Sentence examples for by integrating the second from inspiring English sources

On the other hand, by integrating the second equation in (3.1), we have ∫ Ω v ( m u 1 + u − θ ) d x = 0, which implies that there exists a point y 1 ∈ Ω such that m u ( y 1 ) 1 + u ( y 1 ) − θ = 0, i.e., m u ( y 1 ) = θ ( 1 + u ( y 1 ) ).

We further evaluated the strong signal in EGFR by integrating the second and third regions to form a haplotype spanning seven SNPs in intron 1 (Supplementary Table S2).

(7) By integrating the second line in Equation (7) w.r.t.

The value of the constant is determined as a solvability condition from the second equation by integrating the second equation from 0 to 2 Π and dividing the resulting equation by 2 Π.

Main parameters representing the HPHE are investigated experimentally and theoretically, the optimum operation conditions are determined by integrating the first and the second law of thermodynamics.

The thickness of a turbulent flame brush nondimensionalized by the integral length scale tends to show linear dependence on the H-factor which is obtained by integrating the first moment equation of the reaction progress variable.

The optimum operation conditions were assessed by integrating the first and the second law of thermodynamics for a counter flow PHE employed for a dyeing process in textile industry.

The optimum operation condition was assessed by integrating the first and the second law of thermodynamics for a water water heat pipe heat exchanger (HPHE) for a slag cooling process in steel industry.

On the contrary, our proposed algorithm alleviates two-hop rate mismatch by integrating the first-hop parameters and the timesharing value in relay transmit beamforming design, thus improving the end-to-end sum-rates.

By integrating the first term twice on the right-hand side by parts and taking the conditions into account (1.2), we find that φ ( x, s ) = sin s x + ∫ 0 x sin s ( x − t ) s { A t + q ( t ) } φ ( t, s ) d t, where φ ( t, s ) t ∈ C [ 0, π ]. □.

By integrating the first equation of (2.12), we obtain that aTrgeq aT|x|geq aint_{0}^{T}x s),dsgeqint _{0}^{T}y(s),dsgeq Tsigma|y|, which implies that (|y|leq asigma^{-1}r), a contradiction to ((x,y in Pcap(bar{Omega}_{2}backslashOmega_{1})).