Function of integration time

Figure 4, Minimum detectable concentrations of toluene and naphthalene as a function of integration time for the prototype BBIC containing either the Pseudomonas putida TVA8 (toluene) or Pseudomonas fluorescens 5RL (naphthalene) bioluminescent bioreporters.

Conservation equations are written for all reactive species initiators, monomer, polymer carbon radicals and DTC radicals. They are integrated forward in time using the forward Euler technique, and the results can be presented as functions of either time or conversion. The results for these simulations are given in the following section. 

Related to the approximation of signals with orthogonal series is the widely used description in the frequency domain. Given a function of the time t, one can form the integral ... 

The overall increase in the total integrated Cls level intensity as a function of reaction time is readily interpreted in terms of a cross linking mechanism since the number of carbon atoms per unit area increases in the surface regions consequent upon the decrease in interchain distance on crosslinking. Indeed the kinetic scheme... 

Figure 6. One-sigma measurement uncertainty measured for the 25 p in MCP detector, a fluence rate of 2 x 10 cm-2 s 1 as a function of integration area for three different integration times. The solid curves are estimates based on Eq. (7). The measured and predicted uncertainties are in reasonable agreement.

Fig. 1.85.2. DR as a function of drying time. Plot 1, DR plot 2, integration of plot 1 over time to calculate dW... 

Thus, with the usual experimental procedures, a comparison of conversion data as a function of space velocity (residence time) does not tell us whether the kinetics differ from first order in the region of conversion below 50% for the range of order tested (zeroth to second). On the contrary, first-order kinetics can be used to represent the conversion as a function of residence time for a wide range of situations. Some investigators have been aware of this approximate first-order behavior of integral reactors, as shown by the statement that even complex catalytic systems approximate a pseudo- first order relationship when only space velocity is varied. .. (10). 

The reaction rate in differential theories of bimolecular reactions is always the product of the reactant concentrations and the rate constant, does not matter whether the latter is truly the constant or the time-dependent quantity. In integral theories there are no such constants at all they give way to kernels (memory functions) of integral equations. However, there is a regular procedure that allows reduction the integral equations to differential equations under specificconditions [34,127]. This reduction can be carried out in full measure or partially, but the price for it should be well recognized. 

Figure 10.9 Ratio of evolved H2 and the integration of the silane band as a function of reaction time for diborane-treatment silica gel.

Figure 20. Integrated signals Ei and 2 for OHBA (a), ODBA (b), and HAN (c) plotted as a function of the time delay at the indicated excitation wavelength. Note the change in ordinate time scales. Signal Ei always followed the laser cross-correlation, indicating a rapid proton transfer reaction. The decay of signal 2 was fitted via single exponential decay, yielding the time constant for internal conversion of the Si keto state in each molecule. See color insert.

In the integral mode (e.g. in a batch reactor), the evolution of the concentration can be measured as a function of time. For a plug flow reactor, it is measured as a function of residence time, cf. Section 4.1.2.4.2. 

Once a suitable concentration of enzyme has been established so that three or four samples can be analyzed, the quantitative data can be obtained. A reaction is started, the reaction mixture is sampled at intervals, chromatograms are obtained, and the amount of product formed is determined directly from the chromatogram by means of either peak height or electronic integration of the peaks. These values should be plotted as a function of reaction time. 

The reaction mixture contained FoTP and MgQ2, with Tris-HCl (pH 7.5) as the buffer. The reaction was started by the addition of the enzyme, and samples were removed at intervals and injected onto the HPLC column for analysis. Chromatograms were obtained, and the peak for cyclic FoMP (cFoMP) was integrated to determine the amount of cFoMP formed as a function of reaction time. These data are shown in Figure 9.105 insets show the chromatograms obtained on two samples. 

The integrated intensity of electron spin echoes as a function of the time between one or two pairs of microwave pulses. 

Integrating, we obtain the dead polymer concentrations as a function of scaled time from CRC Mathematical Tables integral number 521 ... 

Copper Removal Rate (Integrated) and Platen Temperature as a Function of Polish Time... 

Fig. 1. Integrated copper removal rate as a function of polish time for two positions in the film. Pad surface temperature shows similar behavior. The uniformity is also shown.

When attempting quantitation of a mixture of polymorphs, the first step is to identify which peaks are due to each polymorph, and to select two well-resolved peaks corresponding to the same carbon in each polymorph. A multiple-contact time experiment is then acquired to determine the rates of magnetization transfer (7ch) and decay (Tip) for each form. If these rates are identical in each form, direct integration of the peaks will provide quantitative data, with the relative areas representing the amount of each form present in the mixture. An example of the results of a multiple-contact time experiment is shown in Fig. 2—a plot of the natural logarithm of relative peak area as a function of contact time for neotame forms A and It is clear from this plot that spectra acquired at any contact time will not give equal peak area for both forms. 

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