Similarity paradox

Table II clearly indicates that none of the previously mentioned OF-KEDF s has the eorreet LR behavior at the FEG limit. Even more interestingly, the TF funetional is supposed to be exact at the FEG limit, but its LR funetion has no momentum dependence. At first glance, one would think that there is some ineonsistency involved. In fact, there is no confliet beeause the TF functional is only the zeroth-order perturbation result, while the Lindhard function is the first-order result. A similar paradox exists for the asymptotic Friedel oscillations in Eq. (87).

Hate offers a similar paradox, beautifully captured in John Donne s "The Prohibition" ... 

The question of how to retain and manage such independent, neutral and able experts in the Technical Secretariat, within such constraints, is itself a challenging subject. Today, almost all international organizations are experiencing a similar paradox and are endlessly searching for new ideas and solutions for better managing hmited resources for the required results. 

Some paradoxes of the turbulence in canopies, or EPRs, were pointed out by Raupach and Thom in their state-of-art review of 1981, [522], The first phenomenon is the value of the drag coefficient of elements that constitute the EPR. The highly precise measurements in aerodynamic tubes brought values that depend on the obstacle shape, the flow turbulence level, and the mutual disposition of obstacles but vary near cf 0.5 for spheres and cf 1 for cylinders in the working range of the local Reynolds number 103 < Re < 105. The same coefficient determined from the field measurements in forests turned out to be several times less (in this case, the indirect calculations were performed). A similar paradox takes place for the exchange coefficients. 

To explain the idea, let s point out that a similar paradox could be formulated for a more trivial case — formation of a crystal, say, crystallization of water how do molecules find their unique positions while they obviously cannot manage to try all of the exponentially large number of possible arrangements Indeed, there are exponentially many configurations, so an attempt to test them all would require an exponentially long time. 

A serious limitation of all similarity-based methods is that chemical spaces are not invariant to the representation (or similarity function) used. Thus, nearest-neighbors in one space may not be nearest-neighbors in another [41], and what is similar to an active compound in one space (hence also potentially active) may not be in another, begging the question of which space should be used. In addition, the presence of activity cliffs [152-156], which occur when small changes in structure are accompanied by large changes in activity, can further confound the application of similarity methods since they violate the similarity-property principle [22] leading to what Stahura and Bajorath [157] have termed the similarity paradox. ... 

Our study of the lead screw drives entails systems with a single bilateral contact with friction (between lead screw threads and nut threads). As demonstrated by the example in Sect. 4.3.4, in order to study the behavior of a system in the paradoxical regions of parameters, a compliant approximation to rigid contact may be used. In Chap. 8, the limit process approach presented in [51] is utilized to determine the true motion of a 1-DOF lead screw drive model under similar paradoxical conditions. In the limit process approach, the behavior of the rigid body system is taken as that of a similar system with compliant contacts when the contact stiffness tends to infinity. Related to this topic, a discussion of the method of penalizing function can be found in Brogliato ([96], Chap. 2). Other examples include [101-103]. 

The future use of lead may be decided by the resolution of an environmental paradox. Some markets for lead are being phased out because of environmental concerns, eg, the use of tetraethyllead as a gasoline additive. However, a 1990 State of California law and similar laws in nine eastern U.S. states require that 2% of new cars meet 2ero-emission standards in 1998. By 2003 this requirement rises to 10% of new vehicles. Zero emission vehicles are generally accepted to mean electric, ie, battery powered cars, and there is considerable research effort to bring suitable electric vehicles to market by 1998. 

Methyl-2-furaldehyde gave a similar overall behaviour, but a penultimate effect was observed in its copolymerization with isopropenylbenzene whereby two molecules of the aldehyde could add together if the penultimate unit in the growing chain was from the olefin. This was borne out by the copolymers composition and spectra. The values of the reactivity ratios showed this interesting behaviour rx = 1.0 0.1, r2 = 0.0 0.1. An apparent paradox occurred the aldehyde, which could not homo-polymerize, had equal probability of homo- and copolymerization and the olefin, which homopolymerized readily, could only alternate. The structure arising from this situation was close to a regular sequence of the type ... 

Before this is done, however, a certain paradox needs to be discussed briefly. Given a matrix A, and a nonsingular matrix V, it is known that A, and V XA V, have the same characteristic polynomial, and the two matrices are said to be similar. Among all matrices similar to a given matrix A, there are matrices of the form... 

Results for these CEBEs are presented in Table 1. As can be seen, for the carvone variants I-V the various substitutions have absolutely no effect at the carbonyl C=0 core, and are barely significant at the chiral center that lies between the carbonyl and substituent groups in these molecules. Only upon fluorine substitution at the tail (molecule VI) does the C=0 CEBE shift by one-half of an electronvolt the second F atom substitution adjacent to the C=0 in the difluoro derivative, VII contributes a further 0.6-eV shift. This effect can be rationalized due to the electron-withdrawing power of an F atom. Paradoxically, it is these fluorine-substituted derivatives, VI, VII, that arguably produce b curves most similar to the original carvone conformer, I, yet they are the only ones to produce a perturbation of the ground-state electron density at the C li core. This contributes further evidence to suggest that, at least for the C li... 

Nuclear decay is a random process, yet it proceeds in a predictable fashion. To resolve this paradox, consider an everyday analogy. An unstable nucleus in a sample of radioactive material is like a popcorn kernel in a batch of popcorn that is being heated. When a kernel pops, it changes form. Similarly, an unstable nucleus changes form when it decays. 

The paradox of persistent poverty in an affluent society is another troubling issue calling for explanation. Reductionist theories are convenient people are simply driven - and limited - by their genes. This again is a time-worn idea. Eugenicists, for example, had explained pauperism as in the blood . In retrospect, it is easy to see the fallacies in such formulations, but similar beliefs have re-emerged in public discourse, appearing in a preoccupation with what makes people different. 

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