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A branch cut is a curve (with ends possibly open, closed, or half-open) in the complex plane across which an analytic multivalued function is discontinuous. For convenience, ...

A general reciprocity theorem for all orders which covered all other known reciprocity theorems when proved by E. Artin in 1927. If R is a number field and R^' a finite ...

The surface given by the parametric equations x = e^(bv)cosv+e^(av)cosucosv (1) y = e^(bv)sinv+e^(av)cosusinv (2) z = e^(av)sinu. (3) For a=b=1, the coefficients of the first ...

A diagonal of a square matrix which is traversed in the "southeast" direction. "The" diagonal (or "main diagonal," or "principal diagonal," or "leading diagonal") of an n×n ...

Interest is a fee (or payment) made for the borrowing (or lending) of money. The two most common types of interest are simple interest, for which interest is paid only on the ...

An element a of a ring which is nonzero, not a unit, and whose only divisors are the trivial ones (i.e., the units and the products ua, where u is a unit). Equivalently, an ...

A proper ideal of a ring that is not the intersection of two ideals which properly contain it. In a principal ideal domain, the ideal I=<a> is irreducible iff a=0 or a is an ...

A line bundle is a special case of a vector bundle in which the fiber is either R, in the case of a real line bundle, or C, in the case of a complex line bundle.

A principal vertex x_i of a simple polygon P is called a mouth if the diagonal [x_(i-1),x_(i+1)] is an extremal diagonal (i.e., the interior of [x_(i-1),x_(i+1)] lies in the ...

Except for convex polygons, every simple polygon has at least one mouth.