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Two open manifolds M and M^' are cobordant if there exists a manifold with boundary W^(n+1) such that an acceptable restrictive relationship holds.

The logarithm of the reciprocal of a number, equal to the negative of the logarithm of the number itself, cologx=log(1/x)=-logx.

A matrix whose eigenvectors are not complete.

The property of being degenerate.

The multiplicity of a multigraph is its maximum edge multiplicity.

The vectors +/-a_1, ..., +/-a_n in a three-space form a normalized eutactic star iff Tx=x for all x in the three-space.

Given a Euclidean n-space, H_n=n+1.

Definitions about a set which depend on the entire set.

The jerk j is defined as the time derivative of the vector acceleration a, j=(da)/(dt).

U_n(f)=int_a^bf(x)K_n(x)dx, where {K_n(x)} is a sequence of continuous functions.