Abstract. In the last years a new theory of Hopf algebras has begun to be developed: that of Hopf algebras in braided categories, or, briefly, braided Hopf algebras. This is a survey of general aspects of the theory with emphasis in H HYD, the Yetter–Drinfeld category over H, where H is the group algebra of a non abelian finite group Γ. We discuss a special class of braided graded Hopf algebras from different points of view following Lusztig, Nichols and Schauenburg. We present some finite dimensional examples arising in an unpublished work by Milinski and Schneider. Sinopsis. En los últimos años comenzó a ser desarrollada una nueva teoría de álgebras de Hopf en categorías trenzadas, o brevemente, álgebras de Hopf trenzadas. Presentamos aquí aspectos generales de la teoría con énfasis en H HYD, la categoría de Yetter–Drinfeld sobre H, donde H es el álgebra de grupo de un grupo finito no abeliano Γ. Discutimos una clase especial de álgebras de Hopf trenzadas graduadas desde diferentes puntos de vista, siguiendo a Lusztig, Nichols y Schauenburg. Presentamos algunos ejemplos de dimensión finita que aparecen en un trabajo inédito de Milinski y Schneider. 0. Introduction and notations 0.1. Introduction.

Abstract. It has been observed repeatedly that the standard safety-liveness classi cation for properties of reactive systems does not t for real-time properties. This is because the implicit \liveness " of time shifts the spectrum towards the safety side. While, for example, response | that \something good " will happen eventually | is a classical liveness property, bounded response | that \something good " will happen soon, within a certain amount of time | has many characteristics of safety. Weaccount for this phenomenon formally by de ning safety and liveness relative to a given condition, such as the progress of time.

Abstract. We describe a new condensation method for computing the submodule lattice of a module for a finite dimensional algebra over a finite field, which exploits the idea of condensation and extends it to the case of primitive idempotents. The method has been implemented in the new C version of the Meat-Axe developed at Aachen, and we give several examples which have been analysed with our method.

Recently, important progress has been made in the study of finite-dimensional semisimple Hopf algebras over a field of characteristic zero (see [Mo] and references therein). Yet, very little is known over a field k of positive characteristic. In this paper we first prove in Theorem 2.1 that any finite-dimensional semisimple and

This is the second in a series of papers devoted to the thorough investigation of (total correctness) re nement based on an underlying partial relational model. This paper investigates operation re nement and data-re nement based on a weakest precondition interpretation for speci cations whose semantics is given by partial relations. We consider three re nement theories based on a weakest precondition interpretation for partial relation semantics: an operation re nement theory, and theories characterising data-re nement with forward and backward simulations. We show that each of these is equivalent to a (corresponding) model-theoretic re nement theory that is based on the standard approach involving relational completion operators. In addition, we demonstrate that each of the three is also equivalent to a (corresponding) proof-theoretic notion of re nement.

Mutual exclusion is a topic that Leslie Lamport has returned to many times throughout his career. This article, which is being written in celebration of Lamport's sixtieth birthday, is an attempt to survey some of his many contributions to research on this topic.

We present the first peer-to-peer data streaming application that guarantees predictable throughput and low latency in the BAR (Byzantine/Altruistic/Rational) model, in which nonaltruistic nodes can behave in ways that are self-serving (rational) or arbitrarily malicious (Byzantine). At the core of our solution is a BARtolerant version of gossip, a well-known technique for scalable and reliable data dissemination. BAR Gossip relies on verifiable pseudo-random partner selection to eliminate non-determinism that can be used to game the system while maintaining the robustness and rapid convergence of traditional gossip. A novel fair enough exchange primitive entices cooperation among selfish nodes on short timescales, avoiding the need for long-term node reputations. Our initial experience provides evidence for BAR Gossip’s robustness. Our BAR-tolerant streaming application provides over 99 % convergence for broadcast updates when all clients are selfish but not colluding, and over 95 % convergence when up to 40 % of clients collude while the rest follow the protocol. BAR Gossip also performs well when the client population consists of both selfish and Byzantine nodes, achieving over 93 % convergence even when 20 % of the nodes are Byzantine. 1

Lattarulo and O. Scheuermann. It contains hypotheses, experimental results and comments; however, some questions which came up during the discussions at the SSG (Shroud Science Group) level, led the author to write the present paper. After a presentation of the main points regarding CD (Corona Discharge), and the definition of the hypotheses regarding the assumed model, some new evidence is presented and discussed here, such as the exsiccation of limited parts of linen fibers. The paper then explains different points raised by the SSG, such as the radiation direction, the 3-D effects of radiation and its mathematical representation, the image resolution, the double draping configurations of the TS, and the color on the linen fibers. The experimental results obtained to support the hypothesized mechanism show no appreciable chemical-physical differences from the image features of the TS. These results confirm that the proposed CD mechanism could have been involve d in the TS body image formation. 1.

One of the outstanding problems in the numerical simulation of mechanical systems is the development of efficient methods for dealing with highly oscillatory systems. These types of systems arise for example in vehicle simulation in modeling the suspension system or tires, in models for contact and impact, in flexible body simulation from vibrations in the structural model, and in molecular dynamics. Simulations involving high frequency vibration can take a huge number of time steps, often as a consequence of oscillations which are not physically important. The components causing the oscillations cannot usually be eliminated from the model because in some situations they are critical to the simulation. The equations of motion of a multibody mechanical system are described by a system of differential-algebraic equations (DAEs). In this paper, we will explore two types of methods. The first class of methods damps out the oscillation via highly stable implicit methods. Even in this relati...

We propose a new elementary definition of the Higman-Sims graph in which the 100 vertices are parametrised with Z 4 5 and adjacencies are described by linear and quadratic equations. This definition extends Robertson's pentagon-pentagram definition of the Ho#man-Singleton graph and is obtained by studying maximum cocliques of the Ho#man-Singleton graph in Robertson's parametrisation. The new description is used to count the 704 Ho#man-Singleton subgraphs in the Higman-Sims graph, and to describe the two orbits of the simple group HS on them, including a description of the doubly transitive action of HS within the Higman-Sims graph. Numerous geometric connections are pointed out. As a by-product we also have a new construction of the Steiner system S(3, 6, 22).