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They derived the corresponding Green function called the fractional Green function and obtained some properties.
Additionally, it is shown that the corresponding Green functions can be used to supply improvable lower bounds.
The modeled quantities are represented by an ensemble of sampling points which are evolved according to the corresponding Green function.
The FTIR spectra of heat-treated samples showed several significant changes from the corresponding green ones (see Figure 5).
While relatively big nanostructured features (10 nm and larger) could be addressed by applying fluctuation dissipation theorem and corresponding Green functions' analysis, smaller objects will require individual approach.
Schneider and Wyss [13] converted the diffusion-wave equation with appropriate initial conditions into the integrodifferential equation and found the corresponding Green functions in terms of Fox functions.
For example, ethene from petroleum has compromised the development of a related market because the price of the corresponding green chemical is higher.
Using the properties of the corresponding Green function and Guo-Krasnosel'skii fixed point theorem on cones, we obtain the existence of positive solutions to problem (1.4).
We prove global sharp estimates for the heat kernel related to certain sub-Laplacians on a real semisimple Lie group, from which we deduce an estimate for the corresponding Green function.
Live and dead bacteria can be separately stained with Syto-9 and propidium iodine, which can be easily distinguished under the fluorescence microscope by their corresponding green and red fluorescence emission, respectively.
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These graphs relate the maximum building settlement caused by tunnelling to the corresponding green-field settlement.
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