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A notation used to describe curves. The fundamental principle of Clebsch-Aronhold notation states that if each of a number of forms be replaced by a power of a linear form in ...

The colon is the symbol ":". It is used in a number of different ways in mathematics. 1. To denote ratio or odds, as in 2:1 (voiced "two to one"). 2. To mean such that in ...

The approximation of a piecewise monotonic function f by a polynomial with the same monotonicity. Such comonotonic approximations can always be accomplished with nth degree ...

Two elements alpha, beta of a field K, which is an extension field of a field F, are called conjugate (over F) if they are both algebraic over F and have the same minimal ...

A curve of order n is generally determined by n(n+3)/2 points. So a conic section is determined by five points and a cubic curve should require nine. But the Maclaurin-Bézout ...

A chord of a graph cycle C is an edge not in the edge set of C whose endpoints lie in the vertex set C (West 2000, p. 225). For example, in the diamond graph as labeled ...

Let j_k(alpha) denote the number of cycles of length k for a permutation alpha expressed as a product of disjoint cycles. The cycle index Z(X) of a permutation group X of ...

Darboux's formula is a theorem on the expansion of functions in infinite series and essentially consists of integration by parts on a specific integrand product of functions. ...

A limiting case in which a class of object changes its nature so as to belong to another, usually simpler, class. For example, the point is a degenerate case of the circle as ...

The operator partial^_ is defined on a complex manifold, and is called the 'del bar operator.' The exterior derivative d takes a function and yields a one-form. It decomposes ...