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A Karnaugh map (KM or K-map) is a diagram that can be used to simplify a Boolean algebra expression. Maurice Karnaugh introduced the technique in 1953 [ 1 ] [ 2 ] as a refinement of Edward W. Veitch 's 1952 Veitch chart , [ 3 ] [ 4 ] which itself was a rediscovery of Allan Marquand 's 1881 logical diagram [ 5 ] [ 6 ] or Marquand diagram . [ 4 ]
The k-Chinese postman problem: find k cycles all starting at a designated location such that each edge is traversed by at least one cycle. The goal is to minimize the cost of the most expensive cycle. The "Rural Postman Problem": solve the problem with some edges not required. [12]
The smallest such value of k is called the Lipschitz constant of f. Contractive maps are sometimes called Lipschitzian maps. If the above condition is instead satisfied for k ≤ 1, then the mapping is said to be a non-expansive map. More generally, the idea of a contractive mapping can be defined for maps between metric spaces.
It has nine edges, one edge for each of the pairings of a house with a utility, or more abstractly one edge for each pair of a vertex in one subset and a vertex in the other subset. Planar graphs are the graphs that can be drawn without crossings in the plane, and if such a drawing could be found, it would solve the three utilities puzzle. [13 ...
The map f → f ∘ g is a ring homomorphism from k[V′] to k[V]. Conversely, every ring homomorphism from k [ V ′] to k [ V ] defines a regular map from V to V ′. This defines an equivalence of categories between the category of algebraic sets and the opposite category of the finitely generated reduced k -algebras.
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This sequence takes a particularly simple form for prime k: 2 ⋅ 2 k − 1 − 1 / k . For example: 2 ⋅ 2 13 − 1 − 1 / 13 = 630 is the number of cycles of length 13. Since this case of the logistic map is chaotic for almost all initial conditions, all of these finite-length cycles are unstable.
UPS's announcement that it will cut back on deliveries for its largest customer, Amazon (), sent its stock tumbling as much as 15% on Thursday.But the company says it made the change with the goal ...