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... 

SWV experiments are usually performed on stationary solid electrodes or static merciuy drop electrodes. The response consists of discrete current-potential points separated by the potential increment AE [1,20-23]. Hence, AE determines the apparent scan rate, which is defined as AE/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 fine 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 A are smaller than the values predicted by the interpolation between two points measured with bigger AE [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 AE 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 procedttre does not distort the square-wave response. 

This expression includes the curvature corrections to the Gaussian function, which play an important role in the averaging procedure they ensure the smoothed spectrum g(E) to be approximated, through the above definition, by its own truncated Taylor expansion. This smoothing procedure of the one-electron spectrum is an application of the method of moments, also used in other systems [23]. 

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 ... 

S. Park and C. Han. A non-linear soft sensor based on multivariate smoothing procedure for quality estimation in distillation columns , Comp, and Chem. Eng. Vol. 24 (2000), pp. 871-877. 

This expression was used for the P ri) extraction directly from f x), but as this did not remove spurious oscillations, a smoothing procedure was applied, and the method was tested on composite specimens prepared by mixing known quantities of samples of nickel hydroxide, whose crystallite size distributions were previously determined. The Fourier method is in principle an exact... 

A second approach is based on an effective smoothing procedure this procedure, given a sequence of numbers, produces a smoother sequence in such a way that unusual values are not only smoothed down (or up) but have very little effect on the resulting smoothed sequence—i.e., it is resistant. A classic smoothing process is the use of running (or moving) linear combinations ... 

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... 

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