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A law in (2-valued) logic which states there is no third alternative to truth or falsehood. In other words, for any statement A, either A or not-A must be true and the other ...

A link invariant is a function from the set of all links to any other set such that the function does not change as the link is changed (up to isotopy). In other words, a ...

Let F be a differential field with constant field K. For f in F, suppose that the equation g^'=f (i.e., g=intf) has a solution g in G, where G is an elementary extension of F ...

An n-cycle is a finite sequence of points Y_0, ..., Y_(n-1) such that, under a map G, Y_1 = G(Y_0) (1) Y_2 = G(Y_1) (2) Y_(n-1) = G(Y_(n-2)) (3) Y_0 = G(Y_(n-1)). (4) In ...

subjMathematics:Discrete Mathematics:Graph Theory:Cliques The maximal clique polynomial C_G(x) for the graph G may be defined as the polynomial ...

The number 1000000=10^6. While one million in the "American" system of numbers means the same thing as one million in the "British" system, the words billion, trillion, etc., ...

If a compact manifold M has nonnegative Ricci curvature tensor, then its fundamental group has at most polynomial growth. On the other hand, if M has negative curvature, then ...

Let f be analytic on a domain U subset= C, and assume that f never vanishes. Then if there is a point z_0 in U such that |f(z_0)|<=|f(z)| for all z in U, then f is constant. ...

A technically defined group characterizing a system of linear differential equations y_j^'=sum_(k=1)^na_(jk)(x)y_k for j=1, ..., n, where a_(jk) are complex analytic ...

A point x in a manifold M is said to be nonwandering if, for every open neighborhood U of x, it is true that phi^nU intersection U!=emptyset for a map phi for some n>0. In ...