0 happening repeatedly over a period of time:
He suffers periodic mental breakdowns.
1 happening repeatedly in a fixed pattern
2 happening repeatedly although not necessarily frequently:
He suffers periodic mental breakdowns.
For the other four types of characteristic structure, we obtain five types of periodic wave solution and five types of soliton.
A substitution with precisely one periodic, hence fixed, bi-infinite word is called proper.
They extensively investigated several branches of periodic solutions and their stability.
The higher-order branches of solutions correspond to rescaled periodic extensions of this fundamental branch.
From 4, there are no positive periodic steady states or zero contact angle touchdown steady states.
This analysis is difficult because the periodic solution changes dramatically along the nearly vertical branch.
A homogenization algorithm is implemented, and asymptotic formulae are derived for the effective elastic moduli of the periodic structures.
In the present paper, agents have heterogeneous beliefs, but the existence of periodic equilibria is not threatened. 10.
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