Note that if a discrete-time nonlinear dynamical system is (globally) bounded with respect to uniformly in, then there exists such that it is (globally) ultimately bounded with respect to uniformly in with an ultimate bound.
Conversely, if a discrete-time nonlinear dynamical system is (globally) ultimately bounded with respect to uniformly in with an ultimate bound, then it is (globally) bounded with respect to uniformly in.
Pragmatists say that beliefs should be judged by their usefulness, and not by any supposed correspondence with an ultimate reality that lurks behind the landscape of everyday life.
The largest of the California heavy oil fields is Midway-Sunset, with an ultimate recovery estimated at more than 3 billion barrels.
The alleged document suggested an operation of one year, with an ultimate goal that "the flow of migrants and smugglers' activities have been significantly reduced".
This partnership improves healthcare provision without commercial gain for individuals or corporations, or the accruement of debt, with an ultimate aim of long-term sustainability.
We expect house prices to fall by 15% this year, with an ultimate decline of 35% over the next three years".
However the plan goes much further with an ultimate goal of being a Eurabian superstate, incorporating Muslim countries of north Africa and the Middle East in the European Union.
"At this point, it appears that the roadless rule may be embroiled in legal controversy and process for a very long time, with an ultimate outcome that is far from certain," Mr. Bosworth wrote.
Therefore, all the solutions for (3) are uniformly bounded with an ultimate bound.
Thus all the solutions for system (4) are uniformly bounded with an ultimate bound.
