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A number of areas of mathematics have the notion of a "dual" which can be applies to objects of that particular area. Whenever an object A has the property that it is equal ...

The Sharpe ratio is a risk-adjusted financial measure developed by Nobel Laureate William Sharpe. It uses a fund's standard deviation and excess return to determine the ...

Find the shape of a soap film (i.e., minimal surface) which will fill two inverted conical funnels facing each other is known as Sinclair's soap film problem (Bliss 1925, p. ...

A flexagon made with square faces. Gardner (1961) shows how to construct a tri-tetraflexagon, tetra-tetraflexagon, and hexa-tetraflexagon.

A transformation of a polynomial equation f(x)=0 which is of the form y=g(x)/h(x) where g and h are polynomials and h(x) does not vanish at a root of f(x)=0. The cubic ...

The vertex set of a graph is simply a set of all vertices of the graph. The cardinality of the vertex set for a given graph g is known as the vertex count of g. The vertex ...

The Zak transform is a signal transform relevant to time-continuous signals sampled at a uniform rate and an arbitrary clock phase (Janssen 1988). The Zak transform of a ...

For any ideal I in a Dedekind ring, there is an ideal I_i such that II_i=z, (1) where z is a principal ideal, (i.e., an ideal of rank 1). Moreover, for a Dedekind ring with a ...

A polyhedral graph is completely regular if the dual graph is also regular. There are only five types. Let rho be the number of graph edges at each node, rho^* the number of ...

A determinant appearing in Padé approximant identities: C_(r/s)=|a_(r-s+1) a_(r-s+2) ... a_r; | | ... |; a_r a_(r+1) ... a_(r+s-1)|.