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An elementary theorem in geometry whose name means "asses' bridge," perhaps in reference to the fact that fools would be unable to pass this point in their geometric studies. ...

The ith Pontryagin class of a vector bundle is (-1)^i times the ith Chern class of the complexification of the vector bundle. It is also in the 4ith cohomology group of the ...

Let G be a locally compact Abelian group. Let G^* be the group of all continuous homeomorphisms G->R/Z, in the compact open topology. Then G^* is also a locally compact ...

A result in control theory. Define H(psi,x,u)=(psi,f(x,u))=sum_(a=0)^npsi_af^a(x,u). Then in order for a control u(t) and a trajectory x(t) to be optimal, it is necessary ...

The Pontryagin number is defined in terms of the Pontryagin class of a manifold as follows. For any collection of Pontryagin classes such that their cup product has the same ...

The upper horizontal line segment in the above figure appears to be longer than the lower line segment despite the fact that both are the same length.

In computer science, a pop is an action which removes the initial element from the top of a queue or stack, turning the list (a_1, a_2, ..., a_n) into (a_2, ..., a_n) and ...

The word population has a number of distinct but closely related meanings in statistics. 1. A finite and actually existing group of objects which, although possibly large, ...

Let X_1 and X_2 be the number of successes in variates taken from two populations. Define p^^_1 = (x_1)/(n_1) (1) p^^_2 = (x_2)/(n_2). (2) The estimator of the difference is ...

The differential equation describing exponential growth is (dN)/(dt)=rN. (1) This can be integrated directly int_(N_0)^N(dN)/N=int_0^trdt (2) to give ln(N/(N_0))=rt, (3) ...