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Whether we treat the convolution as continuous or discrete, its interpretation is the same: for each position x in the output function, we shift the filter function g left or right until it is centered at that position, we flip it left-to-right, we multiply every point on f by the corresponding point on our shifted g, and we add (or integrate) these products together.
This explains our "shifted" convention in defining ( R ( lambda ) ). Elliptic regularity shows that ( R ( zeta ) : {dot{mathcal {C}}^infty }( M ) rightarrow {{mathcal {C}}^infty }( M )), ( {mathrm{Im}},lambda > n/2 ).
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Our shifting global reality only further compounded an already tough situation.
Google's comments disheartening as they might be reflect the reality of our shifting technologies.
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A decade later, our shifting anxieties are reflected in a very different way in Ridley Scott's Alien.
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Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com