Maximum overlap

The overlap in the shifted curves as shown in Fig. 6.15a means that heat transfer is infeasible. At some point this overlap is a maximum. This maximum overlap is added as a hot utility to correct the overlap. The shifted curves now touch at the pinch, as shown in Fig. 6.156. Since the shifted curves just touch, the actual curves are separated by AT ,in at this point (see Fig. 6.156). 

In Fig. 13.7d, the grand composite curve for the reactor and that for the rest of the process are superimposed. To obtain maximum overlap, one of the curves must be taken as a mirror image. It can be seen in Fig. 13.7d that the reactor is appropriately placed relative to the rest of the process. Had the reactor not been appropriately placed, it would have been extremely... 

A double time correlation among the 3 binary temporal sequences of a triplet of transducers are calculated. A maximum of 8 different but overlapping triplets can be predefined. 

Figure Bl.10.10. Schematic diagram of the effect of detector view angles on coincidence rate. The view angles of two detectors are shown along with the common view angle. Maximum signal collection efficiency is achieved when the individual view angles have the maximum overlap and when the overlap coincides with the maximum density of the incident beam.

The size of the move at each iteration is governed by the maximum displacement, Sr ax This is an adjustable parameter whose value is usually chosen so that approximately 50/i of the trial moves are accepted. If the maximum displacement is too small then mam moves will be accepted hut the states will be very similar and the phase space will onb he explored very slowly. Too large a value of Sr,, x and many trial moves will be rejectee because they lead to unfavourable overlaps. The maximum displacement can be adjuster automatically while the program is running to achieve the desired acceptance ratio bi keeping a running score of the proportion of moves that are accepted. Every so often thi maximum displacement is then scaled by a few percent if too many moves have beei accepted then the maximum displacement is increased too few and is reduced. 

An initial assumption is that the reaction takes place with maximum overlap between the HOMO on one molecule and the LUMO on the other. The HOMO ofphenylbutadiene has most density on the terminal carbon atom. 

Figure 7.21 illustrates a particular case where the maximum of the v = 4 wave function near to the classical turning point is vertically above that of the v" = 0 wave function. The maximum contribution to the vibrational overlap integral is indicated by the solid line, but appreciable contributions extend to values of r within the dashed lines. Clearly, overlap integrals for A close to four are also appreciable and give an intensity distribution in the v" = 0 progression like that in Figure 7.22(b). 

Structure. The straiued configuration of ethylene oxide has been a subject for bonding and molecular orbital studies. Valence bond and early molecular orbital studies have been reviewed (28). Intermediate neglect of differential overlap (INDO) and localized molecular orbital (LMO) calculations have also been performed (29—31). The LMO bond density maps show that the bond density is strongly polarized toward the oxygen atom (30). Maximum bond density hes outside of the CCO triangle, as suggested by the bent bonds of valence—bond theory (32). The H-nmr spectmm of ethylene oxide is consistent with these calculations (33). 

The height of the peak and area of the peak ai e traditionally used for calibration techniques in analytical chemistry. Peak maximum can also be evaluated by the height of a triangle formed by the tangents at the inflection points and the asymptotes to the peak branches. We propose to apply the tangent method for the maximum estimation of the overlapped peaks. 

Our calculations show that the systematic errors for the evaluation of the triangle height are lower then for the peak height and peak ar ea. It is to be noted that tangent method allows estimating of the latent peak in the overlapped signals when peak area and peak maximum determination is impossible. 

Overall a customer needs to know under what circumstances it is best to use either the electron-beam techniques of EDS and WDS or the X-ray technique of XRF for an analysis problem. If both are equally available, the choice usually resides in whether high spatial resolution is needed, as would be obtained only with electron-beam techniques. If liquids are to be analyzed, the only viable choice is XRF. If one s choice is to use electron-beam methods, the further decision between EDS and WDS is usually one of operator preference. That is, to commence study on a totally new sample most electron-beam operators will run an EDS spectrum first. If there are no serious peak overlap problems, then EDS may be sufficient. If there is peak overlap or if maximum sensitivity is desired, then WDS is usually preferred. Factored into all of this must be the beam sensitivity of the sample, since for WDS analysis the beam current required is lO-lOOx greater than for EDS. This is of special concern in the analysis of polymer materials. 

On the pinch diagram, the vertical overlap between the two composite streams represents the maximum amount of the pollutant that can be transfeired from the waste streams to the process MSAs. It is referred to as the integrated mass... 

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