Sentence examples for further equivalent to from inspiring English sources

When the circuit power is fixed, minimizing the total power consumption is further equivalent to minimizing the total transmit power.

It follows from the Schur complement again that the above inequality is further equivalent to the following inequality: (3.32).

It follows from the Schur complement that the above inequality is further equivalent to the following inequality: (3.26).

Analogously, f ϵ H ( D ) Open image in new window is called locally univalent if it is injective in a neighborhood of each point of D Open image in new window, which is further equivalent to f′ (z) ≠ 0.

In particular, for y = x we have Φ ′ ( x ) ≤ min 1 ≤ i ≤ m h i ( x ; η ( x, x ) ) = 0. Now Φ ′ ( x ˆ ) = 0 is equivalent to the fact that min 1 ≤ i ≤ m h i ( x ˆ ; η ( y, x ˆ ) ) ≥ 0, ∀ y ∈ K which is further equivalent to the fact that h ( x ˆ ; η ( y, x ˆ ) ) ∈ R + m, ∀ y ∈ K that is, x ˆ solves (SVVLI).

Now Φ ( x ˆ ) = 0 is equivalent to the fact that inf u ∈ B ∗ 〈 u, h ( x ˆ ; η ( y, x ˆ ) ) 〉 ≥ 0, ∀ y ∈ K which is further equivalent to the fact that 〈 u, h ( x ˆ ; η ( y, x ˆ ) ) 〉 ≥ 0, ∀ y ∈ K, ∀ u ∈ C ∗ which holds if and only if h ( x ˆ ; η ( y, x ˆ ) ) ∈ C ∗ ∗, ∀ y ∈ K, that is, x ˆ solves (SVVLI).

A further £3bn (equivalent to £4bn) has been allocated for new infrastructure work at Faslane and Coulport bases.

Independent schools generate £4.7bn in tax and save the taxpayer a further £4bn, equivalent to building 460 schools, by educating children out of the state school sector.

Thereafter, subjected to unprecedented budgetary surveillance by an increased posse of inspectors and advisers, Athens will have to find further savings equivalent to 5% of GDP by the end of 2014.

Ireland's environment agency has announced that Ryanair will receive just under 5.6m permits; since these must represent 85% of its needs, it therefore must need to buy about 980,000 further permits, equivalent to the balance of 15%.

The Malaysian authorities have confirmed some of my core allegations: that $681m was paid into Najib Razak's private bank accounts before the 2013 election, and that a further sum equivalent to more than $10m was channelled into another of his private accounts from a public company, SRC International, that he controlled, and which raised money from a public pension fund.