An introduction to C-infinity schemes and C-infinity algebraic geometry

A Remark on C Infinity-harmonic Functions

In this paper, we prove that any nonconstant, C2 solution of the infinity Laplacian equation uxiuxj uxixj = 0 can not have interior critical points. This result was first proved by Aronsson [2] in two dimensions. When the solution is C4, Evans [6] established a Harnack inequality for |Du|, which implies that non-constant C4 solutions have no interior critical points for any dimension. Our metho...

An Introduction of Infinity Harmonic Functions

This note serves as a basic introduction on the analysis of infinity harmonic functions, a subject that has received considerable interests very recently. The author discusses its connection with absolute minimal Lipschitz extension, present several equivalent characterizations of infinity harmonic functions. He presents the celebrated theorem by R. Jensen [17] on the uniqueness of infinity har...

An approach to rank efficient DMUs in DEA based on combining Manhattan and infinity norms

In many applications, discrimination among decision making units (DMUs) is a problematic technical task procedure to decision makers in data envelopment analysis (DEA). The DEA models unable to discriminate between extremely efficient DMUs. Hence, there is a growing interest in improving discrimination power in DEA yet. The aim of this paper is ranking extreme efficient DMUs in DEA based on exp...

To Infinity and Beyond

We prove that if a group generated by a bireversible Mealy automaton contains an element of infinite order, its growth blows up and is necessarily exponential. As a direct consequence, no infinite virtually nilpotent group can be generated by a bireversible Mealy automaton. The study on how (semi)groups grow has been highlighted since Milnor’s question on the existence of groups of intermediate...

Introduction to Algebraic Geometry