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These questions have traditionally been studied using analytic techniques such as entropy methods or splitting of operators.
By the continuation theorem of topological degree, the Lyapunov functional and analytic techniques such as matrix analysis, the existence and its global exponential stability of ω-periodic solutions are established.
Once sufficient amounts of the desired compound are obtained, structural elucidation can be determined by using additional analytic techniques, such as nuclear magnetic resonance, Fourier transform infrared spectroscopy, x-ray crystallography, and accelerator mass spectrometry.
The development of molecular analytic techniques such as immunohistochemistry and fluorescence in situ hybridization (FISH) has enhanced microscopic examination and has allowed for biomarker discovery.
We chose not to use the term 'factor', because it leads the reader to think of a category of data analytic techniques, such as factor analysis [ 17].
The use of other analytic techniques, such as path or mediation analysis, may help further characterize the causal relationship of these associations.
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Further, this analysis used individual rather than group data, offering advantages over meta-analytic techniques such as the ability to identify the exact populations to be studied and to have access to individual data points.
There are, of course, many other ways for analytical scientists to advance microbiome studies, which we do not review here, such as new quality control methods, large-scale data curation, knowledge mining and novel data-analytic techniques such as metaproteomics and advanced mass spectrometry.
A comprehensive study on physical and chemical properties of Mo/MCM-22 bifunctional catalysts has been made by using combined analytic and spectroscopic techniques, such as adsorption, elemental analysis, and 129Xe and 31P NMR of adsorbed trialkylphosphine oxide probe molecules.
Big data analytics uses various techniques, such as machine learning techniques, to identify the likelihood of future outcomes based on applying those techniques on available datasets.
However, multi-criteria decision-making techniques such as analytic hierarchy process (AHP) could be used to precisely determine the weighting factor.
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