Sentence examples for derived here for from inspiring English sources

The formulation of Green's matrix is based on special (bi- orthogonality relations bi- orthogonalityfunctions, which arelationsd here for the fluid-filled shell.

The equivalent absorption area and averaged damping constants can be estimated theoretically according to the relation derived here for low frequency bands.

In an accompanying paper (Part II), we present an interpretation and analysis methodology based on the analytical solutions derived here for parameter estimation from temperature transient data jointly with pressure transient data.

In addition, general relations have been derived here for the transfer of source characteristics from one station to another station across one or more acoustical elements, and also for combining several sources into a single equivalent source.

The probability of error is derived here for the maximum likelihood receiver and the simulation results obtained here support our analytical finding.

The empirical KL divergence was derived here for GMMs, but in (19) and (20) we can also use HMMs to model the signals.

Finally, all the results derived here apply for systems with a nonzero death rate, and a nonzero rate of cell "awakening", β, see Text S1, Section 3.4.

The pattern derived here provides inference for (a) fire acting as an increasing aggregation & spatial autocorrelation force, (b) tree survival under fire regimes is potentially facilitated by forming patches of trees and (c) scale-dependent facilitation and competition coexisting within the same ecosystem with finer scale facilitation and coarser scale competition.

When comparing the log j distribution derived here to those for other clusters, we find that it is consistent with a population of stars draining angular momentum into disks.

For convenience of exposition, in this Appendix we focus on network communities as the meso-scale structure of interest; however, all of the modeling results derived here also hold for the case of core-periphery structure.

Equation (4) is derived here to solve for the point of intersection of the stress strain curve of partial confinement (Eq. (5)) and the line connecting the ultimate confined and the ultimate unconfined points, see Fig. 1.