Sentence examples for becomes an equality for from inspiring English sources
Obviously, inequality (15) becomes an equality for k = 1.
We also observe that (6.11) becomes an equality for a ^ ( x ) = 1 and a = δ.
Therefore in this case, Kedlaya inequality (3.1) becomes an equality for all (n in mathbb {N}) and a pair (x in mathbb {R}^{n}) with weights (lambdain W^{0}_{n}(mathbb {R})).
Inequality (2.1) or (2.2) becomes an equality for all (x,yin mathbb{R}^) if (t=-1), (-1/2), or 0; otherwise inequality (2.1) or (2.2) becomes an equality only when (x=y).
From the definition of subdifferential, for every t we have begin{aligned} F(x t))ge F(x(t_0))+pcdot (x t -x(t_0))+frac{lambda }{2}|x t -x(t_0)|^2, end{aligned}but this inequality becomes an equality for (t=t_0).
The weighted residual sum of squares (WRSSs) along the path can be written as: (7) Confidence bounds for each parameter are then obtained as the parameter values where (6) becomes an equality for the first time.
Clearly, for case (ii), Equation 1a becomes an equality if and only if.
When for all i, α i =1/n, Eq. 29 becomes an equality.Observing that αmax≤1, the following corollary is immediate.
Their cause became an equality of grievance.
For norm resolvent continuous operator functions we show that the variational inequality becomes an equality.
If access to higher education has become an equality issue for men then access to positions of equal power and pay remain the overwhelming equality issue for women in the UK.
