Reference axis

Although the word balanced is ambiguous and not definitive, the common meaning for a balanced laminate is a laminate in which all equal-thickness laminae at angles 0 other than 0° and 90° to the reference axis occur only in 0 pairs. The individual -n O and - 0 layers are not necessarily adjacent to each other. Note also that balanced laminates are required to be symmetric about the laminate middle surface, so there must be two + Q laminae and two - 0 laminae for each 0 pair. The behavioral characteristics of a balanced laminate are that shear-... 

Consider two laminae with principal material directions at -t- a and - a with respect to a reference axis. Prove that fr orthotropic materials... 

Tool azimuth angle The angle between north and the projection of the tool reference axis onto a horizontal plane. 

Tool high-side angle The angle between the tool reference axis and a line perpendicular to the hole axis and lying in the vertical plane. 

Z-axis construction In RP, it is the reference axis normal (perpendicular) to the X-Y plane (so-called flat plane) of the RP. 

X-axis The axis in the plane of a material used as 0° reference thus the y-axes is the axes in the plane of the material perpendicular to the x-axis thus the z-axes is the reference axis normal to the x-y plane. The term plane or direction is also used in place of axis. 

Fig. 9. The right-handed (R) and left-handed (L) three-fold helices of i-PP. For each handedness, the two different orientations (up or down) with respect to the reference axis are shown. The heights of the methyl groups are expressed ic c/6 units...

Here the summation is over molecules k in the same smectic layer which are neighbours of i and 0 is the angle between the intermolecular vector (q—r ) projected onto the plane normal to the director and a reference axis. The weighting function w(rjk) is introduced to aid in the selection of the nearest neighbours used in the calculation of PsCq). For example w(rjk) might be unity for separations less than say 1.4 times the molecular width and zero for separations greater than 1.8 times the width with some interpolation between these two. The phase structure is then characterised via the bond orientational correlation function... 

ENDOR on VO(II) complexes is facilitated for several reasons289 (a) the EPR transitions can easily be saturated (ENDOR signals are often observed at 100 K), (b) the large anisotropy of the Av tensor allows for a high orientation selectivity in powder samples, and (c) the V=0 bond may be used as internal reference axis. Moreover, the g tensor is nearly isotropic so that contributions to the hf interactions from an unquenched orbital moment may be neglected (Sect. 5.1). 

The dependence of the residual dipolar coupling on the angle that the vector forms with a reference axis explains why the use of dipolar couplings makes possible the determination of the relative orientation of different domains in a multidomain protein and facilitates nucleic acid structure determination. Dipolar couplings can constitute up to 50% of the total structural data available for nucleic acids, while this number drops to 10-15% in proteins. Thus, the impact of the use of dipolar couplings on the structure determination of nucleic acids is generally more substantial than in the case of proteins. Furthermore, the presence or absence of tertiary structure in a protein or nucleic acid does not have a major influence on the number of dipolar couplings that can be measured, in contrast to the case of the NOE. 

In this case, the reference axis is drawn through the metal ion in a fashion perpendicular to the chelate ring. The skew line defining the helical sense (L for left-hand, and D for right-hand) is the bond from the chelate ring to the rest of the molecule. The L and D complexes are diastereomeric and can be separated from each other for direct stereochemical studies of their individual binding and inhibitory properties. 

When the reactants A and B are not spherically symmetric, their mutual reactivity depends on their orientation. Sole and Stockmayer [256] and Schmitz and Schurr [257] have modified the diffusion equation to include rotational diffusion of both reactants. By defining a reference axis in either species, the probability that a B reactant is a distance r away from A at time t, at an orientation (0, 0) with respect to the laboratory axis, and such that A and B are oriented at angles (0A, 0A) and (0B, 0b), respectively, is p(r,0,0 0a,0a> 0b,0b)- It satisfies the expression... 

We have now reached a point of departure in the process of adding further symmetry elements to a C axis. We shall consider (1) the addition of different kinds of symmetry planes to the C axis only, and (2) the addition of symmetry planes to a set of elements consisting of the C axis and the n C2 axes perpendicular to it. In the course of this development it will be useful to have some symbols for several kinds of symmetry planes. In defining such symbols we shall consider the direction of the C axis, which we call the principal axis or reference axis, to be vertical. Hence, a symmetry plane perpendicular to this axis will be called,a horizontal plane and denoted ah. Planes that include the C axis are generally called vertical planes, but there are actually two different types. In some molecules all vertical planes are equivalent and are symbolized av. In others there may be two different sets of vertical planes (as in PtClJ" cf. page 32), in which case those of one set will be called ov and those of the other set crrf, the d standing for dihedral. It will be best to discuss these differences more fully as we meet them. 

Taking the C2 axis lying along thd C==C=C axis of the molecule as the reference axis, we look for a crh. There none, so.the group D2h is eliminated. There are, however, two vertical plants (which lie between C axes), so the group is D2J. 

The third technique for establishing a reference axis for angular correlations can be applied to nuclear reactions when the direction of a particle involved in the reaction is detected. This direction provides a reference axis that can be related to the angular momentum axis, but each nuclear reaction has its own pecu-larities and constr aints on the angular momentum vector. For example, the direction of an a particle from a decay process that feeds an excited state can be detected as indicated in Figure 9.7, but, as is discussed in Chapter 7, the energetics of a decay... 

FIGURE 4.6 Balanced three-phase power system. Phase sequence refers to the order in which phasors move past a reference axis. The positive phase sequence is assigned a counterclockwise rotation. 

In order to elucidate how the total cross section for double photoionization, equ. (5.76), can be derived from the triple-differential cross section, equ. (4.84b), the necessary integration steps will be listed (for details see [HSW91]). Assuming for simplicity completely linearly polarized incident light with the electric field vector defining the reference axis, the triple-differential cross section from equ. (4.84b) including also a constant of proportionality can be reproduced here ... 

Figure 7.2 Coordinates for a plane wave. Having defined a reference point O (origin), an arbitrary spatial point of the wave travelling with wavenumber vector k into the K-direction is indicated by r. Cases (a) and (b) differ in the direction of the selected reference axis z (the quantization axis) which does or does not coincide with the direction of the wave, respectively. In case (c) the spin of an electron wave is also indicated it is shown as the double arrow pointing into the direction e against which the spin projection is assumed to...

Using the tensor operators pkK(El) of equ. (8.99b) defined in the coordinate frame where the electric field vector coincides with the reference axis, one gets... 

Similarly, one obtains (in order to make the reference axis more explicit, the angles (O, 0, x) in the rotation matrix elements of equ. (8.108c) have been replaced by ((P,x))... 

Obviously, different expressions are obtained for the alignment parameters, because these quantities are defined with respect to different quantization axes. However, it is possible to express the alignment properties in a unified manner, e.g., j/2oliin the coordinate frame with the quantization axis along the photon beam direction. Since the alignment tensor s/2k is defined in connection with statistical tensors, equ. (8.115c), one can use the rotation properties in equ. (8.82) to change the reference axis for the representation from the z-axis to the x-axis ... 

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