By induction, suppose that. On the other hand, since.
Combinated with the estimate above, this gives. Hence, for all positive integer q. By definition of M n , we have that, in order to prove Lemma 2.
- Complex Dynamics: Families and Friends.
- Architectural, energy and information engineering : proceedings of the 2015 International Conference on Architectural, Energy and Information Engineering (AEIE 2015), Xiamen, China, May 19-20, 2015;
- The Thousand Names (The Shadow Campaigns, Book 1);
In fact, since ,. Combinated with the estimates above, this gives. Now, we prove Theorem A. By Lemma 2. Suppose by contradiction that M n is not closed.
Hence, there exists a positive integer q such that. It follows that,. Hence, the orbit is not bounded. Therefore, M n is closed, so it is compact. Now, Lemmas 2. Recent Awards. Presidential and Honorary Awards. About Awards. How to Manage Your Award. Grant Policy Manual. Grant General Conditions. Cooperative Agreement Conditions. Special Conditions. Federal Demonstration Partnership. Boston University.
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