Sentence examples for further equivalent from inspiring English sources

Further, equivalent diameter definitions for annular flow are evaluated to determine the friction factor equivalent diameter combination that best describes the experimental data.

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).

In all cases, the sensors responded to 1 equivalent of Zn2+ in MeCN as expected with switch-on fluorescent enhancements of between 2- and 4.5-fold observed, and little or no further enhancement with the addition of further equivalents of Zn2+ (Fig. 4a).

The behaviour of sensor 6 in HEPES buffer proved more complicated than that of the other sensors investigated; addition of further equivalents of Zn2+ led to further significant increases in fluorescence up to a maximum value of 15-fold fluorescence enhancement with 15 equiv.

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.