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.
As a representative example, we derive a simple model for a pair of meshing spur gears as a single-degree-of-freedom oscillator with backlash.
As an example, we derive novel predictor corrector (PCMTS) schemes specifically optimized for the time-integration of damped wave equations on locally refined meshes.
In the next section, as an example, we derive special cases of these results after some specific assumptions, which in turn yield much simpler expressions.
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.
The single-link analysis can be extended to the scenario where the transmitter changes the applied EW RLC code during the transmission (i.e., switches between different Γ. As an example, we derive Pd,l(T) for T>T1, given that the transmitter has applied the EW RLC defined by Γ a during 0≤t≤T1, and the EW RLC defined by Γ b for t>T1.
For example, we derive simple relationships between the clustering coefficient, the heterogeneity, the density, the centralization, and the topological overlap.
