Your English writing platform
Discover LudwigSuggestions(2)
Exact(5)
We model the problem using a sequence of periods, each corresponding to a season.
Let (I_U) be an set of index entries over a sequence of periods of time (U).
Production variations over the horizon are approximated using a sequence of periods, each corresponding to a production season, while the intra-period variations are neglected.
The algorithm identifies a sequence of periods (left { t_{n}right }_{nin mathbb {N} }) such that t 1=1 and (phantom {dot {i}!}t_{n+1}geq r_{t_{n}}+1) for each (nin mathbb {N} ) (t 1=1 is set in step 1 and switching from t n to t n+1 takes place in steps 7, 8, and 9).
There have been a sequence of periods in which I have experimented with various ways of translating ideas and concepts into form.
Similar(55)
end{aligned}It follows from the definition of the basis (mathsf {B}) that the matrix of (pi _infty (a)) is the block-diagonal matrix consisting of the Jordan cells of size p. Consequently, its first diagonal is the periodic sequence of period ((1, 1, ldots, 1, 0)) of length p. Hence, the first diagonal of (a^s) is ((s, s, ldots, s, 0)) repeated periodically.
The numerical simulation demonstrates that there exists a sequence of period-doubling bifurcation to chaos.
Moreover, it is found that the route to chaos is through a sequence of period-doubling bifurcations.
The PLL dynamics in the unstable region is found to have a sequence of period doubling bifurcation and chaos.
Two of the traveling waves lose their stability by Hopf bifurcation and have a sequence of period-doubling bifurcations leading to chaos.
It is shown that with an increase in the amplitude of the forcing that quasiperiodic behaviour occurs, followed by a sequence of period doubling bifurcations leading to chaos.
Write better and faster with AI suggestions while staying true to your unique style.
Since I tried Ludwig back in 2017, I have been constantly using it in both editing and translation. Ever since, I suggest it to my translators at ProSciEditing.

Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com