Monotonical relation

Another example are the sometimes rather complex relations existing between the potential and the reaction rate. The electrode potential influences not only the parameter h [see, e.g., Eq. (14.15)] but also the degree of surface coverage by reactant particles [i.e., the coefficients in Eq. (14.18) or (14.20)]. When a sharp drop in adsorption occurs with increasing electrode polarization (rising values of hj, the monotonic relation between reaction rate and potential may break down and the current actually may decrease within a certain region while polarization increases. 

The microautoclave solvent activity tests measure coal conversion in a small batch reactor under carefully controlled conditions. The tests are described as Kinetic, Equilibrium and SRT. The Kinetic and Equilibrium Tests measure coal conversion to tetrahydrofuran solubles at conditions where conversion should be monotonically related to hydrogen transfer. The Kinetic Test is performed at 399°C for 10 minutes at an 8 to 1 solvent to coal ratio. The combination of high solvent ratio and low time provide a measure of performance at essentially constant solvent composition. The measured conversion is thus related to the rate of hydrogen donation from solvent of roughly a single composition. In contrast, the Equilibrium Test is performed at 399°C for 30 minutes at a 2 to 1 solvent to coal ratio. At these conditions, hydrogen donors can be substantially depleted. Thus performance is related to hydrogen donor... 

Much of our discussion is based on the idea that a variety of forms of psychopathology are taxonic. The critical question is, How common are these taxa . The empirical base is currently too limited to answer this question, although it is reassuring that Table 6.1 includes nine taxonic versus four nontaxonic constructs. Instead, let us evaluate this question conceptually. First, notice that the notion of continuity easily translates into the idea of monotonous relations, such as linear, quadratic, exponential, and asymptotic effects. If a construct is dimensional, it should relate to other dimen-... 

In contrast to the rather weak effects produced by these indole hallucinogens, another indole hallucinogen, 5-MeODMT, produces a marked increase in acoustic startle (44). In this case, the excitatory effect is monotonically related to the dose over a range from 0.03 to 8 mg/kg. In fact, 5-MeODMT is one of the most efficacious drugs we have found in increasing acoustic startle. Thus far, the effects of 5-MeODMT on tactile startle have not been tested. 

The major limit to the practical use of these results is the maximum particle concentration, N, that can he allowed in order to preserve the single scattering condition. Roughly, Nmax(m-3)/wVp l and the probe volume, Vp, is varying as 1/sin. With Ji 1 , the maximum concentration can he about 10 m 3. With higher fi, the range of a monotonic relation between visibility and particle size is dramatically reduced. It has heen found possible, however, to overcome these difficulties and to measure particle size distributions in fuel sprays. 

Note that the most commonly used diagnostics to flag leverage points have traditionally been the diagonal elements / of the hat matrix H = X(X7X) X f These are equivalent to the Mahalanobis distances M/Xx,) because of the monotone relation... 

The monotonic relations between A/x and K invite interpretation in terms of thermodynamic quantities. The enhanced dipole moment might be expected to be determined by the enthalpy of formation of the H bond. Such a dependence would be cast in terms of /T as... 

I will define any phenotype that is monotonically related to fitness as a fitness component. The / s and m s are thus components of fitnesses. 

Since inter-chain interactions are responsible for increasing both conductivity and mechanical properties,, it is not surprising to find that the conductivity and tensile strength of doped polyaniline films are monotonically related,. ... 

The best descriptor, which is normally chosen with a least-squares procedure, is characterized by the lowest standard deviation of the estimates, s, and highest correlation coefficient, r. The minimum requirement is that at least r > 0.84 for a ratio N° AstaJN° indices > 5 (TopUss-Costello rule, Topliss and Costello 911). The best descriptor usually has a high Fischer ratio, F, which is monotonically related tor for constant number (V of data points, and constant number of variables, v. 

When input-output relations are monotonic, then the shape of the CSM plot indicates the namre of this mapping. A positive monotonic relation will lead... 

How does this example apply to the use of multiple similarity methods Each of the similarity methods can be considered to be equivalent to an independent judge, since none of the values produced by the other methods have an explicit impact on the value produced by a given method. This may not always be the case, for example, if two methods use MACCS key fingerprints, but one uses the Tanimoto (Jacard) and the other a closely related similarity function (see Table 15.3). As shown by Gower [76], some molecular similarity functions are monotonically related. Thus, comparisons of these functions based on the same molecular representation will produced linear correlations of the values computed by the two functionally similarity functions. Hence, only one of the functions should be used. 

To find a proper monotone relation, the impacts of the uncertain parameters on the constrained output variables are analyzed. Using the trajectories of the controls by the deterministic optimization, the constrained outputs are computed with values around the expected value of the uncertain parameters by simulation. Simulation shows that the two frequency factors have a strong impact on the output constraints in all regions. They have monotone relations with both restricted output variables. 

In the results below, it Is the contribution which has been listed and employed in conjunction with eq 24 (detailed analysis reveals that only with this choice does one obtain a monotonic relation between H f and (X ) ). 

Mesmer [57] have exhaustively surveyed the literature and have evaluated heterogeneous equilibria for lanthanide and actinide hydroxides and hydrated oxides. The thermodynamic activity products (recommended by this author) to calculate free energies and ), in basic solution are listed in Table 17.3. In general, the values selected by Baes and Mesmer have been adopted however, in some cases more recent results have been selected or averaged [53,60]. These more recent results yield a monotonic relation between Ln(OH)j unit-cell volumes and K. For tetravalent ions, no hydroxides have been characterized and we assume that the dioxides are in equilibrium with hydrated dioxides, if any exist. Hence K values refer to reactions such as the following (see [361]) ... 

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