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The economists sometimes argue that geography came to a halt way back because the mathematical tools of the day were not up to the job.
Shannon's analysis of communication codes led him to apply the mathematical tools of information theory to cryptography in "Communication Theory of Secrecy Systems" (1949).
It is also what humans do in general, and the mathematical tools of probability simply allow us to acknowledge that, and to make the exercise explicitly reproducible, which is surely a good scientific attribute.
We employ the mathematical tools of differential geometry because they offer conceptually clear coordinate-free tools that are suitable for all dimensions.
2, we describe the mathematical tools of CS, tree wavelets and sparse data reconstruction used in the compression/decompression method we are proposing.
In contrast, many of the mathematical tools of chaotic dynamics are holistic in that they extract or reveal information about the behavior of the model system as a whole not readily apparent from the nonlinear equations of the model themselves.
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Calculus is the most useful mathematical tool of all, and scholars eagerly applied its ideas to a range of real-world problems.
For this reason, graph spectral theory became a standard mathematical tool of HMO theory (see [4 6] and [7]).
For this, a recent mathematical tool of the authors' group called the Cluster Treatment of Characteristic Roots (CTCR) is deployed.
The thermal mixing and energy flow in the cavities are visualized using the mathematical tool of heatlines.
The 3D-DWT is a mathematical tool of increasing importance in those applications that require an efficient processing of huge amounts of volumetric info.
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