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By Remark 3.1, the map is well defined.
Since is a cellular map, is well defined and is also a cellular map.
Then the bounded sectional curvature map is well defined, bounded, and independent of the choice of basis on Π.
A function is called a Fourier multiplier in if the map, is well defined and extends to a bounded linear operator in.
end{aligned} This shows that (|Y|_{L^{q}_{mathcal {P}}(Omega L^{q}_{eta}(H))}) is finite provided (eta<0) and (omega+eta<0), so the map is well defined.
UK-wide, outside of the North where Labour has been the traditional party of the working class vote, the election map is well and truly blue.
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The convexity assumptions within the theorem have mainly be imposed to guarantee that the map is well-defined (i.e., the solution to the corresponding optimization problem is unique).
Modified atmosphere packaging (MAP) is well-proven postharvest technology for preserving natural quality of fresh and minimally processed produce, and extending the storage life under optimum MAP design and storage conditions.
Remark 3. The following remarks hold with respect to Theorem 2. (1) The convexity assumptions within the theorem have mainly be imposed to guarantee that the map is well-defined (i.e., the solution to the corresponding optimization problem is unique).
Two homotetramers occupy the asymmetric unit in the crystal of the apo form of PDC, and the electron density map is well-defined for all eight polypeptide chains.
This map clearly shows that both major lineaments having a large vertical displacement, and minor lineaments that are not obvious in the Bouguer anomaly map, are well defined using the Hough transform approach.
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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