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Four or more points P_1, P_2, P_3, P_4, ... which lie on a circle C are said to be concyclic. Three points are trivially concyclic since three noncollinear points determine a ...

The Lyapunov condition, sometimes known as Lyapunov's central limit theorem, states that if the (2+epsilon)th moment (with epsilon>0) exists for a statistical distribution of ...

The Wolstenholme numbers are defined as the numerators of the generalized harmonic number H_(n,2) appearing in Wolstenholme's theorem. The first few are 1, 5, 49, 205, 5269, ...

The only Wiedersehen surfaces are the standard round spheres. The conjecture was proven by combining the Berger-Kazdan comparison theorem with A. Weinstein's results for n ...

Let W(u) be a Wiener process. Then where V_t=f(W(t),tau) for 0<=tau=T-t<=T, and f in C^(2,1)((0,infty)×[0,T]). Note that while Ito's lemma was proved by Kiyoshi Ito (also ...

A set which is connected but not simply connected is called multiply connected. A space is n-multiply connected if it is (n-1)-connected and if every map from the n-sphere ...

The nullity of a linear transformation f:V->W of vector spaces is the dimension of its null space. The nullity and the map rank add up to the dimension of V, a result ...

A surface which is homeomorphic to a finite collection of spheres, each with a finite number of handles, cross-handles, cross-caps, and perforations. A preliminary version of ...

Teichmüller's theorem asserts the existence and uniqueness of the extremal quasiconformal map between two compact Riemann surfaces of the same genus modulo an equivalence ...

Gradshteyn and Ryzhik (2000) define the circulant determinant by (1) where omega_j is the nth root of unity. The second-order circulant determinant is |x_1 x_2; x_2 ...