Frames, defined

The hierarchical structure of the frames defines the relation between them. This hierarchical structure is static, however, and cannot be easily modified. Inheritance is therefore an elegant way to represent taxonomical relations or well-established relations between objects. It is less suited for variables or ill-defined relations between objects. 

Where a is the unit vector defined by the local frame defining the axial quadupole, r is the vector oriented towards r from the monopole to the axial quadupole. Qa is the corresponding matrix element. Following the modification of the charge-dipole interaction, we introduced a modified mono-quad interaction, namely I -mono-quad1 ... 

Under such circumstances, the evolution of a spin system has to be calculated in different rotating frames defined by the corresponding PIPs and a special case may arise, where a spin experiences an on-resonance excitation but off-resonance evolution in the conventional rotating frame. Unpredictable results may occur if the phase coherence in PIPs fails. Unfortunately, to date, no... 

Another rotational diffusion model known as the anisotropic viscosity model156,157 is very similar to the above model, and its main feature is to diagonalize the rotational diffusion tensor in the L frame defined by the director. A similar (but not the same) expression as Eq. (71) is J R(r)co)... 

According to W. E. Deming (1975b), an enumerative study is one in which action will be taken on the material in the frame studied , where frame is defined as an aggregate of identifiable units of some kind, any or all of which may be selected and investigated. The frame may be lists of people, areas, establishments, materials, or other identifiable units that would yield useful results if the whole content were investigated . Thus, the frame defines a specific, well-defined population about which inferences can be made. The correctness of statistical inferences requires random sampling from this population. 

The shape of the H NMRD profiles can be very different according to the different values of Aj, A and the position of the proton with respect to the molecular frame defined by the hyperfine A tensor. As an example, the H NMRD profiles of the copper(II) protein superoxide dismutase are shown in Fig. 5.38 for... 

An mRNA contains the following translated sequence, with the reading frame defined by the grouping of triplets ... 

The angle x of the principal axes with the laboratory frame defined just above is given by ... 

If the symmetry of the site is lower than cubic the full tensor form of the electron-nucleus interaction needs to be used, so that in addition to an isotropic term there is an anisotropic contribution. If in the PAS of the Knight shift tensor the components of the tensor are Kx, Ky and Kz, then in the laboratory frame with its orientation in the frame defined by Bo described by the Euler angles 0 and [Pg.49]

In the cyclic case it is most convenient to transform the spin system to the RF interaction frame, defined by the transformation operator URp t). The total Hamiltonian in the RF interaction frame becomes [26]... 

The form of the RF interaction Hamiltonian in Fourier space in Eq. 23a suggests that we can transform it to a space where it becomes time independent. Transforming the Fourier density operator to a new interaction frame defined by... 

After transformation to a toggling frame defined by the sequence of tt pulses and in the limit of -shaped tt pulses, the Hamiltonian assumes the simple form... 

After transformation to a time-dependent interaction frame defined by... 

The fact that, for each line, a different set of axes has been set up complicates the analysis of the effect of an external magnetic field H on the nuclear moment p. The direct term, - i H, needs to be multiplied by a factor to allow for cross terms involving the Zeeman Hamiltonian and the hyperfine interaction given by (108), as was recognized first by Elliott (1957). But as soon as p is replaced by / (times a factor), we arrive at combinations such as that can be easily evaluated in the basis f, M > only if the coordinate frame defined by the principal axes is used. The required transformation of axes, which varies from line to line, has been described by Cone et al. (1984). 

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