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In mathematics, the capacity of a set in Euclidean space is a measure of the "size" of that set. Unlike, say, Lebesgue measure , which measures a set's volume or physical extent, capacity is a mathematical analogue of a set's ability to hold electrical charge .
Bin-packing with fragmentation or fragmentable object bin-packing is a variant of the bin packing problem in which it is allowed to break items into parts and put each part separately on a different bin. Breaking items into parts may allow for improving the overall performance, for example, minimizing the number of total bin.
A set of objects, some or all of which must be packed into one or more containers. The set may contain different objects with their sizes specified, or a single object of a fixed dimension that can be used repeatedly. Usually the packing must be without overlaps between goods and other goods or the container walls.
A set of polygons in an Euler diagram This set equals the one depicted above since both have the very same elements.. In mathematics, a set is a collection of different [1] things; [2] [3] [4] these things are called elements or members of the set and are typically mathematical objects of any kind: numbers, symbols, points in space, lines, other geometrical shapes, variables, or even other ...
The most common problem being solved is the 0-1 knapsack problem, which restricts the number of copies of each kind of item to zero or one. Given a set of items numbered from 1 up to , each with a weight and a value , along with a maximum weight capacity ,
The power object of a set A is given by its power set, and the exponential object of the sets A and B is given by the set of all functions from A to B. Set is thus a topos (and in particular cartesian closed and exact in the sense of Barr). Set is not abelian, additive nor preadditive. Every non-empty set is an injective object in Set.
The set of all vectors of norm less than one is called the unit ball of a normed space. It is a convex, centrally symmetric set, generally not an ellipsoid; for example, it may be a polygon (in the plane) or, more generally, a polytope (in arbitrary finite dimension). The parallelogram law (called also parallelogram identity)
The terms fractal dimension and fractal were coined by Mandelbrot in 1975, [16] about a decade after he published his paper on self-similarity in the coastline of Britain. . Various historical authorities credit him with also synthesizing centuries of complicated theoretical mathematics and engineering work and applying them in a new way to study complex geometries that defied description in ...