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The Kaprekar routine is an algorithm discovered in 1949 by D. R. Kaprekar for 4-digit numbers, but which can be generalized to k-digit numbers. To apply the Kaprekar routine ...

The Taniyama-Shimura conjecture, since its proof now sometimes known as the modularity theorem, is very general and important conjecture (and now theorem) connecting topology ...

If F(x) is a probability distribution with zero mean and rho=int_(-infty)^infty|x|^3dF(x)<infty, (1) where the above integral is a stieltjes integral, then for all x and n, ...

If the section function of a centered convex body in n-dimensional Euclidean space (n>=3) is smaller than that of another such body, is its volume also smaller? The solution ...

Let V be an n-dimensional linear space over a field K, and let Q be a quadratic form on V. A Clifford algebra is then defined over T(V)/I(Q), where T(V) is the tensor algebra ...

Deck transformations, also called covering transformations, are defined for any cover p:A->X. They act on A by homeomorphisms which preserve the projection p. Deck ...

A means of describing how one state develops into another state over the course of time. Technically, a dynamical system is a smooth action of the reals or the integers on ...

In the most commonly used convention (e.g., Apostol 1967, pp. 202-204), the first fundamental theorem of calculus, also termed "the fundamental theorem, part I" (e.g., Sisson ...

Let I(G) denote the set of all independent sets of vertices of a graph G, and let I(G,u) denote the independent sets of G that contain the vertex u. A fractional coloring of ...

The Gibert point can be defined as follows. Given a reference triangle DeltaABC, reflect the point X_(1157) (which is the inverse point of the Kosnita point in the ...