A generic condition implying o-minimality for restricted C^{\infty }-functions

On O-minimality of Extensions of R by Restricted Generic Smooth Functions

It is shown that the extension of R by a generic smooth function restricted to the unit cube is o-minimal. The generalization to countably many generic smooth functions is indicated. Possible applications are sketched.

Subjacency and the minimality condition

A Minimality Condition and Atmospheric Neutrino Oscillations1

A structure is proposed for the mass matrices of the quarks and leptons that arises in a natural way from the assumption that the breaking of SO(10) gauge symmetry is achieved by the smallest possible set of vacuum expectation values. This structure explains well many features of the observed spectrum of quarks and leptons. It reproduces the Georgi-Jarlskog mass relations and postdicts the char...

Lectures on O-minimality

1. Introduction During the academic year of 1996{97, the Fields Institute hosted a program in Algebraic Model Theory. As a part of that program, a course on topics from the subject of o-minimality was taught jointly by A. Macintyre, M. Spi-vakovsky and myself during the fall semester. The main theme of the course was the study of the expansion of the eld of real numbers by all restricted analyt...

A Second Order Minimality Condition for a Free-Boundary Problem

The goal of this paper is to derive in the two-dimensional case necessary and sufficient minimality conditions in terms of the second variation for the functional v 7→ ∫ Ω ( |∇v| + χ{v>0}Q ) dx, introduced in a classical paper of Alt and Caffarelli. For a special choice of Q this includes water waves. The second variation is obtained by computing the second derivative of the functional along su...