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The commutative diagram used in the proof of the five lemma. In mathematics, and especially in category theory, a commutative diagram is a diagram such that all directed paths in the diagram with the same start and endpoints lead to the same result. [1] It is said that commutative diagrams play the role in category theory that equations play in ...
Relative dating by biostratigraphy is the preferred method in paleontology and is, in some respects, more accurate. [1] The Law of Superposition, which states that older layers will be deeper in a site than more recent layers, was the summary outcome of 'relative dating' as observed in geology from the 17th century to the early 20th century.
Visibility graphs may be used to find Euclidean shortest paths among a set of polygonal obstacles in the plane: the shortest path between two obstacles follows straight line segments except at the vertices of the obstacles, where it may turn, so the Euclidean shortest path is the shortest path in a visibility graph that has as its nodes the start and destination points and the vertices of the ...
A path in is a continuous map : where is a nondegenerate interval (i.e., a connected set containing more than one point) in . A smooth path has μ {\displaystyle \mu } differentiable an appropriate number of times (typically C ∞ {\displaystyle C^{\infty }} ), and a regular path has nonvanishing derivative.
A path is a particularly simple example of a tree, and in fact the paths are exactly the trees in which no vertex has degree 3 or more. A disjoint union of paths is called a linear forest . Paths are fundamental concepts of graph theory, described in the introductory sections of most graph theory texts.
A world line is a special type of curve in spacetime. Below an equivalent definition will be explained: A world line is either a time-like or a null curve in spacetime. Each point of a world line is an event that can be labeled with the time and the spatial position of the object at that time.
Parity graphs include the distance-hereditary graphs, in which every two induced paths between the same two vertices have the same length.They also include the bipartite graphs, which may be characterized analogously as the graphs in which every two paths (not necessarily induced paths) between the same two vertices have the same parity, and the line perfect graphs, a generalization of the ...
In algebraic topology, a branch of mathematics, the (singular) homology of a topological space relative to a subspace is a construction in singular homology, for pairs of spaces. The relative homology is useful and important in several ways. Intuitively, it helps determine what part of an absolute homology group comes from which subspace.