In connection with his interest in selfdistributive algebra, Richard Laver established two deep results with potential applications in low-dimensional topology, namely the existence of what is now known as the Laver tables and the well-foundedness of the standard ordering of positive braids. Here we present these results and discuss the way they could be used in topological applications. Richar...

In this paper, we propose a clustering based linear ordering algorithm which consists of global ordering and local ordering. In the global ordering, the algorithm forms clusters from n given vertices and orders the clusters. In tlhe local ordering, the elements in each cluster are linearly ordered. The linear order, thus produced, is used to obtain optimal k-way partitioning based on scaded cos...

The effect of a helicoidal magnetic field on the dispersion conduction electrons in one- and two-dimensional systems is investigated. In periodic field, there special symmetry with respect to reversal time, which leads peculiarities band structure. Using an example one-dimensional model system, topological properties structure effective corresponding 120 o -ordering are PdCrO 2 , ordering diele...

The ordering of liquid crystals (LCs) is known to be influenced by surfaces and contaminants. Here, we report that picogram per milliliter concentrations of endotoxin in water trigger ordering transitions in micrometer-size LC droplets. The ordering transitions, which occur at surface concentrations of endotoxin that are less than 10(-5) Langmuir, are not due to adsorbate-induced changes in the...

This paper studies the characteristics of synchronous ordering of messages. Synchronous ordering of messages deenes synchronous communication based on the causality relation rather than time. We present the necessary characteristics of any algorithm providing deadlock-free synchronous ordering of the messages. We also present the suucient conditions, based on the causality relations, for any al...