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There are two fundamental limitations on when it is possible to construct a lookup table for a required operation. One is the amount of memory that is available: one cannot construct a lookup table larger than the space available for the table, although it is possible to construct disk-based lookup tables at the expense of lookup time.
Formally, given two categories C and D, an equivalence of categories consists of a functor F : C → D, a functor G : D → C, and two natural isomorphisms ε: FG→I D and η : I C →GF. Here FG : D → D and GF : C → C denote the respective compositions of F and G , and I C : C → C and I D : D → D denote the identity functors on C and ...
OLAP tools enable users to analyse multidimensional data interactively from multiple perspectives. OLAP consists of three basic analytical operations: consolidation (roll-up), drill-down, and slicing and dicing. [6]: 402–403 Consolidation involves the aggregation of data that can be accumulated and computed in one or more dimensions. For ...
The objects are the elements of G, and for any two elements x and y of G, there exists a unique morphism from x to y if and only if. The advantages of regarding an equivalence relation as a special case of a groupoid include:
Probability distributions usually belong to one of two classes. A discrete probability distribution is applicable to the scenarios where the set of possible outcomes is discrete (e.g. a coin toss, a roll of a die) and the probabilities are encoded by a discrete list of the probabilities of the outcomes; in this case the discrete probability ...
Technology is the application of conceptual knowledge to achieve practical goals, especially in a reproducible way. [1] The word technology can also mean the products resulting from such efforts, [2] [3] including both tangible tools such as utensils or machines, and intangible ones such as software.
In classical mechanics, a kinematic pair is a connection between two physical objects that imposes constraints on their relative movement ().German engineer Franz Reuleaux introduced the kinematic pair as a new approach to the study of machines [1] that provided an advance over the notion of elements consisting of simple machines.