Polar coordinates, right-handed

As shown in Fig. 11, the decrease in the Al MAS NMR signal of tetrahedrally coordinated framework aluminum at about 60 ppm is accompanied by the appearance of signals at about 0 ppm and 30 ppm. Furthermore, in the spectra recorded by the application of the cross-polarization technique (right-hand side), the intensities of the signals at 0 ppm and 30 ppm increase inversely to the intensity of the signal at 60 ppm. Therefore, the authors suggested that H- Al CP/MAS NMR experiments preferentially monitor non-framework aluminum atoms. In addition, this observation indicates that the 30-ppm line is an independent signal [90]. 

The number of amino acid units per turn of the helix is 3.6, with five turns of the helix containing 18 residues. The pitch (repeat distance) of the helix, which can be determined experimentally from X-ray diffraction data, is 0.54 nm. Polar coordinates for the a helix have been tabulated.130 With L-amino acids, the right-handed helix, is more stable than the left-handed helix which has so far not been found in proteins. Frequently, however, a few residues have the c ), j/ angles of this helix. The 0, / angles of the a helix are given in Table 2-3 as -57°, -47°, but are much more variable in real helices. In erythrocruorin, for which an accurate structure determination has been made,131... 

Figure 2a. Surface contours of normalized WAXS intensity versus Bragg angle 26 and azimuthal angle fi in polar coordinate form. Only the upper right hand quadrant is shown. Calculated pattern from Structure 3.

Using the standard approach that consists of evaluating the square of the right hand integral in polar coordinates over an area equal to the area of the rectangle determined by the limits of integration we obtain the approximation ... 

Ikeda et al.35 considered solutions of Eqs. (3.34) and (3.35) by the variation method with two-dimensional harmonic oscillator functions in Cartesian and polar coordinates, respectively, as basis functions. Some of the eigenvalues are plotted in Fig. 3.4 as a function of the parameter B. The case of pure pseudorotation corresponds to large negative values of B on the right hand side of the figure. 

The usual spherical polar coordinate system (r, 6, right-handed Cartesian coordinate system whose coordinates occur in the equations. The Z-axis is the unique axis around which r-functions (A = 0) have rotational symmetry. Functions with 0 < A g / are characterized 19) through A by their standard transformation properties when they undergo rotations around the Z-axis ... 

The polarization ellipse along with a designation of the rotation direction (right- or left-handed) fully describes the temporal evolution of the real electric vector at a fixed point in space. This evolution can also be visualized by plotting the curve in (9,tp,t) coordinates described by the tip of the electric vector as a function of time. For example, in the case of an elliptically polarized plane wave with right-handed polarization, the curve is a right-handed helix with an elliptical projection onto the Ocp - plane centered around... 

Figure 8.2 (a) The helix described by the tip of the real electric vector of a plane electromagnetic wave with right-handed polarization in 0, (p, t) coordinates at a fixed point in space, (b) As in (a), but in 6, (p, s) coordinates at a fixed moment in time, (c) As in (b), but for a linearly polarized wave. 

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