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As the conversion to direct space is straightforward, one can obtain from these kinds of residuals as well how much the shape of the direct space unit cell of 2D periodic data differs from the shapes of the quadrilaterals that represent the unit cell of the four primitive 2D Bravais lattices and the unit sub-unit cell of the rectangular centered lattice.
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Also, when the graph of the interpolated function differs from the shape of the polynomial considerably, for example (f(x)) = 1/(x), interpolation is very hard because of existing local extrema and the roots of the polynomial.
Geometric imperfections of the cylinder surface are also considered in the analysis, i.e. the geometry of the structure slightly differs from the shape of a perfect cylinder.
The calculated groove shapes are in good agreement with the experimental data and differ considerably from the shapes predicted by the classical Mullins grooving theory for isotropic surfaces.
This shape is similar to that in Herrerasaurus and Eoraptor but differs from the subtriangular shape of Saturnalia and other basal sauropodomorphs.
When the particles are aligned along the elastically soft directions of the crystal the morphology of the particles differs from the equilibrium shape of isolated particles in a manner which depends on the size of the particles.
Their large recurved oral jaw tooth shape, which differs from the conical tooth shape of true piscivorous species, may also have been suited for biting off small portions from their prey's flank.
Kasparov's reliance on this "insight" meant that the shape of his search trees all the nodes explicitly evaluated no doubt differed dramatically from the shape of Deep Blue's, but this did not constitute an entirely different means of choosing a move.
Scanning electron microscopy showed that induced pLp_2940sAmy containing cells had an elongated shape that differed drastically from the shape of non-induced pLp_2940sAmy containing cells and induced cells containing other secretion constructs such as pLp_0297sAmy.
Ms. Crandall said she was looking at cover ads for future issues that would differ from the triangle-shape ads in the right corners for the April and May covers.
Hubert et al.12 set up a taxonomy of functional outliers that any procedure should detect: shift/magnitude outliers, which have the same shape of the majority, but are shifted away; amplitude outliers, curves that may have the same shape as the majority but their scales differ; and shape outliers, curves whose shape differs from the majority.
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