Sentence examples for by taking a limit from inspiring English sources

Proof: The proof follows trivially from Lemma 4.1 by taking a limit operation of (16).

Indeed, this is how a line charge model can be derived by taking a limit of point charges.

In the continuum limit, a generating functional for a function (x t)) on the real domain (tin[0,T]) is obtained by taking a limit of the generating functional for the vector (x_{j}).

This method was used by Osgood [6] to construct a Green function for U relative to some fixed but arbitrary point of U by taking a limit of Green's functions of the sets V of the sort just described, as one chose finer and finer grids on the plane.

Furthermore, by Fatou's lemma and (3), we have lim inf n → ∞ ∫ Ω ( f 0 ( x, u n ) u n p − 1 − b 0 m ( x ) ) φ 1 p d x ≥ 0. As a result, by taking a limit superior with respect to n in (19), we have 0 ≤ − ( b 0 − λ 1 ( m ) ) ∫ m ( x ) φ 1 p d x < 0. This is a contradiction.

Since we define the total derivative by taking a limit as 'v' goes to zero, f ′('a') must be a linear transformation.

The above stochastic model of a spatially structured lattice of neural populations can be reduced to a stochastic neural field by taking a continuum limit.

Remark 3.1 In the case of multiple roots, we can also have the Green function by taking a suitable limit in (3.3).

And so Gavin touts the company's decision to enter fast-growing India by taking a 26% stake in Jagran Prakashan Limited.

Therefore, to "push the envelope" is to test those limits by taking an aircraft to or beyond those parameters.

by taking the limit a 1 → a 0 in (3.3).