Before the Norm?

The Norm Game - How a Norm Fails

Application of the Norm Estimates for Univalence of Analytic Functions

By using norm estimates of the pre-Schwarzian derivatives for certain family of analytic functions, we shall give simple sufficient conditions for univalence of analytic functions.

8 The norm game - how a norm fails

We discuss the simulations of the norm game between players at nodes of a directed random network. The final boldness of the players can vary with the initial one as the Θ function. One of the conditions of this behaviour is that the player who does not punish automatically becomes a defector. The threshold value of the initial boldness can be interpreted as a norm strength. It increases with t...

On the Minimum Norm

This paper describes a new technique to nd the minimum norm solution of a linear program. The main idea is to reformulate this problem as an unconstrained minimization problem with a convex and smooth objective function. The minimization of this objective function can be carried out by a Newton-type method which is shown to be globally convergent. Furthermore, under certain assumptions, this Ne...

The Thurston Norm

Suppose a 2-handle is attached to a compact orientable 3-manifold M along an annulus A contained in a subsurface N of a M . If N is compressible in M, but N -A is not, then the Thurston norm is unaffected. This generalizes a series of results due to Przytycki, Jaco, and Johannson. Following Thurston [Th],define the complexity X(S) of an oriented surface S to be -x(C), where C is the union of al...