Addition/additive effects definition

Definition of the association (or avidity) constant for such multivalent antibody—antigen reactions must consider not only the heterogeneity of the antibodies and the antigen determinant site(s), but also an apparent additive effect of binding two antigen molecules to a single antibody. Such effects lead... 

The trends of behavior described above are found in solutions containing an excess of foreign electrolyte, which by definition is not involved in the electrode reaction. Without this excess of foreign electrolyte, additional effects arise that are most distinct in binary solutions. An appreciable diffusion potential q) arises in the diffusion layer because of the gradient of overall electrolyte concentration that is present there. Moreover, the conductivity of the solution will decrease and an additional ohmic potential drop will arise when an electrolyte ion is the reactant and the overall concentration decreases. Both of these potential differences are associated with the diffusion layer in the solution, and strictly speaking, are not a part of electrode polarization. But in polarization measurements, the potential of the electrode usually is defined relative to a point in the solution which, although not far from the electrode, is outside the diffusion layer. Hence, in addition to the true polarization AE, the overall potential drop across the diffusion layer, 9 = 9 + 9ohm is included in the measured value of polarization, AE. ... 

The data in Table 4 are not yet sufficient to give a final answer as to when additivity is to be expected and when not. They clearly show however that additivity of substituent effects definitely is not the exception. 

Section 1.4, 92 factors are studied but we find only 11 of these to be important. This is in line with the principle of effect sparsity, see Chapters 1 and 8. The simplest definition of importance occurs when an experiment has a single response (output from computer code) and the factors have only additive effects that is, the input-output relation is modelled by a first-order polynomial in regression terminology or a main effects only model in analysis of variance terminology (also see Chapter 8). The most important factor is then the one that has the largest absolute value for its first-order effect or main effect the least important factor is the one whose effect is closest to zero. 

Table 1 includes additional mathematical definitions of effective membrane permeability coefficient for various transport mechanisms. 

Thus, one can see that the original definition of local hardness, with ( ) = pC I/N nicely embodies electrostatic effects. Far away from the nuclei the local hardness becomes proportional to the electrostatic potential generated by the molecular charge distribution. Since contour diagrams of molecular electrostatic potentials have been widely used to analyze the chemical reactivity of a great number of chemical species [31], it is to be expected that the local hardness index provided by Eq. (15) will incorporate additional effects, and this way it may become a very useful reactivity index. 

Sometimes the additive effects are solely toxic (e.g. additive ototoxicity, nephrotoxicity, bone marrow depression, QT interval prolongation). Examples of these reactions are listed in Table 1.7 , (see below). It is common to use the terms additive , summation , synergy or potentiation to describe what happens if two or more drugs behave like this. These words have precise pharmacological definitions but they are often used rather loosely as synonyms because in practice it is often very difficult to know the extent of the increased activity, that is to say whether the effects are greater or smaller than the sum of the individual effects. 

The expression unusual has been deliberately been left open ended or ill defined since the effect will almost certainly differ between systems having different phenomenological bases for cooperativity or synergism. Nevertheless, a rather useful working definition might be a rate or selectivity dependence which cannot be explained as a strictly additive effect of the metal(s) used. Having said that, the homometallic and heterobimetallic catalytic binuclear elimination reactions (CBERs) which are the focus of this chapter have very well-defined rate dependences which can be traced back to the topology of the reaction mechanisms. 

Since the liquid data were obtained at veiy low solute concentrations, can be converted to through = kj c, where c is the molar density of the solvent liquid. There may be an additional effect not included in Eq. (6.72). If concentration changes result in an increase in surface tension as the liquid flows down the column, the liquid film on the packing becomes stabilized and the mass-transfer rate may become larger. If the surface tension decreases, the film may break up into rivulets and the mass-transfer rate decreases [127]. Definite conclusions cannot yet be drawn [16]. 

With the above definitions, there is no additional overall phase factor to be included in (27). Eqs. (24)-(27) are the CSP approximation.Like TDSCF, CSP is a separable approximation, using a time-dependent mean potential for each degree of freedom. However, the effective potentials in CSP... 

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