Inverse advantages

An alternative way of acquiring the data is to observe the signal. These experiments are referred to as reverse- or inverse-detected experiments, in particular the inverse HETCOR experiment is referred to as a heteronuclear multiple quantum coherence (HMQC) spectmm. The ampHtude of the H nuclei is modulated by the coupled frequencies of the C nuclei in the evolution time. The principal difficulty with this experiment is that the C nuclei must be decoupled from the H spectmm. Techniques used to do this are called GARP and WALTZ sequences. The information is the same as that of the standard HETCOR except that the F and F axes have been switched. The obvious advantage to this experiment is the significant increase in sensitivity that occurs by observing H rather than C. 

Polarimetric determination of the sucrose concentration of a solution is vaUd when sucrose is the only optically active constituent of the sample. In practice, sugar solutions are almost never pure, but contain other optically active substances, most notably the products of sucrose inversion, fmctose and glucose, and sometimes also the microbial polysaccharide dextran, which is dextrorotatory. Corrections can be made for the presence of impurities, such as invert, moisture, and ash. The advantage of polarization is that it is rapid, easy, and very reproducible, having a precision of 0.001°. 

There are various ways to obtain the solutions to this problem. The most straightforward method is to solve the full problem by first computing the Lagrange multipliers from the time-differentiated constraint equations and then using the values obtained to solve the equations of motion [7,8,37]. This method, however, is not computationally cheap because it requires a matrix inversion at every iteration. In practice, therefore, the problem is solved by a simple iterative scheme to satisfy the constraints. This scheme is called SHAKE [6,14] (see Section V.B). Note that the computational advantage has to be balanced against the additional work required to solve the constraint equations. This approach allows a modest increase in speed by a factor of 2 or 3 if all bonds are constrained. 

This teehnique transforms the problem from the time (or t) domain to the Laplaee (or. v) domain. The advantage in doing this is that eomplex time domain differential equations beeome relatively simple. v domain algebraie equations. When a suitable solution is arrived at, it is inverse transformed baek to the time domain. The proeess is shown in Figure 3.2. 

With regard to the enantioselective transport through the membrane, one advantage of liquid membrane separation is the fact that the diffusion coefficient of a solute in a liquid is orders of magnitude higher as compared to the diffusion coefficient in a solid. The flux through the membrane depends linearly on the diffusion coefficient and concentration of the solute, and inversely on the thickness of the membrane [7]. 

The use of tetra-n-butylammonium fluoride (54) in an aprotic solvent such as acetonitrile may be more advantageous. Foster and colleagues (19, 37) have effected an SN2 type of reaction using this reagent in the conversion of l,2 5,6-di-0-isopropylidene-3-0-p-tolylsulfonyl-D-allofura-nose into the C-3 epimeric fluorodeoxy derivative. Note that whereas potassium fluoride is ineffective in displacing secondary sulfonate esters in sugars, tetra-n-butylammonium fluoride is capable of effecting a displacement with Walden inversion even in a furanose drivative. 

The formula has also other interpretations. If the inverse of a certain submatrix of A is known in advance, advantage can be taken of the fact to reduce the work. For suppose A i1 is known. Then by taking LX1 — /, Bn => A, and if Au is of order r, then the problem is... 

Now we are ready to formulate the basic idea of the correction algorithm in order to correct the four-indexed operator f1, it is enough to correct the two-indexed operators fc and f 1 in the supermatrix representation (7.100). The real advantage of this proposal is its compatibility with any definite way of f2 and P7 correction [61, 294], The matrix inversion demanded in (7.99) is divided into two stages. In the fi, v subspace it is possible to find the inverse matrix analytically with the help of the Frobenius formula that is well known in matrix algebra [295]. The... 

Figure 7.14 Pulse sequence for the HMBCS (heteronuclear multiple-bond correlation, selective) experiment, which uses advantageously a 270° Gaussian pulse for exciting the carbonyl resonances. It is also called the semisoft inverse COLOC. (Reprinted from Mag. Reson. Chem. 29, H. Kessler et al., 527, copyright (1991), with permission from John Wiley and Sons Limited, Baffins Lane, Chichester, Sussex P019 lUD, England.)...

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