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Let alpha be a nonzero rational number alpha=+/-p_1^(alpha_1)p_2^(alpha_2)...p_L^(alpha_L), where p_1, ..., p_L are distinct primes, alpha_l in Z and alpha_l!=0. Then ...

The derivative identity d/(dx)[f(x)g(x)] = lim_(h->0)(f(x+h)g(x+h)-f(x)g(x))/h (1) = (2) = lim_(h->0)[f(x+h)(g(x+h)-g(x))/h+g(x)(f(x+h)-f(x))/h] (3) = f(x)g^'(x)+g(x)f^'(x), ...

A Cartesian product equipped with a "product topology" is called a product space (or product topological space, or direct product).

A precise sequence of instructions designed to accomplish a given task. The implementation of an algorithm on a computer using a programming language is an example of a ...

Let H be a Hilbert space and M a closed subspace of H. Corresponding to any vector x in H, there is a unique vector m_0 in M such that |x-m_0|<=|x-m| for all m in M. ...

The projective general linear group PGL_n(q) is the group obtained from the general linear group GL_n(q) on factoring by the scalar matrices contained in that group.

The projective general orthogonal group PGO_n(q) is the group obtained from the general orthogonal group GO_n(q) on factoring the scalar matrices contained in that group.

The projective general unitary group PGU_n(q) is the group obtained from the general unitary group GU_n(q) on factoring the scalar matrices contained in that group.

Virtually nothing is known about dissection of a projective plane using unequal squares.

The two-dimensional space consisting of the set of triples {(a,b,c):a,b,c in K, not all zero}, where triples which are scalar multiples of each other are identified.