Sentence examples for be further simplified as from inspiring English sources

The inequality (40) can be further simplified as follows: (42).

(C.1) can be further simplified as (C.2).

Equation (B.2) can be further simplified as (B.3).

Noting that and, (19) can be further simplified as (20).

When is large enough, (17) can be further simplified as (18).

The equality can be further simplified as CAS x, y ; u, v = D / C (19).

Each phase is further simplified as 2-phase composite material composed of matrix phase (zero porosity) and pore phase (the sum of various scale pores).

In the current paper the technique is further simplified as the resonance and anti-resonance frequencies of the unblocked and the partially blocked duct are determined from a single MLS measurement in the partially blocked duct using an approximation suggested by Wu 1994 (Applied Acoustics41, 229 236) [2].

which is further simplified as (13).

The formula for the coefficient of concordance W is then given by: W = ∑ T 2 − ∑ T 2 / n / n m 2 n 2 − 1 / 12 (7)The formula is further simplified as follows: W = 12 ∑ T 2 − ∑ T 2 / n n m 2 n 2 − 1 (8).

By approximating the exponential term in the right-hand side of the inequality with the first two terms of the well- known Taylor series, for high SNRs ( 1 / γ ̄ ij → 0 ), the cdf in (31) is further simplified as P γ i ≈ ∑ j = 1 N i ∑ k = 0 ∞ ( − 1 ) k k ! ( m ij + k ) Γ ( m ij ) ξ ij γ ̄ ij γ υ ij m ij + k. (32).