The LUT in Fig. 8 b contains the needed information of 16-QAM constellation presented in Fig. 8 a when Gray mapping simplifications of expressions (25) and (26) are applied.
For simplification of the expressions, Z is assumed to be an identity matrix and is omitted.
Especially, in the simplification of the expression of the simulating results, all droplets were divided into groups following their radii subtly.
We present algorithms for efficient symbolic simplification of such large expressions.
They are computed in parallel reducing the critical path and they possess some properties that lead to a simplification of the algebraic expressions minimizing the overall hardware implementation.
The simplification of the base expression,, resulted in another thread shape factor, which is the ratio of the thread inner to outer diameter.
Overall, the comparative genomic analysis of plastid DNA from parasitic plants indicates a bias towards a simplification of the plastid gene expression machinery as a consequence of an increasing dependency on the host plant.
For simplification, from the second to the fifth line of expressions (14) and (15), we have used the basic log rules for multiplication and division.
This could be a simplification of actual mat behavior: mRNA expression evidence and in situ activity assays suggest that a large fraction of nitrogenase synthesis occurs in the morning, when light-derived reducing equivalents are available but before the mat becomes oxic [ 5].
Most students demonstrated poor ability in the simplification of trigonometric functions and in algebraic expressions.
