Sentence examples for by the same limit from inspiring English sources
The alternative t 0, δ > t 0 with lim δ → 0 t 0, δ = t 0 can be proved by the same limit process as in the first case, where the point t 0 is dense.
However, whether the amount of kinetic energy from a black hole, in the form of jets and winds, was constrained by the same limit was unclear.
For instance, the bill would, for the first time, force candidates who are not self-financed but opt out of the public financing system to abide by the same limits on contributions and spending that apply to those within the system.
Nsyght differs from Curated.by in that it's far more geared to archiving realtime streams – Curated.by search is still limited by the same limits Twitter has.
But if the major labels are showing greater interest in ad-supported business models, they're doing so warily, as evinced by Last .fms restriction of only three free streams per user per song, the same limit set by Napster.
(1) The limit case (ptoinfty) of (1.1) (replacing f by (f^{frac{1}{p}}) first) represents (1.3), and the same limit case of (1.2) represents (1.5).
It is known that the sequence {x n } generated by (1.4) converges in norm to the same limit PFix(T u as Browder's implicit scheme (1.3) if the sequence {α n } satisfies the following conditions: (C1) limn→∞α n = 0; (C2) ∑ n = 0 ∞ α n = + ∞ ; (C3) either ∑ n = 0 ∞ α n + 1 - α n < + ∞ or li m n → ∞ α n / α n + 1 = 1.
As a result, the grand canonical mean energy reads in the same limit: (42a) (42bywhat, by means of Eq. (10), immediately leads to the associated heat capacities : (43a) (43b) A comparison of these remarkable results with Eqs.
The U.S. Environmental Protection Agency EPAA) has established an MCL (maximum contaminant level) of 6 ppb for antimony, which is the same limit set by Health Canada; the German Federal Ministry of Environment has set a limit of 5 ppb, whereas the Japanese drinking water standard requires levels of antimony < 2 ppb (Shotyk and Krachler 2007).
The competitive exclusion principle states that two species cannot coexist indefinitely by living off the same limiting resource; one will always outcompete the other.
