Koszul hypersurfaces over the exterior algebras

We prove that if $E$ is an exterior algebra over a field, $h$ is a quadratic form, then $E/(h)$ is Koszul if and only if $h$ is a product of two linear forms.Comment: 4 page

Imagining, making and marketing

Working for an organisation that needs to fund its breeding from plant royalties presents some stiff challenges. Margareth Hop describes the allure of breeding plants that might end up selling 100,000 units a yea

Regularity bounds for complexes and their homology

Let $R$ be a standard graded algebra over a field $k$. We prove an Auslander-Buchsbaum formula for the absolute Castelnuovo-Mumford regularity, extending important cases of previous works of Chardin and R\"omer. For a bounded complex of finitely generated graded $R$-modules $L$, we prove the equality $\text{reg}~ L=\max_{i\in \mathbb Z} \{\text{reg}~ H_i(L)-i\}$ given the condition $\text{depth}~ H_i(L)\ge \dim H_{i+1}(L)-1$ for all $i<\sup L$. As applications, we recover previous bounds on regularity of Tor due to Caviglia, Eisenbud-Huneke-Ulrich, among others. We also obtain strengthened results on regularity bounds for Ext and for the quotient by a linear form of a module.Comment: Final versio

Routing in Wireless Multimedia Home Networks

This paper describes an adapted version of the destination sequenced distance vector routing protocol (DSDV) which is suitable to calculate routes in a wireless real-time home network. The home network is based on a IEEE 802.11b ad hoc network and uses a scheduled token to enforce real-time behaviour to support multimedia streams. The multimedia network protocol works for both single-hop and multi-hop networks, however in the latter case special measures have to be taken to forward streams from node to node and to find routes. Existing routing protocols exhibit non-deterministic behaviour which may interfere with the correct streaming of multimedia. The proposed routing protocol does not rely on flooding, instead it piggy-backs the real-time token and behaves in a predictable manner. Simulation of the routing protocol shows that routes in the network are found in finite time

Communicating Personal Gadgets

This paper focuses on communication in personal area networks. A personal area networks (PAN) is characterized as an informal collection, or community, of connected small, lightweight, and resource-lean devices, or gadgets. Two basic concepts are visible in the development of PANs, the distributed and the centralized concept. The paper introduces a real-time communication protocol that is suitable for both concepts. The communication protocol can deal with several types of traffic: real-time or nonreal- time, bursty or isochronous, high or low bitrate. The protocol is undemanding in terms of resources, so even simple devices can participate in the network. The network is simulated and a prototype is realized