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A path gamma is a continuous mapping gamma:[a,b]|->C^0, where gamma(a) is the initial point, gamma(b) is the final point, and C^0 denotes the space of continuous functions. ...

Let gamma be a path given parametrically by sigma(t). Let s denote arc length from the initial point. Then int_gammaf(s)ds = int_a^bf(sigma(t))|sigma^'(t)|dt (1) = ...

The term "integral" can refer to a number of different concepts in mathematics. The most common meaning is the the fundamenetal object of calculus corresponding to summing ...

In each of the ten cases with zero or unit mass, the finite part of the scalar 3-loop tetrahedral vacuum Feynman diagram reduces to four-letter "words" that represent ...

A simple path is a path which is a simple curve. More precisely, a continuous mapping gamma:[a,b]->C^0 is a simple path if it has no self-intersections. Here, C^0 denotes the ...

A shortest path between two vertices of a graph is a graph path of shortest possible length between them. Such paths are also known as graph geodesics, and the matrix giving ...

A path in a graph G is a subgraph of G that is a path graph (West 2000, p. 20). The length of a path is the number of edges it contains. In most contexts, a path must contain ...

The Leibniz integral rule gives a formula for differentiation of a definite integral whose limits are functions of the differential variable, (1) It is sometimes known as ...

A Hamiltonian path, also called a Hamilton path, is a graph path between two vertices of a graph that visits each vertex exactly once. If a Hamiltonian path exists whose ...

The longest path problem asks to find a path of maximum length in a given graph. The problem is NP-complete, but there exists an efficient dynamic programming solution for ...