Extensive decimal places

Extensive simulations take time a typical, moderately complex material may require a few milhon floating-point complex multiplications to 20 decimal place accuracy It is worth learning some effective time-saving strategies, which we suggest below. 

The dependence of X(T)/X(0) on T/Tq as calculated from Eqs. (12) and (13) is shown as the full curve in Figs. 4 and 5. For weak coupling this dependence is practically independent of NqV. For example, the values of X(T)/X(0) for NqV as large as 0.6 differ from those for NqV = 0.1 only in the third decimal place for most values of T/Tc. Thus X(T)/X(0) is essentially a universal function of T/Tc. In Fig. 4 this dependence is compared with the experimental dependence measured by Cooper et al. (14) for YBa2Cu307-6 while Fig. 5 shows the comparison with the data of Aeppll et al. (1 ) obtained for Lai.85Sro.15Cu0n. The agreement with the extensive data of Cooper et al. is particularly excellent. In Fig. 6 we have plotted the calculated values of X(T)/X(0) versus (T/Tc) in order to check the experimentally reported low temperature T dependence of X(T)-X(0). It is seen that the theoretical dependence is Indeed consistent with a T dependence, provided that T is not too low. We note that in the actual T/Tc 0 limit, Eqs. (12) and (13) predict... 

If a high-resolution infrared spectrophotcaneter is available to them, undergraduates can obtain and analyze in detail the fundamental vibration-rotation spectra of the four common isotopic variants of hydrogen chloride (h,D, C1, Ci) (12,12.). For these molecules the potential curve is significantly enharmonic, and a dependence of the rotational constant on the vibrational quantum number is immediately apparent, since the rotational lines are not evenly spaced. From their data our students have confirmed the constancy of the equilibrium Intemuclear distances in these four molecules to within 0.001 k, and they have confirmed the validity of Eq. 1 to four decimal places. It must be emphasized that when band-origins rather than harmonic frequencies are used in Eq. 1, disagreements occur in the second decimal place. Extensive comparison data are available in the literature for all these molecules (l <-, 15,16,17.18). 

Notice that the hypothetical value reported has four decimal places. It is easy to determine the refractive index to within several parts in 10,000. Therefore, is a very accurate physical constant for a given substance and can be used for identification. However, it is sensitive to even small amounts of impurity in the substance measured. Unless the substance is purified extensively, you will not usually be able to reproduce the last two decimal... 

Mass spectrometry can do more than simply determine the molecular weight of a compound. A high-resolution instrument can determine it to three or more decimal places, and this allows the formula of the molecule to be determined (extensive tables exist). Although we often think... 

A modification of the Dewey system with extensions of certain classes, which has been internationally adopted and is kept abreast of modern developments, is known as the Universal Decimal Classification. It is more suitable for the arrangement of documents as in an information file than for the placing of books on shelves, and for this reason its use is mainly confined to special libraries. It is uncommon in American libraries. 

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