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Any collineation from P(V) to P(V), where V is a three-dimensional vector space, is associated with a semilinear map from V to V.

The Diophantine equation x^2+y^2=p can be solved for p a prime iff p=1 (mod 4) or p=2. The representation is unique except for changes of sign or rearrangements of x and y. ...

A method for predicting the onset of widespread chaos. It is based on the hypothesis that the dissolution of an invariant torus can be associated with the sudden change from ...

The dual polyhedron of the cubohemioctahedron U_(15) and Wenninger dual W_(78). When rendered, the octahemioctacron and hexahemioctacron appear the same.

Given a positive sequence {a_n}, sqrt(sum_(j=-infty)^infty|sum_(n=-infty; n!=j)^infty(a_n)/(j-n)|^2)<=pisqrt(sum_(n=-infty)^infty|a_n|^2), (1) where the a_ns are real and ...

Let two points x and y be picked randomly from a unit n-dimensional hypercube. The expected distance between the points Delta(n), i.e., the mean line segment length, is then ...

The analytic summation of a hypergeometric series. Powerful general techniques of hypergeometric summation include Gosper's algorithm, Sister Celine's method, Wilf-Zeilberger ...

Given a hypergeometric series sum_(k)c_k, c_k is called a hypergeometric term (Koepf 1998, p. 12).

An infinitesimal which is not the differential of an actual function and which cannot be expressed as dz=((partialz)/(partialx))_ydx+((partialz)/(partialy))_xdy, the way an ...

An inner product is a generalization of the dot product. In a vector space, it is a way to multiply vectors together, with the result of this multiplication being a scalar. ...