Stepwise filtering

As in the GrowMol procedure, these tools are used in a stepwise, filtering manner. Thus, for instance, a set of 1669 structures generated in the active site of HIV-1 protease was reduced to 10 for viewing by the following procedure. 

Next, I wish to mention here the work by Pinto et who presented a study of dendrimers where differences in transverse relaxation rates between different layers of the polymer (faster relaxation at the core compared to the periphery) were exploited in T2-edited ID and 2D NMR experiments. The experiments allowed for stepwise filtering of the internal nuclei (which could be H, C or P) according to their topology... 

Polycondensation At room temperature, 0.4% mass of Sn(II) chloride dihydrate (SnCl2-2H20) and 0.4% mass of p-toluenesulfonic acid monohydrate (p-TSA) are introduced into the mixture. The mixture is heated to 180°C under mechanical stirring. The pressure is reduced stepwise to reach 13 mbar, and file reaction is continued for 20 h. The reaction system becomes gradually viscous, and a small amount of L-lactide is formed and refluxed through the reflux condenser. At file end of the reaction, the flask is cooled down, file product is dissolved in chloroform and subsequently precipitated into diethyl ether. The resulting white fibrous solids are filtered and dried under vacuum (average yield 67%). 

Table 40.3. As one can see, the filter introduces a slower response to stepwise changes of the signal, as if it were measured with an instrument with a large response time. Because fluctuations are smoothed, the standard deviation of the signal is decreased, in this example from 2.58 to 1.95. A Gaussian peak is broadened and becomes asymmetric by exponential smoothing (Fig. 40.26).

Descriptions of analytical methods for strong acid and acidic sulfate content of atmospheric aerosols have been reviewed (6-10). Methods for acidic aerosol determination are reviewed in this chapter according to the measurement principle either filter collection and post-collection extraction, deriv-atization or thermal treatment, and analysis or in situ collection (real-time or stepwise) and analysis. 

FIGURE 6.9 Typical wiring of a photomultiplier. Each of the dynodes, beginning in the photocathode, is linked stepwise by resistors RD of the same value. The photocurrent is read as the voltage drop across the load resistor R with high impedance filter (Rf, Cp) and oscilloscope or transient digitizer (detector). 

The Ni-Co-molybdate samples were prepared by co-precipitation of solutions containing Ni and Co nitrates (Merck) and ammonia heptamolybdate (Fluka) at pH between 6.0 and 8.5 followed by steps of filtering, washing, drying (110°C, 12 h) and calcination (500°C, 3 h in air). The amounts of metals used for all preparations correspond to the following stoichiometry Nio.sCoo,5Mo04. The mixed Co and Ni nitrate solution was added stepwise to the ammonium heptamolybdate solution, both heated at 60°C and then the co-precipitation was realized for 8 h. Ammonium hydroxide solution was used to reach and maintain a constant pH at 6.0, 7.5 and 8.5 in successive runs. The catalyst was crushed and sieved in particle sizes of 200-250 pm for catalytic tests. 

The Savitzky-Golay method combines filtering with single or multiple differentiation in one operation. Moreover, as we have already seen in section 8.5, it is very convenient for spreadsheet use. In the spreadsheet exercise we will differentiate a noisy sine wave and compare the result with its analytical derivative, a cosine. Then we will compute the second derivative, and again compare the result with the theoretical second derivative, an inverted sine wave. We could also compute that second derivative stepwise, as the derivative of the derivative, but the present route is simpler and loses fewer points at the edges. 

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