Fictitious Problems in Mathematics

Classification Problems in Mathematics

Fictitious Domain Formulation of Unilateral Problems

The fictitious domain method for the solution of variational inequalities with the Signorini boundary conditions is analyzed.

Ten Problems in Experimental Mathematics

This article was stimulated by the recent SIAM “100 Digit Challenge” of Nick Trefethen, beautifully described in [12]. Indeed, these ten numeric challenge problems are also listed in [14], where they are followed by the ten symbolic/numeric challenge problems that are discussed in this article. Our intent was to present ten problems that are characteristic of the sorts of problems that commonly...

Open Problems in Reverse Mathematics

The basic reference for reverse mathematics is my recently published book Subsystems of Second Order Arithmetic [32]. The web site for the book is www.math.psu.edu/simpson/sosoa/. This article is a write-up of some representative open problems in reverse mathematics. It was originally a handout for my 45-minute invited talk at the AMS-INS-SIAM conference Computability Theory and Applications, J...

Fictitious Students Creation Incentives in School Choice Problems

We identify a new channel through which schools can potentially manipulate the wellknown student and school optimal stable mechanisms. We introduce two different fictitious students creation manipulation notions where one of them is stronger. While the student and school optimal stable mechanisms turn out to be weakly fictitious student-proof under acyclic (Ergin (2002)) and essentially homogen...