Vectors magnitude

Fig. 3.2 Small-angle neutron scattering intensity as a function of wave vector magnitude for a rfPS-PB diblock forming micelles in PB, c = 5x l(T2gcm 3. Symbols, experimental results line, theoretical scattering profile for a uniform sphere (Selb et al. 1983).

Fig. 5.3 SAXS intensity versus scattering vector magnitude for PE-PEE diblocks with ...

As in the original Lifshitz case [Eqs. (L3.27) and (L3.49)], we sum over modes with lateral wave vectors iu + jv with u and v combining into wave-vector magnitude p as... 

Unlike the Lifshitz case, because only the zero-frequency ionic-charge fluctuations count, there is no summation over finite frequencies. There is only the integration over wave-vector magnitudes p to achieve the free energy GLmR(l) [as in Eq. (L3.31)] ... 

Fig. 3. Addition of magnetic moments in an atom with large L-S coupling. Vector magnitudes ...

I. .. I length of vector, magnitude of vector, or absolute value of scalar... 

Friedman et al., 2004). Clusters of pixels with saturated color would be evident only if one vector magnitude... 

A Since the scalar product of these two vectors is negative, and has the value -1 (Worked Problem 5.2), we know that the angle B is obtuse. The next step involves substitution of the vector magnitudes a = and b y/l into equation (5.8), in order to determine the value of cos B ... 

Figure 2. A vector diagram of two PACD experiments (one of each sign) which illustrates how the PACD experiment may be treated as a superposition of two individual PAS experiments—one with left and the other with right circularly polarized light—that are performed 180° out-of-phase with one another. Here, i and 0r are the PAS phase angles of the left (q,) and right (q,) circularly polarized PAS experiments. The vector sum of q, and qr yields Aq, the vector magnitude of the PACD pressure variations, which has phase c (19).

Also Eq. (11.4) implies the corresponding relation betweeen the vector magnitudes... 

In a bulk liquid crystal sample, the wave vector q of a given fluctuation is in principle arbitrary in both magnitude and direction. There are however two hmitations in the limit of small wave-vectors, the dimensions of the sample determine the cut-off, whereas in the limit of large wave-vectors (small wavelengths), the wave vector magnitude is limited by the requirements of the continuum theory. The relaxation times can be calculated using (4.19) and the obtained spectrum of the fluctuation relaxation times is continuous. 

Figure 4.9 The construction of the reciprocal lattice. ai, U2, as are the vectors of a real crystal lattice, foi, fo2i 3 are the vectors of the reciprocal lattice. Units of the vector magnitudes are m and rad respectively.

Figure 5.1 Dependence of energy on the wave vector magnitude for the free electrons in the fe-space. Electrons are in states (that is, the electrons have the energy) from zero to the Fermi energy Ep.

The vector magnitude might be interpreted as an indication of the absolute amount of NaCl and KOH in relation to the solvent, whereas the direction indicates the relative proportions of species in the system. 

A parameter that can describe the overall degree of greenness, or relative greenness, of a synthesis plan, with respect to the ideal green synthesis, may be defined as the vector magnitude ratio (VMR) given by Equation 6.5. 

The underlying assumption is that all six parameters are mutually independent. The root 6 factor applies to the magnitude of the vector when all six parameters have a value of 1. Another possible parameter that could have been chosen is the relative area of the actual and green limit hexagons. However, this is problematic because the area of the actual hexagon will depend on the order of the parameters chosen. The vector magnitude does not depend on the order of the coordinates. In the preceding two examples, the VMR values are 0.830 and 0.139, respectively. 

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