Sentence examples for we thus derive from inspiring English sources

We thus derive tighter bounds in the following.

In this paper we thus derive challenges for monitoring SoS based on an industrial case.

We thus derive the non-occurrence of the Lavrentiev phenomenon for unnecessarily convex functionals of the gradient.

We thus derive simplified formulae for characteristics of a dust ring from the assumption of αmax > 1/2.

We thus derive a probability distribution $P \theta)$ on the basis of a sample $s$, seemingly without assuming a prior probability.

Making use of the linearization at w = 0 we thus derive rather explicit answers to the key questions.

All together, we thus derived the adaptive stepsize NLMS algorithm (initially heuristically proposed in 1982 [34]) by applying fundamental techniques of Bayesian network modeling to a special realization of the fundamental state-space model in (7).

We thus derived 6 shorter and 6 longer "probe" intervals.

We thus derived the following clinical CT acquisition parameters.

At the end of the procedure, we thus derived 30 gene-wise networks from the 30 probe-wise networks.

From such repetitively generated surrogate data, we thus derived the PLV distribution reflecting independent data (Fig. 6).