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The operator partial^_ is defined on a complex manifold, and is called the 'del bar operator.' The exterior derivative d takes a function and yields a one-form. It decomposes ...

A module over a unit ring R is called divisible if, for all r in R which are not zero divisors, every element m of M can be "divided" by r, in the sense that there is an ...

Division by zero is the operation of taking the quotient of any number x and 0, i.e., x/0. The uniqueness of division breaks down when dividing by zero, since the product ...

The elastica formed by bent rods and considered in physics can be generalized to curves in a Riemannian manifold which are a critical point for ...

An epsilon-delta definition is a mathematical definition in which a statement on a real function of one variable f having, for example, the form "for all neighborhoods U of ...

The numbers 2^npq and 2^nr are an amicable pair if the three integers p = 2^m(2^(n-m)+1)-1 (1) q = 2^n(2^(n-m)+1)-1 (2) r = 2^(n+m)(2^(n-m)+1)^2-1 (3) are all prime numbers ...

A module M over a unit ring R is called faithful if for all distinct elements a, b of R, there exists x in M such that ax!=bx. In other words, the multiplications by a and by ...

Let F and G be fibered categories over a topological space X. A morphism phi:F->G of fibered categories consists of: 1. a functor phi(U):F->G(U) for each open subset U ...

Let X(x)=X(x_1,x_2,...,x_n) be a random vector in R^n and let f_X(x) be a probability distribution on X with continuous first and second order partial derivatives. The Fisher ...

For a general two-player zero-sum game, max_(i<=m)min_(j<=n)a_(ij)<=min_(j<=n)max_(i<=m)a_(ij). If the two are equal, then write ...