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If, in a plane or spherical convex polygon ABCDEFG, all of whose sides AB, BC, CD, ..., FG (with the exception of AG) have fixed lengths, one simultaneously increases ...

A graph G is the edge graph of a polyhedron iff G is a simple planar graph which is 3-connected.

A Steinmetz curve is a curve of intersection of two perpendicularly placed cylinders of radii a and b comprising a Steinmetz solid. If the vertical cylinder has radius a and ...

1.5 times the H-spread.

A function on the reals R is a step function if it can be written as a finite linear combination of semi-open intervals [a,b) subset= R. Therefore, a step function f can be ...

The exploration of three-dimensional space from two-dimensional sections of projections of solid bodies.

The Stiefel manifold of orthonormal k-frames in R^n is the collection of vectors (v_1, ..., v_k) where v_i is in R^n for all i, and the k-tuple (v_1, ..., v_k) is ...

Orthogonal polynomials associated with weighting function w(x) = pi^(-1/2)kexp(-k^2ln^2x) (1) = pi^(-1/2)kx^(-k^2lnx) (2) for x in (0,infty) and k>0. Defining ...

The m+1 ellipsoidal harmonics when kappa_1, kappa_2, and kappa_3 are given can be arranged in such a way that the rth function has r-1 zeros between -a^2 and -b^2 and the ...

The integral transform (Kf)(x)=Gamma(p)int_0^infty(x+t)^(-p)f(t)dt. Note the lower limit of 0, not -infty as implied in Samko et al. (1993, p. 23, eqn. 1.101).