Sentence examples for are defined in appendix from inspiring English sources

where D ij are defined in Appendix.

where the auxiliary W variables are defined in Appendix C.1.

The elastic constants for this saturated sandstone are defined in Appendix.

where J2 b,q,t1), and J3 b,q,t1) are defined in Appendix 2. 11671_2011_787_MOESM1_ESM.PDF Additional file 1 Supplementary information.

where the Q variables are defined in Appendix A. Notice the dependence on T ( h ) variables is hidden in Q terms.

with integer indices 0 ≤ | m | ≤ n are (complex-valued) harmonic functions, i.e. ∇ 2 ϒ n m = 0 for all r and ∇ 2 Θ n m = 0 for all r ≠ 0. The ϒ n m are homogeneous polynomials of total degree n in x, y, and z (they are defined in Appendix A.3 without reference to polar coordinates; see also Table 3).

In addition, some notations utilized to model the first and the second models are defined in Appendices 1 and 2, respectively.

and has been defined in Appendix A.2.

where the K function is defined in Appendix 3. The influence of the covariance to the fluctuations will be discussed in the next section.

Solving the integral in (70), C avg 1 is obtained as (53).To solve C avg 2, we set Y=Z/g32, where Z is a RV and is defined in Appendix 33, and the CDF of RV Y is given as F Y ( x ) = Pr Z g 32 < x = Pr Z < x g 32 = ∫ 0 ∞ f g 32 ( y ) × F Z ( xy ) dy (71).

Recall that the free soluble group (mathrm{FSol} k,ell ) = F_k / D^ell F_k) of rank (k) and solubility class (ell ) has been defined in Appendix A. For (k,ell ge 2), the group (mathrm{FSol} k,ell )) is infinitely presented, and any finitely presented cover of it contains non-abelian free subgroups.