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In particular, it is locally and globally time nonhomogeneous (instantaneous substitution rates are not constant on any edge, nor on the whole tree) and it is neither time-reversible nor stationary.
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The first reshuffling method acts globally in time by randomly reassigning the time index to PPI discoveries.
Precisely, they showed that solutions with negative energy continue to exist globally in time if and blow up in finite time if and the initial energy is sufficiently negative.
Recently, Li and Xin [17] showed that the classical solution for 2D Cauchy problem exists globally in time in the case of small initial energy; furthermore, some large-time decay rates of solutions are first presented.
Exactly speaking, if γ > 0 then solutions exist always globally in time; while if γ < 0, then solutions must blow up in a finite time for large initial data.
It has been proved, in particular, that solutions exist globally in time when the initial data are in a stable set and the solution blows up in finite time when the initial data are in an unstable set.
"A more algorithmically driven process allows us to scale Trending to cover more topics and make it available to more people globally over time".
The result has been proved globally in time.
Suppose the corresponding solution exists globally in time.
We prove that the solutions exist globally in time by contradiction.
The result is proved globally in time by a logarithmic Sobolev inequality.
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Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com