Sentence examples for is further equivalent 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).

ORF4-deficient MHV-68 was further equivalent to wild-type in its infection of GAG+ and GAG− CHO cells, whereas gp150-deficient MHV-68 infected GAG− CHO cells much better (Figure 8D).

This decoupled open-loop process is further decomposed into several equivalent single-loop systems, equivalent open-loop processes and disturbances.

The optimal assignment is formulated as an integer linear programming problem and is further converted into an equivalent graph problem.

It is further found that the equivalent solar heat price per kWh is too high under the current solar market cost price and collector technology.

It is further shown that, at equivalent ages, the breast cancers of both Kurdish and Arabic women have HR profiles similar to that of US white women.