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A sum-product number is a number n such that the sum of n's digits times the product of n's digit is n itself, for example 135=(1+3+5)(1·3·5). (1) Obviously, such a number ...

For two polynomials P_1(x)=a_mx^m+...+a_0 and P_2=b_nx^n+...+b_0 of degrees m and n, respectively, the Sylvester matrix is an (m+n)×(m+n) matrix formed by filling the matrix ...

Togliatti (1940, 1949) showed that quintic surfaces having 31 ordinary double points exist, although he did not explicitly derive equations for such surfaces. Beauville ...

The Banach-Saks theorem is a result in functional analysis which proves the existence of a "nicely-convergent" subsequence for any sequence {f_n}={f_n}_(n in Z^*) of ...

There are several attractive polyhedron compounds consisting of three cubes. The first (left figures) arises by joining three cubes such that each shares two C_2 axes (Holden ...

There are a number of attractive polyhedron compounds consisting of five octahedra. The first octahedron 5-compound is a polyhedron compound composed of five octahedra ...

The simplex method is a method for solving problems in linear programming. This method, invented by George Dantzig in 1947, tests adjacent vertices of the feasible set (which ...

The mean tetrahedron volume of a tetrahedron with vertices chosen at random inside another tetrahedron of unit volume is given by V^_ = (13)/(720)-(pi^2)/(15015) (1) = ...

The ideal generated by a set in a vector space.

An n×n square matrix M with M_(ii) = 1 (1) M_(ij) = M_(ji)>1 (2) for all i,j=1, ..., n.