S OF MAIN LECTURES Richard. J. GARDNER (Western Washington Univ.,U.S.A ) The dual Brunn-Minkowski theory and some of its inequalities As the title suggests, the focus of the talk is the dual Brunn-Minkowski theory, initiated by Erwin Lutwak in 1975, and developed since by him and others. First, an elementary introduction is provided to the basics, dual mixed volumes of star bodies, the dual Ale...

This tutorial presents a theory of valid inequalities for mixed integer linear sets. It introduces the necessary tools from polyhedral theory and gives a geometric understanding of several classical families of valid inequalities such as lift-and-project cuts, Gomory mixed integer cuts, mixed integer rounding cuts, split cuts and intersection cuts, and it reveals the relationships between these...

Four decades ago, Gomory introduced the corner polyhedron as a relaxation of a mixed integer set in tableau form and Balas introduced intersection cuts for the corner polyhedron. A recent paper of Andersen, Louveaux, Weismantel and Wolsey has generated a renewed interest in the corner polyhedron and intersection cuts. We survey these two approaches and the recent developments in multi-row cuts....

This tutorial presents a theory of valid inequalities for mixed integer linear sets. It introduces the necessary tools from polyhedral theory and gives a geometric understanding of several classical families of valid inequalities such as lift-and-project cuts, Gomory mixed integer cuts, mixed integer rounding cuts, split cuts and intersection cuts, and it reveals the relationships between these...

Abstract. In this paper we study effective recursion formulae for computing intersection numbers of mixed ψ and κ classes on moduli spaces of curves. By using the celebrated WittenKontsevich theorem, we generalize Mulase-Safnuk form of Mirzakhani’s recursion and prove a recursion formula of higher Weil-Petersson volumes. We also present recursion formulae to compute intersection pairings in the...

‎let $r$ be a commutative ring with non-zero identity. ‎we describe all $c_3$‎- ‎and $c_4$-free intersection graph of non-trivial ideals of $r$ as well as $c_n$-free intersection graph when $r$ is a reduced ring. ‎also, ‎we shall describe all complete, ‎regular and $n$-claw-free intersection graphs. ‎finally, ‎we shall prove that almost all artin rings $r$ have hamiltonian intersection graphs. ...

A proper non-empty subset C of the points of a linear space S = (P; L) is called line-closed if any two intersecting lines of S , each meeting C at least twice, have their intersection in C. We show that when every line has k points and every point lies on r lines the maximum size for such sets is r + k ? 2. In addition it is shown that this cannot happen for projective spaces PG(n; q) unless q...

The station location problem consists of placing new stations along the railway tracks of an existing network in order to increase the number of users. In this paper we consider the problem for a railway network consisting of two intersecting lines forming an angle α. An approach for solving the problem in polynomial time for sufficiently large angles α is presented.

Fuzzy logic has been widely used to develop an adaptive traffic signal controller because it allows qualitative modelling of complex systems. However, existing research has developed Fuzzy Logic Traffic Signal Controller (FLTSC) based on non-mixed traffic conditions. These FLTSC are not appropriate to the mixed traffic conditions of developing countries where the traffic streams consist of diff...

We describe the Nash equilibria set as an intersection of best response graphs. The problem of Nash equilibria set construction for two-person mixed extended 2× 3 games is studied. Mathematics Subject Classification 2000: 91A05, 91A06, 91A10, 91A43, 91A44.