Discrete data obtaining

In practical applications, x(t) is not a continuous function, and the data to be transformed are usually discrete values obtained by sampling at intervals. Under such circumstances, I hi discrete Fourier transform (DFT) is used to obtain the frequency function. Let us. suppose that the time-dependent data values are obtained by sampling at regular intervals separated by [Pg.43]

The measurement of the electrode impedance has also been ealled Faradaie impedanee method. Since measurements are possible by applying either an electrode potential modulated by an AC voltage of discrete frequeney (which is varied subsequently) or by applying a mix of frequencies (pink noise, white noise) followed by Fourier transform analysis, the former method is sometimes called AC impedance method. The optimization of this method for the use with ultramicroelectrodes has been described [91Barl]. (Data obtained with these methods are labelled IP.)... 

Fig. 4.4.2 The discrete data points represent Taylor-Couette-Poiseuille flow regimes observed with MRI for r = 0.5 [41]. The curved boundaries were obtained for r = 0.77 with optical techniques [38]. The two inserts show MRI spin-tagging FLASH images of the SHV and PTV hydrodynamic modes.

Obtaining Eft), t, and of from experimental tracer data involves determining areas under curves defined continuously or by discrete data. The most sophisticated approach involves die use of E-Z Solve or equivalent software to estimate parameters by nonlinear regression. In this case, standard techniques are required to transform experimental concentration versus time data into Eft) or F(t) data the subsequent parameter estimation is based on nonlinear regression of these data using known expressions for Eft) and F t) (developed in Section 19.4). In the least sophisticated approach, discrete data, generated directly from experiment or obtained from a continuous response curve, are... 

We describe two simple ways in which discrete data may be treated to obtain the required areas (1) use of the data in histogram form, and (2) use of the trapezoid rule. These are illustrated in Figures 19.6 and. 7, respectively, in which 10 data points are plotted to represent a response curve. The curve drawn in each case is unnecessary for the calculations, but is included to indicate features of the approximations used. 

To answer the question as to whether the fluorescence decay consists of a few distinct exponentials or should be interpreted in terms of a continuous distribution, it is advantageous to use an approach without a priori assumption of the shape of the distribution. In particular, the maximum entropy method (MEM) is capable of handling both continuous and discrete lifetime distributions in a single analysis of data obtained from pulse fluorometry or phase-modulation fluorometry (Brochon, 1994) (see Box 6.1). 

If our database obtained so far is considered representative for middle, high and low northern latitudes, latitude-height cross-sections of halocarbons can be derived based on the assumption of smooth meridional mixing on sloped surfaces and zonal symmetry. By applying a spline fit to the data obtained at the 3 discrete latitudes, isolines of 90, 80, 70%, - with respect to tropospheric abundance for CFC-12, CFC-11 and CH3CCI3 are shown in figs. 14-16. 

The data obtained from studies 34 36,54,S5) carried out at fixed y and various T (as in Figs. 5 and 61 show that the time dependence of rieff may be approximated by a linear law. The influence of medium deformation on gelatination can not be determined within the limits of experimental uncertainty. This may be seen, for instance, from Fig. 6a where the dependence t eff(T) at 53 °C was obtained for both the discrete (points 1) and continuous deforming modes (points 2). Figure 6 presents only those Tleff which correspond to the moments of discrete measurements. 

Continuous automatic air monitoring for multipoints can provide much more information about the environment. Using the statistical analysis of the data obtained by the continuous multipoints monitoring is the best method to monitor the air cleanliness and to take necessary actions before the data exceed an alert level or an action level. The method has many advantages over the data obtained by discrete monitoring methods. 

The absorption data obtained was input to a minicomputer for analysis, using a discrete form of equation 7. 

The molecular weight data obtained for the fod chelates in chloroform (Table II) show that the species present are discrete monomers. No evidence of polymeric species in solutions of the thd compounds was found (7). 

Although in vivo studies are the most important and comprehensive for any nasal drug application, in vitro studies can provide discrete information on permeation mechanism, metabolism in the epithelium, and so on. It goes without saying that data obtained by well-defined and controlled in vitro studies can be often useful for discussing and supporting in vivo data. 

Multiple concentration fields are used here in an attempt to capture the dominant effects brought about by equations 1 and 2 on the spatially discrete anodic and cathodic areas formed during exposure to 5% NaCl solution. Multiion electrolyte simulation has also been documented [12] using a nested radial basis function (RBF) approach to predict concentration profiles around a rotating disk. Here, the evolution of Mr", [02], [OH ] and [H+] fields around a planar interface is predicted, governed by corrosion rates determined using data obtained from the rotating disc technique. 

Situations may arise, where the boundary conditions are unknown and only some experimental data in certain locations are known. In this case, the problem is defined as an inverse one. This situation often occurs in many branches of science and mathematics where only the values of some model parameters can be obtained from observed data or measured data. Data on electric potential can be obtained in galvanic corrosion as a set of discrete data with one free parameter due to measuring potential differences. This situation, where measurements on electric potential can be provided as a set of discrete data within simply connected domain Q imposes the problem to be inverse. 

In a few exceptional cases, the long-range transport of a discrete cloud of a chemical has been tracked. Figure 4-27, portraying data obtained by a spectrometer on the Nimbus 7 satellite, shows a time sequence of a cloud of sulfur dioxide (S02) emitted from the Cerro Hudson volcano in Chile (Doiron et al., 1991). In this case, advection carried the cloud in an easterly direction around Earth, during which time the cloud became larger but more dilute as a result of dispersion and mass deposition onto Earth s surface. 

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