For a MS/MS spectrum x, let T x = (V x, E x) be the corresponding fragmentation tree, with root losses E x and loss multiplicities N x.
The characteristic equation associated to (36) is (lambda ^{2}-clambda -bd=0), from which it follows that lambda _{1,2}=frac{cpmsqrt{c^{2}+4bd}}{2}, are the corresponding characteristic roots.
A suitable wire rope of 3 mm diameter was then selected and the corresponding root diameter of the pulley required was 0.036 m (4 cm root diameter pulley was used).
The results for this case are shown in Figure 3, and the corresponding Root Mean Square Error (RMSE) values are shown in Table 2. Table 2 Root Mean Square Error (RMSE) values for the case where the active speakers are estimated, where the RMSE values are calculated from distance estimation in meters (m).
The possible causes are 23%, 39%and10%0% increase in the corresponding root biomass of the varieties, resulting in higher water uptake in the vegetative stage treatment plots.
The data is analyzed and the vibration transmissibility is calculated using the corresponding root-mean-square values of acceleration.
Let μ = α − α 0, then system (2.3) undergoes the Hopf bifurcation at E 0 ( 0, 0, 0 ) near μ = 0. Assume that ± i ω 0 is the corresponding purely imaginary roots of Eq. (2.6) at steady state E 0 ( 0, 0, 0 ) for μ = 0. We transform system (2.4) into an FDE in C ( ( − ∞, 0 ], R 3 ) as y ˙ t = A y t + R y t, (3.1).
As is well known [[13], Section 5.4.4], A has a discrete spectrum σ ( A ) and the corresponding root subspaces are independent of q.
For each integer (N>1), (mathbb {G}_N) denotes the group of Nth roots of unity in (mathbb {k}), and (mathbb {G}'_N) is the corresponding subset of primitive roots (of order N).
