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A collection of cubes in K and the collection of the faces of all dimensions of cubes in K forms a polyhedral complex with K as its generating collection.
We're psyched to see smart toys from companies like Sifteo, with a collection of cubes that communicate wirelessly and respond to your gestures -- tilt, stack, shake and combine them into various games.
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At the Galerie Jousse, men and women, dressed in Rick Owens designs, chatted among pieces from his furniture line an unsettling collection of cube-shaped chairs, sofas, and side tables upholstered in mink, sable, and felt, some of them decorated with deer antlers.
At the Galerie Jousse, men and women, dressed in Rick Owens designs, chatted among pieces from his furniture line — an unsettling collection of cube-shaped chairs, sofas, and side tables upholstered in mink, sable, and felt, some of them decorated with deer antlers.
That is, (Omegasubsetmathbb{R}^{n}) is the union of a collection of cube (Omega_{k}), whose sides are parallel to the axes, whose interiors are mutually disjoint, and whose diameters are approximately proportional to their distances from F, where F is the complement of Ω in (mathbb{R}^{n}).
For any (alpha>0) and any finite collection of dyadic cubes Q and associated positive scalars (lambda_{Q}), there exists a collection of pairwise disjoint dyadic cubes S such that (1) (sum_{Qsubset S}lambda_{Q}leq2^{n}alpha|S|), for all S; (2) (sum|S|leqalpha^{-1}sumlambda_{Q}); (3) (Vert sum_{Qnsubseteq mathrm{any} S}lambda _{Q}|Q|^{-1}chi_{Q} Vert _{L^{infty}(mathbb{R}^{n})}leqalpha). .
Let (mathcal{D}_{nu}) be the collection of dyadic cubes.
Take the finite collection of dyadic cubes (Q_{j,k_{j}}), which is associated with the positive scalars (lambda_{Q_{j,k_{j}}}) in the given atomic decomposition of (f_{j}).
The cube functionalization protocol was optimized to avoid aggregation of cubes; as with commercially available particles.
Nordtvedt's ideas were largely responsible for NASA's decision to put retroreflectors--collections of "corner cubes," which, because of their geometry, reflect light precisely back toward its source--on the moon.
Let (|E|) denote the Lebesgue measure of E. Let (mathcal{D}(mathbb{R}^{n})) be the collection of all dyadic cubes on (mathbb{R}^{n}).
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Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com