Isometric Representations of Totally Ordered Semigroups

Let S be a subsemigroup of an abelian torsion-free group G. If S is a positive cone of G, then all C*-algebras generated by faithful isometrical non-unitary representations of S are canonically isomorphic. Proved by Murphy, this statement generalized the well-known theorems of Coburn and Douglas. In this note we prove the reverse. If all C*-algebras generated by faithful isometrical non-unitary representations of S are canonically isomorphic, then S is a positive cone of G. Also we consider G = Z\times Z and prove that if S induces total order on G, then there exist at least two unitarily not equivalent irreducible isometrical representation of S. And if the order is lexicographical-product order, then all such representations are unitarily equivalent.Comment: February 21, 2012. Kazan, Russi

Putative spin liquid in the triangle-based iridate Ba3_3IrTi2_2O9_9

We report on thermodynamic, magnetization, and muon spin relaxation measurements of the strong spin-orbit coupled iridate Ba$_3$IrTi$_2$O$_9$, which constitutes a new frustration motif made up a mixture of edge- and corner-sharing triangles. In spite of strong antiferromagnetic exchange interaction of the order of 100~K, we find no hint for long-range magnetic order down to 23 mK. The magnetic specific heat data unveil the $T$-linear and -squared dependences at low temperatures below 1~K. At the respective temperatures, the zero-field muon spin relaxation features a persistent spin dynamics, indicative of unconventional low-energy excitations. A comparison to the $4d$ isostructural compound Ba$_3$RuTi$_2$O$_9$ suggests that a concerted interplay of compass-like magnetic interactions and frustrated geometry promotes a dynamically fluctuating state in a triangle-based iridate.Comment: Physical Review B accepte

Identifying cross country skiing techniques using power meters in ski poles

Power meters are becoming a widely used tool for measuring training and racing effort in cycling, and are now spreading also to other sports. This means that increasing volumes of data can be collected from athletes, with the aim of helping coaches and athletes analyse and understanding training load, racing efforts, technique etc. In this project, we have collaborated with Skisens AB, a company producing handles for cross country ski poles equipped with power meters. We have conducted a pilot study in the use of machine learning techniques on data from Skisens poles to identify which "gear" a skier is using (double poling or gears 2-4 in skating), based only on the sensor data from the ski poles. The dataset for this pilot study contained labelled time-series data from three individual skiers using four different gears recorded in varied locations and varied terrain. We systematically evaluated a number of machine learning techniques based on neural networks with best results obtained by a LSTM network (accuracy of 95% correctly classified strokes), when a subset of data from all three skiers was used for training. As expected, accuracy dropped to 78% when the model was trained on data from only two skiers and tested on the third. To achieve better generalisation to individuals not appearing in the training set more data is required, which is ongoing work.Comment: Presented at the Norwegian Artificial Intelligence Symposium 201

Charge states and magnetic ordering in LaMnO3/SrTiO3 superlattices

We investigated the magnetic and optical properties of [(LaMnO3)n/(SrTiO3)8]20 (n = 1, 2, and 8) superlattices grown by pulsed laser deposition. We found a weak ferromagnetic and semiconducting state developed in all superlattices. An analysis of the optical conductivity showed that the LaMnO3 layers in the superlattices were slightly doped. The amount of doping was almost identical regardless of the LaMnO3 layer thickness up to eight unit cells, suggesting that the effect is not limited to the interface. On the other hand, the magnetic ordering became less stable as the LaMnO3 layer thickness decreased, probably due to a dimensional effect.Comment: 17 pages including 4 figures, accepted for publication in Phys. Rev.

Accelerated Curing and Enhanced Material Properties of Conductive Polymer Nanocomposites by Joule Heating

Joule heating is useful for fast and reliable manufacturing of conductive composite materials. In this study, we investigated the influence of Joule heating on curing conditions and material properties of polymer-based conductive composite materials consisting of carbon nanotubes (CNTs) and polydimethylsiloxane (PDMS). We applied different voltages to the CNT nanocomposites to investigate their electrical stabilization, curing temperature, and curing time. The result showed that highly conductive CNT/PDMS composites were successfully cured by Joule heating with uniform and fast heat distribution. For a 7.0 wt % CNT/PDMS composite, a high curing temperature of around 100 °C was achieved at 20 V with rapid temperature increase. The conductive nanocomposite cured by Joule heating also revealed an enhancement in mechanical properties without changing the electrical conductivities. Therefore, CNT/PDMS composites cured by Joule heating are useful for expediting the manufacturing process for particulate conductive composites in the field of flexible and large-area sensors and electronics, where fast and uniform curing is critical to their performance

A micro optical probe for edge contour evaluation of diamond cutting tools

This paper presents a micro optical probe, which is employed to evaluate edge contours of single point diamond tools with a size in a range of several millimetres. The micro optical probe consists of a laser source with a wavelength of 405 nm, an objective lens with a numerical aperture of 0.25, a photodiode for measurement, and a compensating optical system including another photodiode for compensation of laser intensity. A collimated laser beam, which is divided by a beam splitter in the compensating optical system, is focused by the objective lens so that the focused spot can be used as the micro optical probe. The micro optical probe traces over an edge contour of an objective tool while the signals of both the two photodiodes are monitored. The output of the photodiode for measurement is compensated by using that of the photodiode for laser intensity compensation to eliminate the influence of the laser instability. The signal of the photodiode for measurement is used to define the deviation of edge contour within the diameter of the micro optical probe. To verify the feasibility of the developed optical probe, the optical system was mounted on a diamond turning machine, and some experiments were carried out. Two types of edge contours of the diamond tools having a straight cutting edge and a round cutting edge were measured on the machine