Comparing ideas

Three products have been observed from the (V-nitration of the dihydrochloride salt of 2,5,7,9-tetraazabicyclo[4.3.0]nonan-8-one (41) with various nitrating agents, and two products observed for the A-nitration of 2,4,6,8-tetraazabicyclo[3.3.0]octan-3-one dihydrochloride (45). Table 5.2 and Table 5.3 give a comparative idea of the efficiency and nitrating power of different nitrating agents. 

Lockspeiser, E. Music and Painting A Study in Comparative Ideas from Turner to Schoenberg. New York Icon, 1973. 

The first difficulty is that decisions have to be taken before you have the products. At this point you do not know enough to make a proper decision A second difficulty is that one often has to compare ideas that are incomparable ideas of a very different level. A third difficulty occurs when team members invest time in a certain concept, and become attached to it. If their baby is killed this can lead to bad feelings. A fourth problem is not getting lost in the almost infinite number of ideas, variants and combinations that one might consider. 

Injection of produced water is not a new idea, but the technique has met resistance due to concerns about reservoir impairment (solids or oil in the water may block the reservoir pores and reducing permeability). However, as a field produces at increasingly high water cuts, the potential savings through reduced treatment costs compared with the consequences of impairment become more attractive. 

The projector augmented-wave (PAW) DFT method was invented by Blochl to generalize both the pseudopotential and the LAPW DFT teclmiques [M]- PAW, however, provides all-electron one-particle wavefiinctions not accessible with the pseudopotential approach. The central idea of the PAW is to express the all-electron quantities in tenns of a pseudo-wavefiinction (easily expanded in plane waves) tenn that describes mterstitial contributions well, and one-centre corrections expanded in tenns of atom-centred fiinctions, that allow for the recovery of the all-electron quantities. The LAPW method is a special case of the PAW method and the pseudopotential fonnalism is obtained by an approximation. Comparisons of the PAW method to other all-electron methods show an accuracy similar to the FLAPW results and an efficiency comparable to plane wave pseudopotential calculations [, ]. PAW is also fonnulated to carry out DFT dynamics, where the forces on nuclei and wavefiinctions are calculated from the PAW wavefiinctions. (Another all-electron DFT molecular dynamics teclmique using a mixed-basis approach is applied in [84].)... 

In a way, the limit set is thus the entire funnel between the two extreme cases qlc, and g o, Fig. 5. This effect is called Takens-chaos, [21, 5, 7]. As a consequence of this theorem each momentum uncertainty effects a kind of disintegration" process at the crossing. Thus, one can reasonably expect to reproduce the true excitation process by using QCMD trajectory bundles for sampling the funnel. To realize this idea, we have to study the full quantum solution and compare it to suitable QCMD trajectory bundles. 

Comparable but equally specific considerations must be applied to other condensation polymer systems. The following example is an illustration of the application of these ideas to the molecular weight of polyamides. 

To obtain an idea of the energy that may be released and the destruction that it can cause, one may compare it with the energy of 8 x 10 ergs released during the atomic explosion at Hiroshima, Japan, in 1945. This is equivalent to an earthquake of M 6.33. The extent of destruction may be equivalent to an explosion of 10 such bomb.s if M is 7.0 and many times more at yet higher magnitudes. 

Methods for quick sizing trayed fractionation and absorption column diameter have been reduced here to equations to facilitate programming for calculators or computers. Three methods are discussed and it is not a bad idea to compare results with all three. 

The idea of kinetic versus thermodynamic control can be illustrated by discussing briefly the case of formation of enolate anions from unsymmetrical ketones. This is a very important matter for synthesis and will be discussed more fully in Chapter 1 of Part B. Most ketones, highly symmetric ones being the exception, can give rise to more than one enolate. Many studies have shown tiiat the ratio among the possible enolates that are formed depends on the reaction conditions. This can be illustrated for the case of 3-methyl-2-butanone. If the base chosen is a strong, sterically hindered one and the solvent is aptotic, the major enolate formed is 3. If a protic solvent is used or if a weaker base (one comparable in basicity to the ketone enolate) is used, the dominant enolate is 2. Enolate 3 is the kinetic enolate whereas 2 is the thermodynamically favored enolate. 

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