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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 .
In Computers and Intractability [8]: 226 Garey and Johnson list the bin packing problem under the reference [SR1]. They define its decision variant as follows. Instance: Finite set of items, a size () + for each , a positive integer bin capacity , and a positive integer .
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.
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 upper bound for the density of a strictly jammed sphere packing with any set of radii is 1 – an example of such a packing of spheres is the Apollonian sphere packing. The lower bound for such a sphere packing is 0 – an example is the Dionysian sphere packing. [27]
Capacity of a set, in Euclidean space, the total charge a set can hold while maintaining a given potential energy; Capacity factor, the ratio of the actual output of a power plant to its theoretical potential output; Storage capacity (energy), the amount of energy that the storage system of a power plant can hold
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A set of lecture notes surveying "without too many precise details, the basic theory of probability, random differential equations and some applications", as the author himself states. Frehse, Jens (1972), "On the regularity of the solution of a second order variational inequality", Bolletino della Unione Matematica Italiana , Serie IV, vol. 6 ...