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The biological role of Grb10 in promoting insulin signaling has been proven using a mouse model (Smith et al., 2007; Wang et al., 2007).
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Convergence is proven, using a Lyapounov function.
The efficient injectability of HPMC/Fe3O4 was proven using a very small needle.
The stability of the closed-loop system is proven using a Lyapunov approach.
This technique was proven using a sequence of near real time neutron images obtained during the drying process.
The stability and robustness properties of the controller are proven using a smooth and homogeneous strict Lyapunov function (LF).
While the 3D-QSAR models were created for a training set of 33 compounds, their external predictivity was proven using a test set of 12 compounds.
The TDC algorithm design is created with a low-order dynamic model, and its superior performances are proven using a real-time control experiment.
Although the overall system is infinite dimensional, convergence of the observer is proven using a standard Lyapunov approach along with classic mathematical tools such as Cauchy series, Parseval equality, and compact embeddings of Hilbert spaces.
Instead, non-conserved miRNAs must be proven using a combination of detailed analyses of their sequence, biogenesis, secondary structure, expression patterns, and silencing functions.
Stability is proved using a Lyapunov approach.
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CEO of Professional Science Editing for Scientists @ prosciediting.com