Tarski monoids: Matui's spatial realization theorem

We introduce a class of inverse monoids, called Tarski monoids, that can be regarded as non-commutative generalizations of the unique countable, atomless Boolean algebra. These inverse monoids are related to a class of etale topological groupoids under a non-commutative generalization of classical Stone duality and, significantly, they arise naturally in the theory of dynamical systems as developed by Matui. We are thereby able to reinterpret a theorem of Matui on a class of \'etale groupoids as an equivalent theorem about a class of Tarski monoids: two simple Tarski monoids are isomorphic if and only if their groups of units are isomorphic. The inverse monoids in question may also be viewed as countably infinite generalizations of finite symmetric inverse monoids. Their groups of units therefore generalize the finite symmetric groups and include amongst their number the classical Thompson groups.Comment: arXiv admin note: text overlap with arXiv:1407.147

Educational campaign to support pregnant women and new mothers in enjoying and benefiting from an active lifestyle. Insight report.

Recent research has shown that pregnant women who were physically active at the time of their booking appointment with a midwife (8-12 weeks) were most likely to initiate further discussion about maintaining their physical activity, however, it has also been found that there is a lack of consistent and clear information pertaining to physical activity messages with many health professionals either providing no such information or giving inappropriate guidance to women of childbearing age. A lack of training, knowledge, and resources regarding physical activity have resulted in healthcare professionals relying on common sense and their own experience to advise and guide pregnant women and new mothers. In turn, this often results in pregnant women and new mothers turning to informal sources, such as the internet, for guidance. In response, this project aims to develop a toolkit to support the delivery of consistent and clear messages regarding physical activity by healthcare professionals (in line with current guidance), as well as helping to stimulate engagement with physical activity in our target audiences. Through increasing the confidence, skills, and knowledge of healthcare professionals, it is expected that pregnant women and new mothers will be empowered to make informed physical activity choices throughout pregnancy and beyond. This report brings together the insights from the scoping activities carried out to facilitate the development of an educational campaign to support pregnant women and new mothers in enjoying and benefiting from an active lifestyle. The report provides an overview of the key themes that became apparent and conclude with points for discussion and next steps in the project delivery

ESR studies of the slow tumbling of vanadyl spin probes in nematic liquid crystals

ESR line shapes that are appropriate for slowly tumbling vanadyl spin probes in viscous nematic liquid crystals were calculated by the stochastic Liouville method. Because of the symmetry possessed by vanadyl, the analysis and interpretation of these line shapes was simplified considerably. Spectral line shapes agreed well with experimental spectra of VOAcAc in the nematic liquid crystal Phase V and BEPC. Deviations from Brownian rotational diffusion were noted. A slowly fluctuating torque analysis yielded good agreement with the experimental spectra

Efficient operation of a high-power X-band gyroklystron

Experimental studies of amplification in a two-cavity X-band gyroklystron are reported. The system utilizes a thermionic magnetron injection gun at voltages up to 440 kV and currents up to 190 A in 1-μs pulses. Optimum performance is achieved by tapering the magnetic-field profile. Peak powers of 20 MW in the TE01 mode at 9.87 GHz are measured with calibrated crystals and with methanol calorimetry. Resultant efficiencies are in excess of 31% and large-signal gains surpass 26 dB. The experimental results are in good agreement with simulated results from a partially self-consistent, nonlinear, steady-state code

High power operation of an X-band gyrotwistron

We report the first experimental verification of a gyrotwistron amplifier. The device utilized a single 9.858 GHz, TE011 cavity, a heavily attenuated drift tube, and a long tapered output waveguide section. With a 440 kV, 200-245 A, 1 μs electron beam and a sharply tapered axial magnetic field, peak powers above 21 MW were achieved with a gain near 24 dB. Performance was limited by competition from a fundamental TE11 mode. A multimode code was developed to analyze this system, and simulations were in good agreement with the experiment

Composite fermions from the algebraic point of view

Composite fermion wavefuctions have been used to describe electrons in a strong magnetic field. We show that the polynomial part of these wavefunctions can be obtained by applying a normal ordered product of suitably defined annihilation and creation operators to an even power of the Vandermonde determinant, which can been considered as a kind of a non-trivial Fermi sea. In the case of the harmonic interaction we solve the system exactly in the lowest Landau level. The solution makes explicit the boson-fermion correspondence proposed recently.Comment: 11 pages 1 figur

High-power operation of a K-band second harmonic gyroklystron

Amplification studies of a two-cavity second-harmonic gyroklystron are reported. A magnetron injection gun produces a 440 kV, 200–245 A, 1 μs beam with an average perpendicular-to-parallel velocity ratio slightly less than 1. The TE011 input cavity is driven near 9.88 GHz and the TE021 output cavity resonates near 19.76 GHz. Peak powers exceeding 21 MW are achieved with an efficiency near 21% and a large signal gain above 25 dB. This performance represents the current state of the art for gyroklystrons in terms of the peak power normalized to the output wavelength squared