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For any real alpha and beta such that beta>alpha, let p(alpha)!=0 and p(beta)!=0 be real polynomials of degree n, and v(x) denote the number of sign changes in the sequence ...

A closed curve associated with a knot which is displaced along the normal by a small amount. For a knot K parameterized as x^mu(s) for 0<=s<=L along the length of the knot by ...

If f^'(x) is continuous and the integral converges, int_0^infty(f(ax)-f(bx))/xdx=[f(0)-f(infty)]ln(b/a).

A non-Euclidean space with constant negative Gaussian curvature.

A triangle formed by the arcs of three geodesics on a smooth surface.

If the abstract simplicial complex S is isomorphic with the vertex scheme of the simplicial complex K, then K is said to be a geometric realization of S, and is uniquely ...

The dual of the great truncated cuboctahedron U_(20) and Wenninger dual W_(93).

The dual of the great stellated truncated dodecahedron U_(66) and Wenninger dual W_(104).

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 kernel of a group homomorphism f:G-->G^' is the set of all elements of G which are mapped to the identity element of G^'. The kernel is a normal subgroup of G, and always ...