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The tail of a vector AB^-> is the initial point A, i.e., the point at which the vector originates. The tails of a statistical distribution with probability density function ...

A vector field u satisfying the vector identity ux(del xu)=0 where AxB is the cross product and del xA is the curl is said to be a Beltrami field.

A three-dimensional surface with constant vector field on its boundary which traps at least one trajectory which enters it.

Also known as the Serret-Frenet formulas, these vector differential equations relate inherent properties of a parametrized curve. In matrix form, they can be written [T^.; ...

Let V=R^k be a k-dimensional vector space over R, let S subset V, and let W={w in V:w·n^^=0} be a subspace of V of dimension k-1, where n^^ is a unit normal vector of W. Then ...

The plane spanned by the three points x(t), x(t+h_1), and x(t+h_2) on a curve as h_1,h_2->0. Let z be a point on the osculating plane, then [(z-x),x^',x^('')]=0, where ...

A generalization of the p-adic norm first proposed by Kürschák in 1913. A valuation |·| on a field K is a function from K to the real numbers R such that the following ...

A Pisot number is a positive algebraic integer greater than 1 all of whose conjugate elements have absolute value less than 1. A real quadratic algebraic integer greater than ...

There are several definitions of a ray. When viewed as a vector, a ray is a vector AB^-> from a point A to a point B. In geometry, a ray is usually taken as a half-infinite ...

A closed subspace of a Banach space X is called weakly complemented if the dual i^* of the natural embedding i:M↪X has a right inverse as a bounded operator. For example, the ...