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A k-factor of a graph is a k-regular subgraph of order n. k-factors are a generalization of complete matchings. A perfect matching is a 1-factor (Skiena 1990, p. 244).

Given f:X->Y, the image of x is f(x). The preimage of y is then f^(-1)(y)={x|f(x)=y}, or all x whose image is y. Images are elements of the range, while preimages are subsets ...

The universal cover of a connected topological space X is a simply connected space Y with a map f:Y->X that is a covering map. If X is simply connected, i.e., has a trivial ...

A field K is said to be an extension field (or field extension, or extension), denoted K/F, of a field F if F is a subfield of K. For example, the complex numbers are an ...

The Condon-Shortley phase is the factor of (-1)^m that occurs in some definitions of the spherical harmonics (e.g., Arfken 1985, p. 682) to compensate for the lack of ...

The hypersine (n-dimensional sine function) is a function of a vertex angle of an n-dimensional parallelotope or simplex. If the content of the parallelotope is P and the ...

An integrating factor is a function by which an ordinary differential equation can be multiplied in order to make it integrable. For example, a linear first-order ordinary ...

"Much greater" is used to indicate a strong inequality in which a is not only greater than b, but much greater (by some convention), is denoted a>>b. For an astronomer, ...

The polar sine is a function of a vertex angle of an n-dimensional parallelotope or simplex. If the content of the parallelotope is P and the lengths of the n edges of the ...

The Prelle-Singer method is a semi-decision procedure for solving nonlinear first-order ordinary differential equations of the form y^'=P(x,y)/Q(x,y), where P and Q are ...