Known Facts

Undercoordination-induced global bond contraction in solid and liquid skins, terrace edges, gaseous phases, skins of nanosolids, and associated with impurities and interfaces are in accordance with the BOLS correlation mechanism— bonds between the undercoordinated atoms are shorter and stronger. 

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It is a well-known fact that substances like water and acetic acid can be cooled below the freezing point in this condition they are said to be supercooled (compare supersaturated solution). Such supercooled substances have vapour pressures which change in a normal manner with temperature the vapour pressure curve is represented by the dotted line ML —a continuation of ML. The curve ML lies above the vapour pressure curve of the solid and it is apparent that the vapour pressure of the supersaturated liquid is greater than that of the solid. The supercooled liquid is in a condition of metastabUity. As soon as crystallisation sets in, the temperature rises to the true freezing or melting point. It will be observed that no dotted continuation of the vapour pressure curve of the solid is shown this would mean a suspended transformation in the change from the solid to the liquid state. Such a change has not been observed nor is it theoretically possible. 

This reaction, applicable only to the preparation of hydroxy-aldehydee, is alternative to the Gattermann aldehyde reaction (or the Adams modification of it) given under 4. The yields are usually smaller, but a large quantity of the phenol may be recovered. The following mechanism is consistent with the known facts ... 

The scientific method is taught starting in elementary school. The first step in the scientific method is to form a hypothesis. A hypothesis is just an educated guess or logical conclusion from known facts. It is then compared against all available data and its details developed. If the hypothesis is found to be consistent with known facts, it is called a theory and usually published. The characteristics most theories have in common are that they explain observed phenomena, predict the results of future experiments, and can be presented in mathematical form. When a theory is found to be always correct for many years, it is eventually referred to as a scientific law. However useful this process is, we often use constructs that do not fit in the scientific method scheme as it is typically described. 

It is a well-known fact that the Hartree-Fock model does not describe bond dissociation correctly. For example, the H2 molecule will dissociate to an H+ and an atom rather than two H atoms as the bond length is increased. Other methods will dissociate to the correct products however, the difference in energy between the molecule and its dissociated parts will not be correct. There are several different reasons for these problems size-consistency, size-extensivity, wave function construction, and basis set superposition error. 

Much progress has been made ia understanding how to create and use catalysts, but the design and preparation of practical catalysts stUl rehes on a substantial amount of art that is, the appHcation of known facts and iatuition to trial and error methods. General principles are described ia a number of texts (18—21). Very few completely new catalyst systems have been designed from first principles or completely theoretical considerations. New catalysts are much more likely to be discovered as a result of an adventitious observation than designed by iatent. 

J) the atmosphere inside a particular reactor contains hydrogen, and (4) the reactor is at a high temperature, the additional fact that air has leaked into the feed to the reactor leads to the conclusion that an explosion can take place. The conclusion is based on applying deductive logic to the known facts. This is representative of the logic-based approach to knowledge-based systems. 

To introduce the transfer matrix method we repeat some well-known facts for a 1-D lattice gas of sites with nearest neighbor interactions [31]. Its grand canonical partition function is given by... 

With a phosphorus content of 7.9%, PCP showed FR behavior mainly in oxygenated polymers. This is in agreement with the well-known fact that phosphorus compounds are more effective in oxygenated polymers in bringing out flame retardancy than in other polymers [177]. Thus, Table 10 shows that at 20% loading, PCP... 

It is a well-known fact in drilling practice that clear (fresh) water is the best drilling fluid as far as penetration rate is concerned. Therefore, whenever possible, drilling operators try to use minimum density and minimum solids drilling fluids to achieve the fastest drilling rate. Originally, the low solids-clear (fresh) water muds were used in hard formations, but now they are also applied to other areas. 

It is a well known fact, called the Wiener-Khintchine Theorem [gardi85], that the correlation function and power spectrum are Fourier Transforms of one another ... 

Inequality (3.12) ensues from the well-known fact that a given structure which contains a asymmetric carbon atoms gives rise to 2 in general distinct, stereoisomers and in some exceptional cases to fewer than 2 stereoisomers. Nevertheless, the purely analytical deduction of inequality (3.12) from (7) and (2.22) corroborates the observation. The exception, that is the case in which there are fewer than 2 stereoisomers in the presence of a asymmetric carbon atoms, involves compensation of asymmetries. The corollary of (3.12) indicates that compensation of asymmetries in cannot occur... 

How do we know that the carbocation mechanism for electrophilic addition reactions of alkenes is correct The answer is that we don t know it s correct at least we don t know with complete certainty. Although an incorrect reaction mechanism can be disproved by demonstrating that it doesn t account for observed data, a correct reaction mechanism can never be entirely proved. The best we can do is to show that a proposed mechanism is consistent with all known facts. If enough facts are accounted for, the mechanism is probably correct. 

Although this mechanism seems plausible, it s not fully consistent with known facts. In particular, it doesn t explain the stereochemistry of the addition reaction. That is, the mechanism doesn t tell which product stereoisomer is formed. 

Scientists always seek the simplest explanation that fits the known facts. Since we find it convenient to describe water vapor as a collection of groups of atoms (called molecules), the simplest assumption we can make about the con-... 

Finally, it is to be remarked that the molecular symmetry in itself may be sufficient to modify radiation resistance. This is suggested by the well-known fact that a change in symmetry may transform a forbidden transition into an allowed one.31 This case is realized for n-n transitions in benzene and its less symmetrical halogen derivatives. The phenomenon might occur on condition that the transitions considered play a sufficient relative part in radiation resistance. 

