Algebras associated to acyclic directed graphs

We construct and study a class of algebras associated to generalized layered graphs, i.e. directed graphs with a ranking function on their vertices. Each finite directed acyclic graph admits countably many structures of a generalized layered graph. We construct linear bases in such algebras and compute their Hilbert series. Our interest to generalized layered graphs and algebras associated to those graphs is motivated by their relations to factorizations of polynomials over noncommutative rings.Comment: 20 pages, Latex; an expanded and corrected version; to appear in "Advances of Applied Mathematics

A mathematical model of fluid flow in a scraped-surface heat exchanger

A simple mathematical model of fluid flow in a common type of scraped-surface heat exchanger in which the gaps between the blades and the device walls are narrow, so that a lubrication-theory description of the flow is valid, is presented. Specifically steady isothermal flow of a Newtonian fluid around a periodic array of pivoted scraper blades in a channel with one stationary and one moving wall, when there is an applied pressure gradient in a direction perpendicular to the wall motion, is analysed. The flow is three-dimensional, but decomposes naturally into a two-dimensional "transverse" flow driven by the boundary motion and a "longitudinal" pressure-driven flow. First details of the structure of the transverse flow are derived, and, in particular, the equilibrium positions of the blades are calculated. It is shown that the desired contact between blades and the moving wall will be attained, provided that the blades are pivoted sufficiently close to their ends. When the desired contact is achieved, the model predicts that the forces and torques on the blades are singular, and so the model is generalised to include three additional physical effects, namely non-Newtonian power-law behaviour, slip at rigid boundaries, and cavitation in regions of very low pressure, each of which is shown to resolve these singularities. Lastly the nature of the longitudinal flow is discussed

Hilbert series of algebras associated to directed graphs

Few changes. We compute the Hilbert series of some algebras associated to directed graphs and related to factorizations of noncommutative polynomials.Comment: AMSLaTeX, 9 page

On a class of Koszul algebras associated to directed graphs

In math.QA/0506507 I. Gelfand and the authors introduced and studied a new class of algebras associated to directed graphs. In this paper we show that these algebras are Koszul for a large class of layered (i.e. ranked) graphs.Comment: 15 pages; AMSTE

The construction and administration of a questionnaire on children's reaction to educational television

Thesis (Ed.M.)--Boston University N.B.: Missing pages 93-111. Possibly misnumbered

Hemosuccus Pancreaticus as a Rare Complication of Bariatric Surgery.

Hemosuccus pancreaticus is a rare cause of gastrointestinal bleeding from the duct of Wirsung into the duodenum via the ampulla of Vater. Hemosuccus pancreaticus is difficult to diagnose because the bleeding is usually intermittent, and the clinical findings are often discordant. Patients present with pain, either left upper quadrant or epigastric, and bleeding, which may present as melena, bright red blood per rectum, or even shock, if the hemorrhage is severe. Hemosuccus pancreaticus is usually caused by rupture of a pseudoaneurysm of a peri-pancreatic artery, often the splenic artery, in the setting of pancreatitis; other causes are very rare. In this report, for the first time to our knowledge, we present a case of hemosuccus pancreaticus that occurred as a complication of bariatric surgery