The normalized fluorescence signals corresponding to different source-detector (S-D) pairs and time gates (left term in Eq. (15)) can be stacked up as a vector γ ∈ R N m (N m is the total number of measurements, that is, the product of the number of S-D pairs and the number of time gates) where it can be used as part of an inverse problem.
Such equation in terms of conversion and suggesting a constant density ratio between the density of the total volume and the density of the catalyst that can be included in the apparent reaction rate constant as k**, will result in (Eq. 5): - ln left( {1 - X_{A} } right) = k^ frac{{m_{text{Cat}} }}{{m_{text{Tot}} }}t + C (5).
Knowing that 1 eq of methanol is required for a theoretical complete transesterification, the maximum amount of methanol left in the system that might inhibit phospholipases, would be 0.5 eqs.
Thus, the EQ-5D Index at discharge was left in the analysis (block I).
Method Distributivity comes in two forms, left (Eq. 7) and right (Eq. 8) distributivity.
The results from the independent component analysis on the field-dependent XDM data are shown in Fig. 2c, d, which represent the spatial projections of the source [i.e., (varvec{A}_{i} left( varvec{r} right)) in Eq. 1] and the field-evolution of the sources [i.e., (S_{i} (varvec{E}))], respectively.
The exact equation that links nominal and real interest rates is represented in (Eq. 3): left(1 + rright) = left(1 + iright)left(1 + fright) (3).
Hence, the sEXP rule's metric, ( {m}_{i,k}^{sEXPkern0.5em Rule} ), is left with the mathematical equation given in Eq. 11: {m}_{i,k}^{sEXP rule}= exp left({D}_{HOL,i}right){m}_{i, k}^{PF} (11).
Jaeger and Cook (1979) concluded the stress distribution equations of borehole wall when subject to isotropic formations, as shown in Eq. 12: left.
Comparison of the pixel width of the rail with the mutation points are shown in Eq. 3. left|{y}_{q+1}-{y}_qright|le {w}_{mathrm{r}} (3).
