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Contracting tensors lambda with nu in the Bianchi identities R_(lambdamunukappa;eta)+R_(lambdamuetanu;kappa)+R_(lambdamukappaeta;nu)=0 (1) gives ...

The usual type of vector, which can be viewed as a contravariant tensor ("ket") of tensor rank 1. Contravariant vectors are dual to one-forms ("bras," a.k.a. covariant ...

The acceleration of an element of fluid, given by the convective derivative of the velocity v, (Dv)/(Dt)=(partialv)/(partialt)+v·del v, where del is the gradient operator.

Defined for a vector field A by (A·del ), where del is the gradient operator. Applied in arbitrary orthogonal three-dimensional coordinates to a vector field B, the ...

A subset A of a vector space V is said to be convex if lambdax+(1-lambda)y for all vectors x,y in A, and all scalars lambda in [0,1]. Via induction, this can be seen to be ...

A set X is a called a "convex cone" if for any x,y in X and any scalars a>=0 and b>=0, ax+by in X.

A set S in a vector space over R is called a convex set if the line segment joining any pair of points of S lies entirely in S.

A sphere with four punctures occurring where a knot passes through the surface.

Maximize the number of cookies you can cut from a given expanse of dough (Hoffman 1998, p. 173).

The plane spanned by two coordinate axes in the three-dimensional Euclidean space. The coordinate plane spanned by the x- and the y-axis is called xy-plane.