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Let H be a two-dimensional distribution function with marginal distribution functions F and G. Then there exists a copula C such that H(x,y)=C(F(x),G(y)). Conversely, for any ...

The slope-intercept form of a line in the Cartesian plane is given by y=mx+b, where b is the y-intercept and m is the slope.

If M^n is a differentiable homotopy sphere of dimension n>=5, then M^n is homeomorphic to S^n. In fact, M^n is diffeomorphic to a manifold obtained by gluing together the ...

The polyhedron compound of the icosahedron (U_(22)) and the great dodecahedron (U_(35)), sometimes known as the small cid. Four faces meet at each edge of the small complex ...

The dual polyhedron of the small dodecahemicosahedron U_(62) and Wenninger dual W_(100). When rendered, the small dodecahemicosacron and great dodecahemicosacron appear the ...

The dual polyhedron of the small dodecahemidodecahedron U_(51) and Wenninger dual W_(91). When rendered, the small icosihemidodecacron and small dodecahemidodecacron appear ...

The dual polyhedron of the small snub icosicosidodecahedron U_(32) and Wenninger dual W_(110).

An odd composite number N is called a Somer-Lucas d-pseudoprime (with d>=1) if there exists a nondegenerate Lucas sequence U(P,Q) with U_0=0, U_1=1, D=P^2-4Q, such that ...

where R[mu+nu-lambda+1]>0, R[lambda]>-1, 0<a<b, J_nu(x) is a Bessel function of the first kind, Gamma(x) is the gamma function, and _2F_1(a,b;c;x) is a hypergeometric ...

A local source is a node of a directed graph with no entering edges (Borowski and Borwein 1991, p. 401; left figure), and a global source (often simply called a source) is a ...