Sentence examples for proved a bound from inspiring English sources

Matthews and Michel (2005) [29] investigated the minimum distances of certain algebraic-geometry codes arising from a higher degree place P. In terms of the Weierstrass gap sequence at P, they proved a bound that gives an improvement on the designed minimum distance.

First we will prove a bound on the difference between any two regularized solutions (2.4).

In this work, we prove a bound on the multiplicity of the singular spectrum for a certain class of Anderson Hamiltonians.

In this section we use the previous result to prove a bound for the solution of our main problem.

In the most interesting cases, we prove a bound of the type N r)⩽Anrn+o(rn) with an explicit An.

To prove the proposition, we utilize an interpolation technique first introduced by Bourgain [2] when he was proving a bound for the spherical maximal operator.

We want to prove a bound for the solution v of the above problem (see Lemma 3.1 below), which will be the primary technical tool in the proof of our main result (see the next Section).

We prove a bound on the number of patients required to detect all driver genes with high probability using a single gene test of recurrence.

In the first model we prove a bound on the number of patients required to detect all driver genes with high probability using a single gene test, while in the second model it is not possible to identify the driver genes using such a test for any number of patients.

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.

Finally, we show a general lower bound on the budget balance factor for cost sharing methods, which can be used to prove a lower bound of Ω(n) on the budget balance factor for completion and flow time scheduling objectives.