Ad hoc arguments

The only weak point of this procedure is the existence of the matching point determined by this ad-hoc argument. In fact, no solution for the original Ashby-... 

The notion of a polar, oriented interface layer of water molecules— while based on an ad hoc argument—is consistent with experimental data. It is in accord, for example, with the large electric potentials that develop... 

PCM are explicated in Table 11.1. Also listed in this table are the forms of K and R for the so-called conductor-like model, C-PCM [25]. This model is considerably simpler in that the matrix D is absent. C-PCM is identical to the generalized conductor-iike screening modei (GCOSMO) [78], and almost identical to the original COSMO [37]. (G]COSMO was introduced prior to SS(V)PE/1EF-PCM, based on ad hoc arguments and designed to achieve the correct oo limit. We... 

As several of the Gottingen physicists who were exposed to these ideas by Bohr s own lectures later commented, the work rested on a mixture of ad hoc arguments and chemical facts without any derivations from the principles of quantum theory, to which Bohr frequently alluded. According to the German physicist Heisenberg,... 

Proof. This follows from an ad hoc argument by a direct analysis of point descriptions see Subsection 9.2.3. The crucial fact is that the cells are mapped to cells of equal or smaller dimension. ... 

A convenient and popular summary of such a posterior distribution is the maximum probability interpolant (known as the MAP, maximum a posteriori probability estimate). If this is calculated using the calculus of variations, then a minimisation problem, similar to that of the Tikhonov methods is obtained. In the Bayesian formulation however, the free parameters need less ad hoc arguments for their assignment and have a clearer interpretation. 

What are the objections to these ideas The equivalence between students ideas and scientific conceptions had often been doubted. The main argument of many authors has been that both sides are incommensurable. Students conceptions with limited empirical foundation, often ad hoc formulated or post hoc reconstmcted by researchers, have a completely different ontological status to empirically based ideas that are carefully formulated and sharpened by debate among scientific peers. Gault (1991) sketches some cmcial differences as follows ... 

Many experimental results on viscosity were empirically correlated by Rutgers (1962a,b) and Thomas (1965). A useful semiempirical formula is that of Mooney (1951). Its derivation is based on an approximate functional argument together with the introduction of an ad hoc crowding factor k. Upon contemplating two possible ways of reaching the same total concentration + 2, Mooney proposed the formula... 

This argument has descended onto the equation of state as a principal determinant of peculiar temperature dependences of hydrophobic effects. The statistical thermodynamic model discussed above, however, started with probabilities and fluctuations. But equations of state and fluctuations are connected by the most basic of results of Gibbsian statistical mechanics, e.g. Eq. (2.24), p. 27. Ad hoc models, such as the more simplistic lattice gas models, can be adjusted to agree with solubility at a thermodynamic state point, but if they don t agree with the equation of state of liquid water more broadly they can t be expected to describe molecular fluctuations of liquid water consistently and realistically. Thus, models of that sort are unlikely to be consistent with the picture explored here. 

We therefore end up again with the problem of finding a canonical decomposition of the overall thermal density operator of some molecular species into pure states. Based on such a canonical decomposition of (and dynamical arguments see subsequent text), one can introduce effective thermal states in some ad hoc manner. 

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