On finite complete rewriting systems and large subsemigroups

Let $S$ be a semigroup and $T$ be a subsemigroup of finite index in $S$ (that is, the set $S\setminus T$ is finite). The subsemigroup $T$ is also called a large subsemigroup of $S$. It is well known that if $T$ has a finite complete rewriting system then so does $S$. In this paper, we will prove the converse, that is, if $S$ has a finite complete rewriting system then so does $T$. Our proof is purely combinatorial and also constructive.Comment: We have made major changes to the paper and simplified most of the proof

Developing an Intelligent Table Tennis Umpiring System: Identifying the ball from the scene

This paper reports further development of an intelligent table tennis umpiring system, of which the idea and plan was previously published at this conference in 2007. Briefly, table tennis is a fast sport. A service usually takes a few seconds to complete but an umpire needs to make many observations and makes a judgment before or soon after the service is complete. This is a complex task and the author believes the employment of videography, image processing and artificial intelligence (AI) technologies could help evaluating the service. The aim of this research is to develop an intelligent system which is able to identify and track the location of the ball from live video images and evaluate the service according to the service rules. In this paper, the techniques of identifying a table tennis ball from the scene is described and discussed. A number of image processing techniques have been employed to identify and measure the characteristics of the ball. Artificial neural networks have been applied as a classifier. It classifies whether the detected object is not-a- ball, a ball on the palm or a ball in mid air. The system has been tested on 21 still images which contain pictures of ball-like objects, balls on the palm and in mid air. The preliminary results are very promising. Out of 83 objects, 82 have been correctly classified. The system will be further tested on video images once the video is captured and processed. This paper also discusses the idea of implementing the final system as a multi-agent system, which the author believes it is appropriate for this application because multiple cameras will have to be employed to obtain accurate results

Self-Organization of Balanced Nodes in Random Networks with Transportation Bandwidths

We apply statistical physics to study the task of resource allocation in random networks with limited bandwidths along the transportation links. The mean-field approach is applicable when the connectivity is sufficiently high. It allows us to derive the resource shortage of a node as a well-defined function of its capacity. For networks with uniformly high connectivity, an efficient profile of the allocated resources is obtained, which exhibits features similar to the Maxwell construction. These results have good agreements with simulations, where nodes self-organize to balance their shortages, forming extensive clusters of nodes interconnected by unsaturated links. The deviations from the mean-field analyses show that nodes are likely to be rich in the locality of gifted neighbors. In scale-free networks, hubs make sacrifice for enhanced balancing of nodes with low connectivity.Comment: 7 pages, 8 figure

Non-Langevin behaviour of the uncompensated magnetisation in nanoparticles of artificial ferritin

The magnetic behaviour of nanoparticles of antiferromagnetic ferritin has been investigated by 57Fe Mossbauer absorption spectroscopy and magnetisation measurements, in the temperature range 2.5K-250K and with magnetic fields up to 7T. Samples containing nanoparticles with an average number of Fe atoms ranging from 400 to 2500 were studied. The value of the anisotropy energy per unit volume was determined and found to be in the range 3-6 10**5 ergs/cm3, which is a value typical for ferric oxides. By comparing the results of the two experimental methods at large field, we show that, contratry to what is currently assumed, the uncompensated magnetisation of the feritin cores in the superparamagnetic regime does not follow a Langevin law. For magnetic fields below the spin-flop field, we propose an approximate law for the field and temperature variation of the uncompensated magnetisation which has so far never been applied in antiferromagnetic systems. This approach should more generally hold for randomly oriented antiferro- magnetic nanoparticles systems with weak uncompensated moments.Comment: 11 pages, 11 figure

Reestimation of the production spectra of cosmic ray secondary positrons and electrons in the ISM

A detailed calculation of the production spectra of charged hadrons produced by interactions of cosmic rays in the interstellar medium is presented along with a thorough treatment of pion and muon decays. Newly parameterized inclusive cross sections of hadrons were used and exact kinematic limitations were taken into account. Single parametrized expressions for the production spectra of both secondary positrons and electrons in the energy range .1 to 100 GeV are presented. The results are compared with other authors' predictions. Equilibrium spectra using various models are also presented