Sentence examples for bound was improved to from inspiring English sources
This bound was improved to 246 in 2014, and by assuming either the Elliott-Halberstam conjecture or a generalized form of that conjecture, the difference was 12 and 6, respectively.
This upper bound is improved at low signal-to-noise ratio for IM/DD channels with pulse amplitude modulation in [9].
The lower bound is improved when the number of factors is large, and designs attaining the improved bounds are constructed by using the complements of designs with small number of factors.
We show that the bound on k can be improved to(0.2 1⩽k⩽δ Ω,N,p εN, which is optimal.
This bound can further be improved to O(m + log n) time by using auxiliary data structures [ 13].
This lower bound was later improved in [16] where the authors proved using the Garfunkel-Bankoff inequality [17, 18] that one can take (psi^ =psi_{1}^) where psi_{1}^(t)=sqrt{frac{4-t}{3}}, (2.3) which is stronger than (psi_{0}^) and more beautiful!
This improved bound is used to prove E s2 -optimality of thE s2 -optimalitybtained via algofitheic search in all cases with N="10, 12, 14, and 16 runs (except the N="14 run, m="16 factor case).
By satisfying the links with the greatest demand for capacity as indicated by λ l *, the lower bound can be improved most.
A class of designs that are optimal under certain conditions is also presented; while these designs are of limited practical value, they show that the derived bound cannot be improved in the general case.
Recently, Peng et al. [5] introduced so-called self-regular barrier functions for primal-dual IPMs for LO, the iteration bound for large-update methods for LO was improved from O ( n log n ε ) to O ( n log n log n ε ), which almost closes the gap between the iteration bounds for large- and small-update methods.
