A Mahonian d-function is a Mahonian statistic that can be expressed as a linear combination of vincular pattern statistics of length at most d. Babson and Steingŕımsson classified all Mahonian 3-functions up to trivial bijections and identified many of them with well-known Mahonian statistics in the literature. We prove a host of Mahonian 3-function equidistributions over pattern avoiding sets ...

M obile Ad Hoc networks are collections of mobile nodes, dynamically forming a temporary network without pre-existing network infrastructure or centralized administration. Transmission control protocol (TCP) provides connection oriented, reliable and end to end mechanism. Comparing to wire networks, there are many different characteristics in wireless environments. In this paper an improved mec...

. On considère une classe de systèmes non-linéaires pour lesquels la technique de synthèse par backstepping n’est pas applicable. On présente un critère pour la synthèse d’une commande hybride faisant l’union d’une commande par backstepping et d’une commande locale. Cette commande hybride rend le système bouclé globalement asymptotiquement stable. Le critère de sélection repose sur le choix de ...

A random geometric irrigation graph Γn(rn, ξ) has n vertices identified by n independent uniformly distributed points X1, . . . , Xn in the unit square [0, 1]. Each point Xi selects ξi neighbors at random, without replacement, among those points Xj (j 6= i) for which ‖Xi − Xj‖ < rn, and the selected vertices are connected to Xi by an edge. The number ξi of the neighbors is an integer-valued ran...

We design new approximation algorithms for the Multiway Cut problem, improving the previously known factor of 1.32388 [Buchbinder et al., 2013]. We proceed in three steps. First, we analyze the rounding scheme of Buchbinder et al. [2013] and design a modification that improves the approximation to 3+ √ 5 4 ≈ 1.309017. We also present a tight example showing that this is the best approximation o...

I sometimes have difficulty walking and use a cane. Recently on a journey to Northern Arizona, I knew I was going to pass near an iconic image of the Colorado River and the desire to witness that sight kept teasing me. I had read about the access to Horseshoe Bend and knew that it included a walk through sand that was about a mile from the parking lot. Although the hike was described in the gui...