"shown through analysis" is a valid and usable phrase in written English.
It can be used when discussing a topic or idea that has been analyzed and the results or findings are being presented. Example: The impact of climate change on polar bears is shown through analysis of their declining population and habitat loss.
The effectiveness of these algorithms in achieving fairness and providing delay guarantee is shown through analysis and simulation work.
It has been shown through analysis that we can either eliminate the substrate radiation mode or totally match the substrate radiation mode with the film region.
It is shown through analysis that the use of a coincidence horizon of one greatly simplifies coding, tuning, constraint handling and implementation.
It is shown through analysis, simulation and experiment that variations are present in the DC reference voltages prior to the presence of a short-circuit.
Furthermore, several behavioral properties of the optimal control of the useful information diffusion with respect to the number of infected/informed nodes and the evolving user interest are shown through analysis and verified via simulations.
It is shown, through analysis of both types of data, that a non-zero rate of change in the direction of the new coordinate is required and a phenomenological description of this rate is proposed.
Furthermore, we show through analysis and numerical simulations that the data interference terms are well modeled by a Gaussian distribution for which we derive the second order statistics.
We show through analysis and experiments that the new design, by alleviating the edge constrains, can provide significantly larger diaphragm deformation and consequently higher flow rate.
Obara (2012) found that triggered tremors occurred near a volcano and an active fault zone in Hokkaido, Japan and Kita et al. (2014) showed through analysis of seismic attenuation that such tremors occurred in a collision zone.
We also show, through analysis and experiment, that near field operation is feasible and can provide sufficient force and the necessary degrees of freedom to accurately position and orient small satellites relative to one another.
We show through analysis of experimental data that the vortex-induced vibrations of long flexible risers are characterized by time intervals of chaotic response, followed or preceded by periods of statistically stationary response.
