Normal form for a Pfaffian

Pfaffian Presentations of Elliptic Normal Curves

We investigate certain alternating matrices of linear forms whose Pfaffians generate the homogeneous ideal of an elliptic normal curve, or one of its higher secant varieties.

A Normal Form for Braids

We present a seemingly new normal form for braids, where every braid is expressed using a word in a regular language on some simple alphabet of elementary braids. This normal form stems from analysing the geometric action of braid groups on curves in a punctured disk.

A Normal Form for XML

A Normal Form for Elliptic Curves

The normal form x2+y2 = a2+a2x2y2 for elliptic curves simplifies formulas in the theory of elliptic curves and functions. Its principal advantage is that it allows the addition law, the group law on the elliptic curve, to be

A normal form for excitable media.

We present a normal form for traveling waves in one-dimensional excitable media in the form of a differential delay equation. The normal form is built around the well-known saddle-node bifurcation generically present in excitable media. Finite wavelength effects are captured by a delay. The normal form describes the behavior of single pulses in a periodic domain and also the richer behavior of ...