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3 is the only integer which is the sum of the preceding positive integers (1+2=3) and the only number which is the sum of the factorials of the preceding positive integers ...

How can a delegation of six regiments, each of which sends a colonel, a lieutenant-colonel, a major, a captain, a lieutenant, and a sub-lieutenant be arranged in a regular ...

The coordinate system obtained by inversion of Cartesian coordinates, with u,v,w in (-infty,infty). The transformation equations are x = u/(u^2+v^2+w^2) (1) y = ...

In general, groups are not Abelian. However, there is always a group homomorphism h:G->G^' to an Abelian group, and this homomorphism is called Abelianization. The ...

The pure equation x^p=C of prime degree p is irreducible over a field when C is a number of the field but not the pth power of an element of the field. Jeffreys and Jeffreys ...

A measure lambda is absolutely continuous with respect to another measure mu if lambda(E)=0 for every set with mu(E)=0. This makes sense as long as mu is a positive measure, ...

The combining of two or more quantities using the plus operator. The individual numbers being combined are called addends, and the total is called the sum. The first of ...

The word adjoint has a number of related meanings. In linear algebra, it refers to the conjugate transpose and is most commonly denoted A^(H). The analogous concept applied ...

A two-dimensional affine geometry constructed over a finite field. For a field F of size n, the affine plane consists of the set of points which are ordered pairs of elements ...

Let P be the set of prime ideals of a commutative ring A. Then an affine scheme is a technical mathematical object defined as the ring spectrum sigma(A) of P, regarded as a ...