Affinely-Adjustable Robust Counterparts provide tractable alternatives to (two-stage) robust programs with arbitrary recourse. We apply them to robust network design with polyhedral demand uncertainty, introducing the affine routing principle. We compare the affine routing to the well-studied static and dynamic routing schemes for robust network design. All three schemes are embedded into the g...

the study of stability problems of functional equations was motivated by a question of s.m. ulam asked in 1940. the first result giving answer to this question is due to d.h. hyers. subsequently, his result was extended and generalized in several ways.we prove some hyperstability results for the equation g(ax+by)+g(cx+dy)=ag(x)+bg(y)on restricted domain. namely, we show, under some weak natural...

Affine term structure models have gained significant attention in the finance literature, mainly due to their analytical tractability and statistical flexibility. The aim of this article is to present both theoretical foundations as well as empirical aspects of the affine model class. Starting from the original one-factor shortrate models of Vasiček and Cox et al, we provide an overview of the ...

We give a self–contained introduction into the metric–affine gauge theory of gravity. Starting from the equivalence of reference frames, the prototype of a gauge theory is presented and illustrated by the example of Yang–Mills theory. Along the same lines we perform a gauging of the affine group and establish the geometry of metric–affine gravity. The results are put into the dynamical framewor...

In this paper we give mathematical proofs of two new results relevant to evaluating algebraic functions over a box-shaped region: (i) using interval arithmetic in centered form is always more accurate than standard affine arithmetic, and (ii) modified affine arithmetic is always more accurate than interval arithmetic in centered form. Test results show that modified affine arithmetic is not onl...

These are (mostly) expository notes for lectures on affine Stanley symmetric functions given at the Fields Institute in 2010. We focus on the algebraic and combinatorial parts of the theory. The notes contain a number of exercises and open problems. Stanley symmetric functions are a family {Fw | w ∈ Sn} of symmetric functions indexed by permutations. They were invented by Stanley [Sta] to enume...