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Given a map f from a space X to a space Y and another map g from a space Z to a space Y, a lift is a map h from X to Z such that gh=f. In other words, a lift of f is a map h ...

An orientation on an n-dimensional manifold is given by a nowhere vanishing differential n-form. Alternatively, it is an bundle orientation for the tangent bundle. If an ...

A marked point process with mark space E is a double sequence (T,Y)=((T_n)_(n>=1),(Y_n)_(n>=1)) of R^^^+-valued random variables and E^_-valued random variables Y_n defined ...

The center of any sphere which has a contact of (at least) first-order with a curve C at a point P lies in the normal plane to C at P. The center of any sphere which has a ...

The Pippenger product is an unexpected Wallis-like formula for e given by e/2=(2/1)^(1/2)(2/34/3)^(1/4)(4/56/56/78/7)^(1/8)... (1) (OEIS A084148 and A084149; Pippenger 1980). ...

A symbol used to distinguish one quantity x^' ("x prime") from another related x. Prime marks are most commonly used to denote 1. Transformed coordinates, 2. Conjugate ...

A repeated integral is an integral taken multiple times over a single variable (as distinguished from a multiple integral, which consists of a number of integrals taken with ...

The time required for a given principal to double (assuming n=1 conversion period) for compound interest is given by solving 2P=P(1+r)^t, (1) or t=(ln2)/(ln(1+r)), (2) where ...

The term "snark" was first popularized by Gardner (1976) as a class of minimal cubic graphs with edge chromatic number 4 and certain connectivity requirements. (By Vizing's ...

A swirl is a generic word to describe a function having arcs which double back around each other. The plots above correspond to the function f(r,theta)=sin(6cosr-ntheta) for ...