Sentence examples for bound of the order from inspiring English sources
It is shown that our algorithms converge strongly with an error bound of the order O(1/N).
Roughly speaking, Holland showed a lower bound of the order of n3c1√l to the number of schemata usefully processed by the genetic algorithm in a population of n = c1 · 2l binary strings, with c1 a small integer.
That means we have to estimate the lower bound of the order of solutions.
As many papers (see [8, 11]) obtained the lower bound of the order of solutions of difference equations.
Work on the fingerprinting game described above started in the late 1990s, and lower bounds on the code length were established of the order (ell propto c ln n) [2], until in 2003, Tardos [3] proved a lower bound of the order (ell propto c^{2} ln n) and described a scheme with (ell = O(c^{2} ln n)), showing this bound is tight.
The natural question arises of the upper bound of the order of the solutions of (1.1).
Among these results were Cantor's Theorem, and the theorem of real analysis which states that every set X of real numbers that is bounded above has a least upper bound of the same order as the real numbers in X. Ramified type theory appeared powerless to prove these results.
This lower run-time cost is obtained while keeping an error bound of the same order of magnitude as the original algorithm.
In other words, our estimations are probably the lower bound of the rupture process, revealing the first-order rupture features for the 2008 Wenchuan earthquake, namely, the main energy release process.
Finally, when (1le alpha <2-frac{2}{d}) the cardinality (O(n^{frac{2d-2}{alpha }})) of admissible meshes provided by Theorem 3 is essentially better than the bound of order (O(n^{2d/alpha })) which can be deduced by a routine application of Markov type inequality (Vert DpVert _K=O(n^{2/alpha }), Vert pVert _K=1) (see [5] for details).
