Proof Multiplying the first equation of (1.1) by u t and the second equation by v t, respectively, integrating the results over Ω, performing integration by parts and noting that F t ( u, v ) = f 1 ( u, v ) u t + f 2 ( u, v ) v t, we can easily get (3.1).
By multiplying the first and second equation of (1.1) by u t and v t, respectively, integrating over Ω and summing them up, we obtain d d t E ( t ) = − ( ∥ u t ∥ m + 1 m + 1 + ∥ v t ∥ r + 1 r + 1 ) + 1 2 ( g ′ ∘ ∇ u + h ′ ∘ ∇ v ) − 1 2 ( g ( t ) ∥ ∇ u ∥ 2 + h ( t ) ∥ ∇ v ∥ 2 ).
It is seen that nine single nanowires are respectively integrated on a piece of Si substrate with a cover layer of SiO2.
To account for egg and larval mortality, the connectivity matrices were multiplied by fixed daily mortality rates of 0.036 and 0.048 d−1 for eggs (ze) and larvae (zl), respectively, integrated over the planktonic periods.
In fact, it is becoming evident that the balance between mesenchymal and epithelial master regulators (i.e., Snail and HNF4 α and HNF1 α, respectively), integrated by specific microRNAs regulation, is responsible for stable maintenance of hepatocyte identity, as well as for the EMT/MET dynamics.
The conversion factor was applied to the rates of N2 fixation (Fig. 1) using the percentage of AR assay and N2 assimilation (Table 1) to provide a lower and upper estimate of biological H2 consumption respectively, integrated across the 0 45 m depth horizon.
Multiplying (1.2) by, respectively, then integrating the resulting equation with respect to on and using integration by parts, we get (3.1).
The male maps of LG14 and LG18, which were split to two LG on the first generation map respectively [ 6] due to the limited number of markers, were merged to one LG respectively by integrating new microsatellites located in single BAC clones.
The two male linkage groups (i.e. LG14 and LG18) which were split to two LG on the first generation map respectively [ 6] due to the limited number of markers on these LG, were merged to one LG respectively by integrating new microsatellites located in single BAC clones, which improved the quality of the linkage map of L. calcarifer.
Moreover, under the condition (5), multiplying r and r ( r ; μ ) on both sides of the equation in (8), respectively, and integrating over [ 0, 1 ] yields ∫ 0 1 f ( ω ( r ; μ ) ) r d r = − ( r ; μ ) ) r | r = 1 μ, (10).
Firstly, taking the L 2 ( R 3 ) inner product of v +, w and v − with the above equations, respectively, and integrating by parts, we can obtain the energy estimates similar to (2.2).
