the isoeiectronic series and related data. 

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