Prediction definition

Another simple approach assumes temperature-dependent AH and AS and a nonlinear dependence of log k on T (123, 124, 130). When this dependence is assumed in a particular form, a linear relation between AH and AS can arise for a given temperature interval. This condition is met, for example, when ACp = aT" (124, 213). Further theoretical derivatives of general validity have also been attempted besides the early work (20, 29-32), particularly the treatment of Riietschi (96) in the framework of statistical mechanics and of Thorn (125) in thermodynamics are to be mentioned. All of the too general derivations in their utmost consequences predict isokinetic behavior for any reaction series, and this prediction is clearly at variance with the facts. Only Riietschi s theory makes allowance for nonisokinetic behavior (96), and Thorn first attempted to define the reaction series in terms of monotonicity of AS and AH (125, 209). It follows further from pure thermodynamics that a qualitative compensation effect (not exactly a linear dependence) is to be expected either for constant volume or for constant pressure parameters in all cases, when the free energy changes only slightly (214). The reaction series would thus be defined by small differences in reactivity. However, any more definite prediction, whether the isokinetic relationship will hold or not, seems not to be feasible at present. 

The steric outcome in the above cyclization can be explained on the basis of either a zwitterionic intermediate or a concerted [7t2s -I- 7t2s] process , depending on the nature of the reactants . Definite predictions are practically impossible as yet. The more stable trans-isomers (i.e. 221a) can be obtained by stirring the isomeric mixture with catalytic amounts of potassium t-butoxide in t-butyl alcohol for several days . 

The value of B. on the other hand, is in our approach directly linked to the transition temperature, B rb 3Tc4. Since Tc rs 160 MeV is measured on the lattice, we have a definite prediction for the absolute scale in the equation of state. 

If the substituent is situated on the central carbon the model fails to make a clear-cut prediction. This is because the effect of substitution on the gap and slope factor /are opposed. For example, an electron-withdrawing substituent (e.g. CH2C12 compared to CH3C1) is expected to decrease the gap and increase the slope factor, so that without more extensive informaton on the effect of the substituent on the above parameters, no definitive prediction is possible. A second limitation of the model is that it does not readily lend itself to treating mechanistic variations. Since its more detailed structure favours its application with just two state curves, in this case ground and charge transfer states, it is less readily extended to situations in which mechanistic variations are explicitly considered (e.g. the SN2-SN1 spectrum). 

Extrapolation results are, by definition, predictions on the performance of entities for which data are lacking. Both from a scientific perspective as well as from the perspective of practical decisions based on extrapolation, there is a need to consider not only the outcomes of an extrapolation per se but also the question of whether the outcome is supported by a certain degree of validity. All this relates to the issue generally referred to as validation. ... 

Phase space theory can be thought of as, in effect, considering a loose or, as it is sometimes called, orbiting [333] transition state regardless of the nature of the reaction. The need to select transition state properties for each individual reaction considered is avoided and it has been argued that a virtue of the theory is that it gives definite predictions [452]. 

Einstein s hypothesis, then, led to two definite predictions. In the first place, there should be a photoelectric threshold frequencies less than a certain limit, equal to 4>/h, should be incapable of ejecting photoelectrons from a metal. This prediction proved to be verified experimentally, and with more and more accurate determinations of work function it continues to hold true. It is interesting to see where this threshold comes in the spectrum. For this purpose, it is more convenient to find the wave length X = c/v corresponding to the frequency /h. If we express in electron volts, as is commonly done, (see Eq. (1.1), Chap. IX), we have the relation... 

In DLVO theory, the secondary minimum can only be created by the van der Waals force, which is essentially independent of the salt concentration across the concentration range 0.001 M < c < 0.1 M. This force has to be balanced with a force that decays exponentially as a function of k, which means that it decays by a factor exp(-10) across this range. The unhappy consequence of this prediction is that the position of the secondary minimum, and therefore the interlayer d value, varies very rapidly as a function of k, in contradiction to the experimental results. A further unhappy consequence of this balance is that it always produces a primary minimum much deeper than the secondary minimum. The full, standard DLVO thermodynamic potential energy curve, which also includes a very-short-range Bom repulsion, is shown in Figure 1.13 [23], It is therefore a definite prediction of DLVO theory that charge-stabilized colloids can only be kinetically, as opposed to thermodynamically, stable. The theory does not mean anything at all if we cannot identify the crystalline... 

The pH-solubility profiles are very similar to the pH-log D profiles however, it is more difficult to estimate the solubility of the charged form of molecules. The reason for this is that the counter-ions in the aqueous solutions influence the solubility of the charged species so while we can estimate the partition for the charged species into octanol, we cannot make definitive predictions or estimations of the solubility of the charged species in the presence of various counter-ions in the aqueous buffer solution. 

The presence of two substituents on a ring makes the problem of orientation more complicated, but even here we can frequently make very definite predictions. First of all, the two substituents may be located so that the directive influence of... 

Fast extrusion furnace black with a particle size of 360 A, was used to verify different theoretical concepts of percolation which by definition predicts a rapid change in conductance when volume fraction of conductive particles attains a critical value. Figure 15.38 shows the effect of a carbon black addition to polychloroprene. Up to 30 phr carbon black, the conductivity of poly chloroprene is almost constant and then it increases linearly as concentration of carbon black increases. The following equation applies o = o (P - P Jwhere c is constant, P is concentration of conducting particles, Pc is percolation threshold, and P is exponent which accounts for cluster size."" When data from the Figure 15.38 are replotted as in Figure 15.39 it is evident that the percolation law is valid. 

We were initially informed that OD2 was insoluble/inactive, whereas we expected from the various 7]ib( —1) values that this phospholipid should have a very low EDso value. The most recent data (Table 7) suggest EDso = 3 pM. It is also worth pointing out that the T g values for the series with a free amine group were computeid before the virology data became available to us. In this way we were able to predict that OD3 and OL3 would both have low ED50 values, but that HX3 would be inactive. For DD3 we observed moderately high Tab values relative to both HXl and OL2, and so it was impossible to make a definitive prediction in this case. 

A theory Li just a model of the universe, or a restricted part of it, and a set of rules that relate quantities in the model to observations that make. It exists only in our minds and does not have any other reality (whatever that might mean). A theory is a good theory if it satisfies two requirements it must accurately describe a large class of observations on the basis of the mode that contains only a few arbitrary elements, and it must make definite predictions about the results of future observatiom. 

The deviation from Cram s rule has been attributed to the cyclic nature of the transition state of the Meerwein-Ponndorf-Verley reaction129. The situation may be further complicated by hydride transfer from external aluminum isopropoxide units not involved in the cyclic six-mem-bered transition state49,5S-13°. These competitive mechanistic pathways (external vs internal hydride transfer) depend on the experimental conditions (concentrations of reactants etc.). These have also been observed in the reduction of cyclic 1,2-diones where an internal hydride transfer to the intermediate a-hydroxy ketones may be sterically hindered. In these cases the stereochemical outcome of Meerwein-Ponndorf-Verley reactions cannot be definitely predicted. 

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