The Smoothing Procedure

In order to keep the average signal amplitude unaffected a scaling factor NORM is introduced, which is the sum off all convolutes, here 35. The smoothing procedure is now... 

Such occupation numbers can be the hi s obtained within the smoothing procedure described above. Since these numbers are very close to the ground-state occupation numbers i.e the increments 5n.i = — Hi are... 

SAP produces a set of virtual excitations from the fully occupied to the unoccupied Kohn-Sham orbitals thus producing a fictitious statistical ensemble. A thermodynamic interpretation of SAP is presented in [50] (see [51,52] as well), where two main observations are given. First, the redistribution of single particle states in the smoothing procedure leads to... 

The technique of seasonal decomposition uses the same additive and multiplicative models as in exponential smoothing, but without the smoothing procedure. 

It must be noted that the expression (5.14) was obtained in Ref.36) not as a result of the smoothing procedure, but with the help of some other more formal consideration. The main idea of this consideration can be outlined as follows. It is well known24 that the smoothing procedure for the model of beads leads to the operator of the type g a= 1 + a2 A, and in the same approximation the partition function reduces to the Wiener integral33 . In Ref.36) it was shown that the role of the operator (5.14) for the integration over the space of smooth curves is the same as the role of the Laplace operator for the usual Wiener integral... 

Upon application of the smoothing procedure (see Sect. 3.3) to Eq. (5.3), it is possible to find the following expression for the conformational entropy of the globule formed by the persistent chain ... 

The smoothing procedure of Denbigh and Vickery diverts attention from a feature which occurs irregularly among different families of compounds the refractivities of CH2 groups (i.e. the values of b above) sometimes alternate as methylenes are inserted to extend the lengths of... 

FIGURE 5-13 The operation of an unweighted moving average smoothing function noisy spectral data ( ). smoothed data (A). See lexl for a description of the smoothing procedure. 

Structure of the top surface. The top surface of the oriented films, as in Fig. 15, is rough due to the misorientation of colimms. The (001) top facets follow this misorientation. When the smoothing procedure is applied to such a rough surface, a question arises about how to describe the surface crystallographicaUy. Is the surface composed of microvicinal planes Vicinal planes in this case can have Miller indices of (11. ), where is a number larger than 10. Smooth surface films are not necessarily crystal-lographically perfect films. 

The sets of coupled, integro-differential equations of Eqs. (31-50) and (31-51) are an exact restatement of Maxwell s equations for waveguides with continuous profiles. This restriction follows because we have used the expansions of Eq. (31-46). However, the coupled mode equations also apply to discontinuous profiles if we adopt the smoothing procedure described in Section 31-10. The coupled mode equations can be solved by perturbation analysis, provided n = n,for reasons given in Section 31-10. 

SWV experiments are usually performed on stationary solid electrodes or static mercury drop electrodes. The response consists of discrete current-potential points separated by the potential increment A [1,20-23]. Hence, A determines the apparent scan rate, which is defined as A /t, and the density of information in the response, which is a number of current-potential points within a certain potential range. The currents increase proportionally to the apparent scan rate. For better graphical presentation, the points can be interconnected, but the line between two points has no physical significance, as there is no theoretical reason to interpolate any mathematical function between two experimentally determined current-potential points. The currents measured with smaller hE are smaller than the values predicted by the interpolation between two points measured with bigger A [3], Frequently, the response is distorted by electronic noise and a smoothing procedure is necessary for its correct interpretation. In this case, it is better if A is as small as possible. By smoothing, the set of discrete points is transformed into a continuous current-potential curve. Care should be taken that the smoothing procedure does not distort the square-wave response. 

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