Nevertheless it is important to be able to give a verbal description of the origin of barrier forces in terms of conventional quantum-mechanical language. Such a description might be of no use for quantitative predictions, but it could at least be plausible and not in conflict with known facts. It would strengthen the belief that a reliable theory only awaited the further refinement of the approximations used. 

It is observed that sixfold barriers are very small. On the above theory, Pauling says that this is due to the fact that i orbitals would be required to give a sixfold contribution and these are too high to be much involved. Actually the combination of / with / and p with g should give such terms. The absence of a reliable way of making quantitative estimates again detracts from the value of these explanations of known facts. 

Departing from the known fact that PVC melts have a nodular structure, about 1 micron in size, the authors assumed that white ash particles invaded the inter-nodular spaces, thereby causing the nodules to move apart and the chains between them to be broken as a result the nodules acquire more freedom to move. As the filler concentration is increased, the contribution to viscosity increase... 

On the other hand, the known facts point to an alternative interpretation. The stereochemical course of the reaction may be explained in terms of a polar [2s + 2s] cycloaddition15 which is observed in reactions between very electron-poor and very electron-rich alkcnes. Namely, polar [2 + 2] cycloadditions usually proceed with high regioselectivity ( head to head ) and stereoselectivity under mild conditions33 35. This mechanism is also supported by the fact that a closely related reaction (between an ynamine and iminium salts) passes through a cyclic 4-membered intermediate36, which is probably the result of a polar [2 + 2] cycloaddition (see refs 10 and 37). 

The splitting of catalyst macrograins during the polymerization of olefins is a well-known fact (93, 113). Thus, the increase of the polymerization rate during the initial period can also result from an increase in Sett (93). 

We verify the steady state18 results on the last two equations using the well-known fact required for the steady state, i.e., (A/2p) < 1 (and hence the arrival rate must not exceed the service rate) and the theorem from Laplace transforms ... 

Much of the kinetics and products work already described has been due to Banthorpe et al. who have produced a mechanism for the benzidine rearrangement42 which adequately explains the known facts. This has been called the Polar-Transition-State Mechanism and is currently accepted as being the most satisfactory description of the rearrangement. Other mechanisms have been proposed over the years and their limitations discussed (for detailed account see ref. 48). 

So far as the rearrangement is concerned, the scheme consistent with all the known facts, for the reactions of N-nitrosoaromatic amines in acid solution is set out below. It incorporates the rearrangement and the de-nitrosation, viz. 

The well-known fact that enantiomers exhibit different reactivity towards chiral reagents has been used to obtain optically active sulphoxides in a process which is called kinetic resolution. Kinetic resolution of sulphoxides usually involves either oxidation to the corresponding sulphones or reduction to sulphides by means of proper chiral oxidizing or reducing agents. 

According to part 4.1.4 of this article, an increase in cation stability leads to an increase in cationic polymerizability. The latter order agrees satisfactorily with the well-known fact that vinyl ethers (which have an oxygen atom in the neighboring position... 

The mechanism of ATP synthesis discussed here assumes that protons extruded during electron transport are in the bulk phase surrounding the inner mitochondrial membrane (intermembrane and extramitochondrial spaces). An alternative view is that there are local proton circuits within or close to the respiratory chain and complex V, and that these protons may not be in free equilibrium with the bulk phase (Williams, 1978), although this has not been supported experimentally (for references see Nicholls and Ferguson, 1992). The chemiosmotic mechanism is both elegant and simple and explains all the known facts about ATP synthesis and its dependence on the structural integrity of the mitochondria, although the details may appear complex. This mechanism will now be discussed in more detail. 

The derivation outlined may thus serve to explain such scattered graphs however, no possibility is offered of estimating pi and 2- The situation is complicated by the known fact that the plot of AH versus AS is statistically erroneous. The same objections apply to Leffler s special case (153) when experimental error is formally treated as an additional interaction mechanism with P2 - Texp Even in this case, no possibility is given of estimating the real Pi. 

The effect of structure of the alkyl group on the stability of monoalkyl-thallium(III) compounds can best be understood by reference to the different mechanisms by which these compounds undergo decomposition. A number of authors have attributed the instability of monoalkylthallium(III) compounds to facile C—T1 bond heterolysis and formation of carbonium ions [Eq. (25)] (52, 66, 79). This explanation is, however, somewhat suspect in cases where primary carbonium ions would be involved and either the two-step sequence shown in Eqs. (26), (27), or the fully synchronous 8 2 displacement shown in Eq. (28), is more compatible with the known facts. Examination of the oxythallation reactions that have been described reveals that Eq. (27) [or, for concerted reactions, Eq. (28)] can be elaborated, and that five major types of decomposition can be recognized for RTlXj compounds. These are outlined in Scheme 8, where Y, the nucleophile... 

It is a well-known fact (or urban myth. ) that small-scale operations favor batch processes while large-scale manufacture requires continuous processing. Consider the typically assumed general trends (Figure 14.5) where the capital costs of batch... 

Feedback inhibition of amino acid transporters by amino acids synthesized by the cells might be responsible for the well known fact that blocking protein synthesis by cycloheximide in Saccharomyces cerevisiae inhibits the uptake of most amino acids [56]. Indeed, under these conditions, endogenous amino acids continue to accumulate. This situation, which precludes studying amino acid transport in yeast in the presence of inhibitors of protein synthesis, is very different from that observed in bacteria, where amino acid uptake is commonly measured in the presence of chloramphenicol in order to isolate the uptake process from further metabolism of accumulated substances. In yeast, when nitrogen starvation rather than cycloheximide is used to block protein synthesis, this leads to very high uptake activity. This fact supports the feedback inhibition interpretation of the observed cycloheximide effect. 

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