Exponential similarity indices

In addition, linear and exponential similarity indices, L b and E b (eqs. 214 and 215), have been defined [972,1065,1074] to evaluate electrostatic similarities in grid points the sum over all individual grid point values is divided by the number of grid points n. 

To attain a transverse field profile that is confined within the defect, the profile must exponentially increase for p < pdef, and exponentially decrease for p > pdef. This requirement determines which index-interfaces (lowhigh or highlow) should be positioned at zeros of the field and which at the extrema of the field. The constraints on the index profile are similar to the Cartesian case and differ for the TE and TM polarizations. For the TE polarization, the interfaces for decreasing (increasing) field should be at the zeros (extrema) of If, if nip ) > n(p 1) at the interface and at the extrema (zeros) of Hz if nip ) < nip 1) at the interface. For the TM polarization, the interfaces for decreasing (increasing) field should be at the extrema (zeros) of E, if n(p ) > n(p+) at the interface and at the zeros (extrema) of E, if n(p ) < nip 1) at the interface. The interfaces of the defect must be located at zeros of II, for TE and of E, for TM. 

This list of reactions is useful for estimating A, G ° and Ar Ah for similar reactions because reactions of a given type are grouped together. However, estimation methods should be based on Af G of species and their pXs. An index in the Appendix of this chapter shows the reactions in which each of the reactants is involved. This index shows that if Af G values were not known for atp, this list of reactions would be shorter by 45. But if the Af G for urea was not known, the list would only be shorter by one. In general, the addition of a reactant to BasicBiochemData3 introduces a number of new reactions, and so the length of such a list of reactions increases exponentially with the number of reactants in the database. There are three ways that Af G° and Af H° values of species of reactants can be obtained ... 

In a similar context, Nayak and Ramaswamy have shown that the maximum Liapunov exponent (MLE) rises very steeply just as the Lindemann index and thereby can detect the aforementioned transition very well [20]. Since MLE is well established to measure the exponential divergence of the distance between nearby trajectories in phase space [21,22], their numerical results seem to suggest that the phase-transition could be a consequence of strong chaos behind the dynamics. We henceforth examine the resultant phenomena, the geometry on which the dynamics is characterized, and a statistical law of associated isomerization reaction. 

Control experiments showed that synchronous divisions, as reflected in changes of the division index, can be induced normally with heat shocks in the presence of either uridine, thymidine, or methotrexate. With uridine or with thymidine added before the shocks the pattern of synchronous divisions is similar to what is seen in the control, but with methotrexate the first division is slightly delayed and the second division much delayed, resembling what was observed with exponentially multiplying cells. On the other hand, when the inhibitor complex of DNA synthesis, methotrexate + uridine, is added just before the seven heat shocks, all later division activity is practially eliminated. When it is added during the period of heat shocks, more and more cells will take part in division 1 the later the agent is supphed. When the inhibitor is added in the interval between shocks 6 and 7 there is extensive participation in the first division, but no cells ever divide a second time. When the inhibitor is added at EH7 there is nearly full participation in division 1, and a few calls can take part also in the second division. From such... 

The use of diamond as an ATR crystal began in the mid-1990s and has increased exponentially since then. Diamond is in some ways the perfect ATR crystal material. Its refractive index is almost identical to that of ZnSe, which means the two crystals produce similar-looking spectra, which is very useful when performing spectral... 

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