In the examples of the previous section, and in most other applications, the coefficients rn and gn are not just a collection of numbers, but are given as simple analytic functions r(n), g(n) of the variable n. If that were not so, there could be no hope to find explicit solutions (unless the number of states is very small). However, it also implies that the special equations (1.3) and (1.5) at the boundaries are to be taken seriously and cannot be incorporated in the general equation by the simple trick described in (1.4) and (1.6) without spoiling the analytic character. Hence it is necessary, in the case of two boundaries, to write the master equation in three separate lines, [Pg.147]

Radon Rn is the 86th element of the periodic system. It is the heaviest of the noble gases. It is highly radioactive and its natural abundance is so low that it could not be identified when W. Ramsay and M. Travers discovered other inert elements. Only application of the radiometric method made possible the discovery of radon. [Pg.183]

Using consistent units, q is in kg adsorbate/kg solid and K is in kg adsorbafc/rn Although the equation itself is based on theory, its constants must still be determined to match experimental data. This equation has been found to fit certain processes, but as is the case of the other isotherms, it has to be tested for any given application. [Pg.635]

Several other modifications of cellulose have been used to examine the retention parameters of various nucleic acid samples. For specific applications a nitrocellulose phase (61), a mercurial cellulose (62). and a sulihydryl-ccllulose (6J) were examined in separating RN A. It is evident that the mixed properties of these supports increase the selectivity for specific nucleic acid separations. [Pg.193]

In solid-state NMR experiments, a central theme is that of resolution. For C CP MAS NMR, a critical factor in this respect is the efficiency of H decouphng. The simplest method, which is termed continuous wave (CW) decoupling, involves the application of a continuous rf pulse of fixed phase for the duration of the acquisition of the FID [28]. Recently, more sophisticated decoupling methods, such as TPPM [29] or other sequences possessing a RN symmetry [30], have been introduced an explanation of why these methods yield narrower C hnewidths than [Pg.282]

Figure 2-2 The scheme illustrating the construction of the regularizing operators. The bold point tiif denotes the true solution, and the point dt D denotes the true data. The noisy data are shown by a point dj = d( + (5d. Application of a formal inverse operator to the noisy data generates formal solutions, and m, which are unstable with respect to a small perturbation in the data, d or d. Howevei application of the regularizing operators, i (d, a) to any of the observed data, d or d, produces stable results the inverse models and rn are close to each other and to the true solution, if the observed data, d and d, are close to each other and to the true data d. |

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