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(1) for p in [0,1], where delta is the central difference and E_(2n) = G_(2n)-G_(2n+1) (2) = B_(2n)-B_(2n+1) (3) F_(2n) = G_(2n+1) (4) = B_(2n)+B_(2n+1), (5) where G_k are ...

A curve on the unit sphere S^2 is an eversion if it has no corners or cusps (but it may be self-intersecting). These properties are guaranteed by requiring that the curve's ...

A differential of the form df=P(x,y)dx+Q(x,y)dy (1) is exact (also called a total differential) if intdf is path-independent. This will be true if ...

A functor between categories of groups or modules is called exact if it preserves the exactness of sequences, or equivalently, if it transforms short exact sequences into ...

An exact sequence is a sequence of maps alpha_i:A_i->A_(i+1) (1) between a sequence of spaces A_i, which satisfies Im(alpha_i)=Ker(alpha_(i+1)), (2) where Im denotes the ...

The trilinear coordinates alpha:beta:gamma of a point P relative to a reference triangle are proportional to the directed distances a^':b^':c^' from P to the side lines of ...

The center J_i of an excircle. There are three excenters for a given triangle, denoted J_1, J_2, J_3. The incenter I and excenters J_i of a triangle are an orthocentric ...

A Lie algebra over an algebraically closed field is called exceptional if it is constructed from one of the root systems E_6, E_7, E_8, F_4, and G_2 by the Chevalley ...

A theorem stating the existence of an object, such as the solution to a problem or equation. Strictly speaking, it need not tell how many such objects there are, nor give ...

In predicate calculus, an existential formula is a prenex normal form formula (i.e., a formula written as a string of quantifiers and bound variables followed by a ...