Counterintuitive results

Both steric and electrostatic factors appear to favor the trans configuration, in which the bulkier and anionically charged F atoms are separated as far as possible. Nevertheless, 27a is actually found to be the energetically favored isomer by 0.80 kcal mol-1, a counterintuitive result that has been attributed to steric attraction. 83... 

The Dempser s rule of combination is often open to criticism since it entails two drawbacks. On the one hand, it has the effect of masking the aspect of conflict of the sources in question. Hence, there is a loss of information. On the other hand, when the conflict is great, renormalization may lead to counterintuitive results [20]. To solve this problem, several other combination rules have been defined and they often differ by the way the mass of evidence of an empty intersection is allocated. The choice of the combination rule reflects the interpretation of the mass allocated to the empty set. 

Two disadvantages of multipole partitioning should be mentioned. The first is that any density not fitted by the model is discarded in the partitioning process. Examination of the residual density is required to ensure the completeness of the set of modeling functions. The second is that very diffuse functions of the model, if included, violate the requirement of locality discussed above, and may lead to counterintuitive results. 

That is, the higher the initial concentration, the shorter the half-life This counterintuitive result is due to the reaction rate being proportional to the square of the concentration, meaning that the rate increases more rapidly than the concentration itself. Nonetheless, for [A] to reach 0.01 M, it takes a longer time starting from 0.2 M than starting from 0.1 M by the extra time for [A] to attain from 0.2 to 0.1 M. The half-lives of various reactions are listed in Table 1-2. 

Some work has been performed with bis (arene)vanadium and bis(heteroarene) vanadium complexes [7-10]. As indicated for the selected complexes shown in Table 1, replacement of benzene by phos-phabenzene and arsabenzene lowers the reduction potential. This counterintuitive result has been explained in terms of a greater positive charge on the metal... 

Michael Schrage There are two important characteristics of models accessibility and generation of novel, sometimes counterintuitive, results. 

Belton and Stewart (2002, p. 239) criticize that with the ELECTRE methods it is not possible to perform sensitivity or robustness analyses on the weights and the thresholds in an automated or interactive way. Also, they point out that weights and thresholds have no clear interpretation in terms of the decision maker s preferences and thus are often modified in an ad-hoc manner to obtain adequate outranking relations (Roy (1990b, pp. 176-179) discusses how to assign numerical values to these parameters). Additionally, Belton and Stewart (2002, pp. 246-247) criticize that the aggregation procedure of ELECTRE II and III is difficult to communicate and that with ELECTRE III counterintuitive results and rank reversal may occur if an alternative is added or removed. 

Figure 5.11 shows one of the most counterintuitive results of quantum mechanics. There are fundamental limits to our ability to make certain measurements—the act of determining the state of a system intrinsically perturbs it. For example, it is impossible to measure position and momentum simultaneously to arbitrarily high accuracy any attempt to measure position automatically introduces uncertainty into the momentum. Similarly, a molecule which is excited for a finite period of time cannot have a perfectly well-defined energy. As a result, classical determinism fails. It is not possible, even in principle, to completely specify the state of the universe at any instant, hence the future need not be completely defined by the past. These results are usually phrased something like ... 

The hit rate within a set of molecules selected by a virtual screen is primarily determined by two parameters the unknown proportion of p hits that exist in the set of molecules scored and the false positive error rate (a) of the classifier used for virtual screening. To a large extent, the statistics of rare events (true hits within a large compound collection) leads to some initially counterintuitive results in the magnitude of a hit rate within a set of molecules selected by a model. 

While the majority of SBC products possess discrete styrene and diene blocks, some discussion of the copolymerization of styrene and diene monomers is warranted. While the rate of homopolymerization of styrene in hydrocarbon solvents is known to be substantially faster that of butadiene, when a mixture of butadiene and styrene is polymerized the butadiene is consumed first [21]. Once the cross-propagation rates were determined (k and in Figure 21.1) the cause of this counterintuitive result became apparent [22]. The rate of addition of butadiene to a growing polystyryllithium chain (ksd) was found to be fairly fast, faster in fact than the rate of addition of another styrene monomer. On the other hand, the rate of addition of styrene to a growing polybutadienyllithium chain (k s) was found to be rather slow, comparable to the rate of butadiene homopolymerization. Thus, until the concentration of butadiene becomes low, whenever a chain adds styrene it is converted back to a butadienyllithium chain before it can add more styrene. Similar results were found for the copolymerization of styrene and isoprene. Monomer reactivity ratios have been measured under a variety of conditions [23]. Values for rs are typically <0.2, while values for dienes (rd) typically range from 7 to 15. Since... 

Many reactions of organic chemistry are catalyzed by complexes of transition-metal ions, most notably those of Group VIII. Here, die catalyst is a system of different complexes that are linked by ligand-exchange and ligand-dissociation equilibria and differ in their catalytic properties, occasionally with rather counterintuitive results such as a decrease in rate with increase in pressure in a reaction in which gas is consumed. 

It is interesting to consider the dependence of Deff on the molecular diffusion coefficient. For small molecular diffusivity, D < UL, i.e. large Peclet number, the second term dominates in (2.51) and Deff U2L2/D ( DPe2). Thus weak molecular diffusion leads to large effective diffusivity. This somewhat counterintuitive result can be explained as follows. Longitudinal dispersion arises due to... 

There is another surprising result which comes out of the energy analysis. Fig. 13.8 shows that, for the highest charged species Hf(CO)i and lr(CO)6, the covalent bonding is larger than the electrostatic bonding while for W(CO)g, Re(CO) and Os(CO)6 it holds that < AE. ls. This is a counterintuitive result because it means that... 

The advantage of using metaheuristics over other search methods in some problems is that one often need know very little about the task at hand. Furthermore, these search methods often produce counterintuitive results that a human would be unlikely to have derived. 

The more efficient G2 plan has more reaction steps and stages, uses more input materials, and has a lower overall atom economy. It also utilizes a higher molecular weight fraction of sacrificial reagents. These apparent counterintuitive results are rationalized when one examines the high reaction yield efficiencies of each step compared with the G1 plan. The main bottlenecks in the G1 plan are a 20% reaction yield for an intramolecular Friedel-Crafts alkylation in step 7,... 

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