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Packing identical rectangles in a rectangle: The problem of packing multiple instances of a single rectangle of size (l,w), allowing for 90° rotation, in a bigger rectangle of size (L,W) has some applications such as loading of boxes on pallets and, specifically, woodpulp stowage. For example, it is possible to pack 147 rectangles of size (137 ...
This result is interesting because it shows how a dimension derived from a measure (packing dimension) agrees with one derived without using a measure (the modified box dimension). Note, however, that the packing dimension is not equal to the box dimension. For example, the set of rationals Q has box dimension one and packing dimension zero.
Based on the Transporter, the size and capacity of the Conex were about the same, [nb 1] but the system was made modular, by the addition of a smaller, half-size unit of 6 ft 3 in (1.91 m) long, 4 ft 3 in (1.30 m) wide and 6 ft 10 + 1 ⁄ 2 in (2.10 m) high.
of the d-box interiors lie to each side of the hyperplane. For the special case when k = N − 1 (i.e. each point is contained in at most N − 1 boxes), the following theorem holds: [5] Given N axis-parallel d-boxes whose interiors are (N − 1)-thick, there exists an axis-parallel hyperplane that separates two of them.
Dimensioners are weighing and volume measuring systems for measuring three-dimensional or cuboid-shaped objects such as packages, parcels, pallets, cartons and boxes. They are frequently used as part of a much larger logistical system in a distribution center , warehouse or trucking terminal facility.
For many well behaved fractals all these dimensions are equal; in particular, these dimensions coincide whenever the fractal satisfies the open set condition (OSC). [1] For example, the Hausdorff dimension, lower box dimension, and upper box dimension of the Cantor set are all equal to log(2)/log(3). However, the definitions are not equivalent.