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Let (a)_i be a sequence of complex numbers and let the lower triangular matrices F=(f)_(nk) and G=(g)_(nk) be defined as f_(nk)=(product_(j=k)^(n-1)(a_j+k))/((n-k)!) and ...

For the hyperbolic partial differential equation u_(xy) = F(x,y,u,p,q) (1) p = u_x (2) q = u_y (3) on a domain Omega, Goursat's problem asks to find a solution u(x,y) of (3) ...

A general quartic surface defined by x^4+y^4+z^4+a(x^2+y^2+z^2)^2+b(x^2+y^2+z^2)+c=0 (1) (Gray 1997, p. 314). The above two images correspond to (a,b,c)=(0,0,-1), and ...

A graceful permutation sigma on n letters is a permutation such that {|sigma(i)-sigma(i+1)|:i=1,2,...,n-1}={1,2,...,n-1}. For example, there are four graceful permutations on ...

Let a Gram point g_n be called "good" if (-1)^nZ(g_n)>0, and "bad" otherwise (Rosser et al. 1969; Edwards 2001, p. 180). Then the interval between two consecutive good Gram ...

Gram's law (Hutchinson 1925; Edwards 2001, pp. 125, 127, and 171) is the tendency for zeros of the Riemann-Siegel function Z(t) to alternate with Gram points. Stated more ...

In Season 4 episode "Black Swan" of the television crime drama NUMB3RS, the character Amita Ramanujan refers to graph entropies when studying a map of the Los Angeles while ...

An (m+1)-dimensional subspace W of an (n+1)-dimensional vector space V can be specified by an (m+1)×(n+1) matrix whose rows are the coordinates of a basis of W. The set of ...

The polyhedron compound of the great icosahedron (U_(53)) and the small stellated dodecahedron (U_(34)), sometimes known as the great cid. Four faces meet at each edge of the ...

700 The great dodecahemicosahedron is the uniform polyhedron with Maeder index 65 (Maeder 1997), Wenninger index 102 (Wenninger 1989), Coxeter index 81 (Coxeter et al. 1954), ...