Here, for example, we derive the following corollaries from our Theorem 11.
And then taking the discrete ( T="ℤ) nonholonomic system for example, we derive the corresponding discrete Lie symmetry theory.
Instead of using a random P tx we interpret P tx in terms of different parameters in flooding schemes, for example we derive a P tx for counter-based flooding based on the counter value and the threshold.
For example, we derive formulae for the time that an individual is expected to spend in its current patch i, and for the time that it will spend in the matrix, both conditional on the individual hitting next a given patch j before hitting any of the other patches or dying.
For example, we derive simple relationships between the clustering coefficient, the heterogeneity, the density, the centralization, and the topological overlap.
For example, we derive the analytic expressions of the map expansions in one synthetic population with L founder strains.
For example, we have derived exact analytical expressions for the PDF, CDF, LCR, and ADF of the channel capacity.
For example, we have derived the model Mpdf (eq. (17)) in this paper for the scoring function we used.
For example, we can derive standard population genetic models for change in frequency of an allele, A, by defining the phenotype of an individual as the frequency of A within that individual's genotype (ϕ is therefore 0, 0.5, or 1).
