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If E = H, a Hilbert space, then the duality mapping becomes the identity map on H.
The output layer of feature mapping becomes the input layer for acoustic modeling, which is also a linear hidden layer of the whole network.
Theorem 1.1 is a generalization of the Banach contraction principle, since for the mapping F of the form (F t)=ln t), an F-contraction mapping becomes the Banach contraction condition (2).
As remote-sensing assisted carbon mapping becomes the basic tool with which to assess carbon stocks, this lingering uncertainty will be addressed on a regional or ecosystem level with direct harvests and direct measurements of carbon stocks.
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If the agricultural areas are considered as SDTF, the LCM map becomes the best performing map with 62.7% of specimens mapping under the correct biome (Table 3).
His maps became the standard navigational charts for the North American East Coast for the next fifty years.
His cholera-cluster maps became the motif of a new science, premised on the belief that disease, in the dawning age of the germ theory, could be chased from the shadows of superstition and hunted to the ground.
The map became the basis for a bus tour, which developed into an international attraction, and it received publicity around the world and even placed second among British travel writers as the world's best tourist initiative.
The maps became the backbone of a book he wrote and self-published in 1994, which I used to retrace their footsteps from the labour camp in Kaluga – where they were being punished for partisan activity – to Wrocław where the rest of their family had fled.
The shorter the seed length is, the more sensitive and accurate the mapping becomes, but at the expense of running time.
In the case of discrete measurments the mapping becomes where ℳ represents the sampling of the potential Uscalp at a set of detectors.
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Since I tried Ludwig back in 2017, I have been constantly using it in both editing and translation. Ever since, I suggest it to my translators at ProSciEditing.

Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com