Sentence examples for further we derive from inspiring English sources
Further, we derive necessary and sufficient conditions for a positive clone to be unresolved and gave a modified construction which avoids this necessary condition, thus resulting in a ˉ3-separable matrix.
end{aligned} According to the operator Lie algebras, we shall introduce different isospectral problems according to deforms of the spectral problem (54) to deduce various lattice integrable systems, including the Toda lattice system, further we derive their Lax pairs by using the r-matrix theory.
To analyze this further, we derive the expected energy consumption per node as the sum of the weighted probabilities that either a node is sending, listening, or receiving: E ( n, s, p →, e S, e R, τ ) = = ∑ j = 1 s [ p j e S + ( 1 − p j ) 1 − p j n − 1 τ e R + ( 1 − p j ) 1 − ( 1 − p j ) n − 1 e R ] · [ 1 − R ( n, j − 1, p → ) ], (25).
Further, we derived a beam model to predict back stiffness from the morphology of the vertebral spines.
Further, we derived few new indices to delineate chromitite and associated ultramafites in satellite image acquired by Advanced Spaceborne Thermal Emission Reflection Radiometer ASTERR) sensor.
Further, we derived a sufficient and necessary condition on recoverability of modified-CS and investigated the recoverability in a probability way [10].
Further, we derived spatially explicit characterization factors (CFs) that distinguish between surface water and groundwater consumption.
Further, we derived likely targets for these hits by incorporating other high-throughput/computational datasets.
To analyse this further, we derived 'residual' traces (Fig. 4C), which represent the difference between the decays of the nth transient in the train and the time-shifted, singlet response.
Further, applying Theorem 1, we derive the following.
