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In mathematics, and especially in category theory, a commutative diagram is a diagram of objects, also known as vertices, and morphisms, also known as arrows or edges, such that when selecting two objects any directed path through the diagram leads to the same result by composition.
Framed link diagrams are link diagrams with each component marked, to indicate framing, by an integer representing a slope with respect to the meridian and preferred longitude. A standard way to view a link diagram without markings as representing a framed link is to use the blackboard framing. This framing is obtained by converting each ...
The system context diagram is a necessary tool in developing a baseline interaction between systems and actors; actors and a system or systems and systems. Alternatives to the system context diagram are: Example of an Architecture Interconnect Diagram. [7]
Algebraic link diagram for the Borromean rings. The vertical dotted black midline is a Conway sphere separating the diagram into 2-tangles. In knot theory, the Borromean rings are a simple example of a Brunnian link, a link that cannot be separated but that falls apart into separate unknotted loops as soon as any one of its components is ...
Mathematical statistics is the application of probability theory and other mathematical concepts to statistics, as opposed to techniques for collecting statistical data. [1] Specific mathematical techniques that are commonly used in statistics include mathematical analysis , linear algebra , stochastic analysis , differential equations , and ...
In mathematics and computer science, connectivity is one of the basic concepts of graph theory: it asks for the minimum number of elements (nodes or edges) that need to be removed to separate the remaining nodes into two or more isolated subgraphs. [1] It is closely related to the theory of network flow problems. The connectivity of a graph is ...
Let M be a structure in a first-order language L.An extended language L(M) is obtained by adding to L a constant symbol c a for every element a of M.The structure M can be viewed as an L(M) structure in which the symbols in L are interpreted as before, and each new constant c a is interpreted as the element a.
In particular, there is a bipartite "incidence graph" or "Levi graph" corresponding to every hypergraph, and conversely, every bipartite graph can be regarded as the incidence graph of a hypergraph when it is 2-colored and it is indicated which color class corresponds to hypergraph vertices and which to hypergraph edges.