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Inverse drawbacks

The single most severe drawback to reflectivity techniques in general is that the concentration profile in a specimen is not measured directly. Reflectivity is the optical transform of the concentration profile in the specimen. Since the reflectivity measured is an intensity of reflected neutrons, phase information is lost and one encounters the e-old inverse problem. However, the use of reflectivity with other techniques that place constraints on the concentration profiles circumvents this problem. [Pg.661]

So, the calculation of the shape of an IR spectrum in the case of anticorrelated jumps of the orienting field in a complete vibrational-rotational basis reduces to inversion of matrix (7.38). This may be done with routine numerical methods, but it is impossible to carry out this procedure analytically. To elucidate qualitatively the nature of this phenomenon, one should consider a simplified energy scheme, containing only the states with j = 0,1. In [18] this scheme had four levels, because the authors neglected degeneracy of states with j = 1. Solution (7.39) [275] is free of this drawback and allows one to get a complete notion of the spectrum of such a system. [Pg.237]

Wiener inverse-filter however yields, possibly, unphysical solution with negative values and ripples around sharp features (e.g. bright stars) as can be seen in Fig. 3b. Another drawback of Wiener inverse-filter is that spectral densities of noise and signal are usually unknown and must be guessed from the data. For instance, for white noise and assuming that the spectral density of object brightness distribution follows a simple parametric law, e.g. a power law, then ... [Pg.403]

The a priori penalty prior(x) oc — log Pr x allows us to account for additional constraints not carried out by the data alone (i.e. by the likelihood term). For instance, the prior can enforce agreement with some preferred (e.g. smoothness) and/or exact (e.g. non-negativity) properties of the solution. At least, the prior penalty is responsible of regularizing the inverse problem. This implies that the prior must provide information where the data alone fail to do so (in particular in regions where the noise dominates the signal or where data are missing). Not all prior constraints have such properties and the enforced a priori must be chosen with care. Taking into account additional a priori constraints has also some drawbacks it must be realized that the solution will be biased toward the prior. [Pg.410]

Points with a constant Euclidean distance from a reference point (like the center) are located on a hypersphere (in two dimensions on a circle) points with a constant Mahalanobis distance to the center are located on a hyperellipsoid (in two dimensions on an ellipse) that envelops the cluster of object points (Figure 2.11). That means the Mahalanobis distance depends on the direction. Mahalanobis distances are used in classification methods, by measuring the distances of an unknown object to prototypes (centers, centroids) of object classes (Chapter 5). Problematic with the Mahalanobis distance is the need of the inverse of the covariance matrix which cannot be calculated with highly correlating variables. A similar approach without this drawback is the classification method SIMCA based on PC A (Section 5.3.1, Brereton 2006 Eriksson et al. 2006). [Pg.60]

Johnson demonstrated that the conversion of (+)-(5 -164 into (-)-(/ )-163 takes place with retention of configuration, whereas the nucleophilic substitution reactions occurred with inversion of configuration at sulfur. The only drawback to this study involved the... [Pg.381]

Addressing first the limitations of a periodic representation, such as with the DFT or Fourier series, we see that it is evident that these forms are adequate only to represent either periodic functions or data over a finite interval. Because data can be taken only over a finite interval, this is not in itself a serious drawback. However, under convolution, because the function represented over the interval repeats indefinitely, serious overlapping with the adjacent periods could occur. This is generally true for deconvolution also, because it is simply convolution with the inverse filter 1 1/t(w). If the data go to zero at the end points, one way of minimizing this type of error is simply to pad more zeros beyond one or both end points to minimize overlapping. Making the separation across the end points between the respective functions equal to the effective width of the impulse response function is usually sufficient for most practical purposes. See Stockham (1966) for further discussion of endpoint extension of the data in cyclic convolution. [Pg.272]

One drawback of dye lasers as compared to solid-state lasers is the short fluorescence lifetime rp or energy storage time, which implies a quick inversion decay when pumping stops. For this reason one cannot Q-switch a dye laser. On the other hand, dye lasers can be mode-locked by saturable absorbers 52> in much the same way as solid-state lasers, and many investigations have shown that one can obtain psec pulse in this way over a wide spectral region 53,54)... [Pg.26]

The thermoplastic-rich phase may be separated in the course of polymerization (Sec. 13.4.2) or can be incorporated as a dispersed powder in the initial formulation (Sec. 13.4.3). A strong drawback of the in situ-phase separation for processing purposes is the high viscosity of the initial solution which results from the much higher average molar mass of the TP compared with the liquid rubbers. Also, for the same reason, the critical concentration crit has a smaller value (phase inversion is observed at smaller concentrations of modifier). [Pg.414]

As indicated, agglomerative methods start with single objects or pairs of objects step by step clusters are formed which are finally united in one cluster. Divisive methods, on the other hand, start from the one cluster of all objects and divide it step by step. One drawback of the commonly used agglomerative methods is that clusters formed may not be broken up in a subsequent step. With certain algorithms this sometimes leads to so-called inversions in the dendrogram, i.e. crossing lines in the diagram. [Pg.156]

A big advantage of this type of interpolation is that the matrices in the linear system of equations of coefficients,always have an inverse. A drawback is that in order to obtain the coefficients of the interpolation, we must solve very large systems of equations with full matrices. The most common radial functions are... [Pg.358]

Bockhom et al. (2002) have introduced an approach, by which a calculated signal course is fitted to the whole experimental signal decay under the variation of different distribution parameters such as the width or the mean primary particle diameter. A major drawback of this method is the relative high computing effort for the evaluation which makes the application for online measurements questionable. Roth and Filippov (1996) have introduced an inversion algorithm that also suffers from a complicated and time-consuming calculation procedure and does not lead to unique solutions. [Pg.231]

Clearly, in the framework of the proposed physicochemical approach, it is impossible to theoretically predict the values of chemical constants k0 for each particular reaction couple A-B. This drawback is known to be characteristic of any phenomenological consideration. Therefore, the inverse task is exercised in practice, namely, experimentally determined kinetic dependences x - t and y - t are used to calculate appropriate constants. [Pg.87]


See other pages where Inverse drawbacks is mentioned: [Pg.404]    [Pg.415]    [Pg.239]    [Pg.286]    [Pg.1]    [Pg.773]    [Pg.43]    [Pg.130]    [Pg.140]    [Pg.152]    [Pg.250]    [Pg.108]    [Pg.94]    [Pg.357]    [Pg.263]    [Pg.147]    [Pg.71]    [Pg.103]    [Pg.159]    [Pg.332]    [Pg.166]    [Pg.254]    [Pg.439]    [Pg.53]    [Pg.562]    [Pg.118]    [Pg.1137]    [Pg.232]    [Pg.426]    [Pg.241]    [Pg.359]    [Pg.200]    [Pg.88]    [Pg.303]    [Pg.173]    [Pg.90]    [Pg.213]    [Pg.207]   
See also in sourсe #XX -- [ Pg.341 , Pg.342 ]




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