Codes Based on Complete Graphs

We consider the problem of embedding the even graphical code based on the complete graph onn vertices into a shortening of a Hamming code of length 2^m-1, wherem = h(n) should be as small as possible. As it turns out, this problem is equivalent to the existence problem for optimal codes with minimum distance 5, and optimal embeddings can always be realized as graphical codes based onK _n. As a consequence, we are able to determineh(n) exactly for alln of the form 2 ^k + 1 and to narrow down the possibilities in general to two or three conceivable values.Dedicated to Hanfried Lenz on the occasion of his 80th birthdayThe research for this note was done while the first author was visiting the University of Waterloo and the University of Rome, respectively. He thanks his colleagues there for their hospitality and also acknowledges the financial support of the Consiglio Nazionale delle Ricerche (Italy). The third author acknowledges the support of the National Science and Engineering Research Council of Canada given under grant #0GP0009258.     

A tandem of discrete-time queues with arrivals and departures at each stage

A discrete-time system of a tandem of queues with exogenous arrivals and departures at each stage is considered. A customer leaving queuek–1 departs the system with probability 1– ^[k] and continues to queuek with probability ^[k] . Exogenous arrivals to each stage are i.i.d. at each time slot. An approximate analysis of the occupancy and busy-period distributions of each stage based on a General Busy-period with batches and Memoryless (geometric) Idle period renewal Process (GBMIP) provides improved performance over two-state Markov approximations and gives exact results when there are no interstage departures.This research was supported in part by NSF grant NCR-8708282.     

Boundary value estimates for harmonic forms

We prove a bound for the -norm of harmonic forms in terms of certain -norms of their normal and tangential components. In turn, this is used to show the -norm equivalence of the normal and tangential components of harmonic forms on manifolds.

     

Noise Characterization for Laser Interferometer Gravitational Wave Detectors

This work incorporates a review of the status, in Australia, of data analysis for gravitational wave detection using laser interferometers, within an overview of the present state of such research in the world generally. In this context, data analysis refers not so much to signal simulation as to what might be called the thorough process of noise characterization and the subsequent, quality-controlled signal extraction. To the extent that problems identified here arise for all currently planned instruments, there is necessarily a global component to the discussion presented. In Australia, there are unique circumstances, associated with attempting to carry out work in gravitational wave detection, which demand also a local aspect to the ensuing discussion.     

Oxygen transfer processes in (La,Sr)MnO3/Y2O3-stabilized ZrO2 cathodes: an impedance spectroscopy study

Impedance spectroscopy was used to study the oxygen reaction kinetics of La_0.8Sr_0.2MnO₃ (LSM)-based electrodes on Y₂O₃-stabilized ZrO₂ (YSZ) electrolytes. Three types of electrodes were studied: pure LSM, LSM–YSZ composites, and LSM/LSM–YSZ bilayers. The electrodes were formed by spin coating and sintering on single-crystal YSZ substrates. Measurements were taken at temperatures ranging from 550 to 850°C and oxygen partial pressures from 1×10⁻³ to 1 atm. An arc whose resistance R_el had a high activation energy, E_a=1.61±0.05 eV, and a weak oxygen partial pressure dependence, (P_O2)^−1/6, was observed for the LSM electrodes. A similar arc was observed for LSM–YSZ electrodes, where R_el(P_O2)^−0.29 and the activation energy was 1.49±0.02 eV. The combination of a high activation energy and a weak P_O2 dependence was attributed to oxygen dissociation and adsorption rate-limiting steps for both types of electrodes. LSM–YSZ composite cathodes showed substantially lower overall interfacial resistance values than LSM, but exhibited an additional arc attributed to the resistance of YSZ grain boundaries within the LSM–YSZ. At 850°C and low P_O2, an additional arc was observed with size varying as (P_O2)^−0.80 for LSM and (P_O2)^−0.57 for LSM–YSZ, suggesting that diffusion had become an additional rate limiting step. Bilayer LSM/LSM–YSZ electrodes yielded results intermediate between LSM and LSM–YSZ. The results showed that most of the improvement in electrode performance was achieved for a LSM–YSZ layer only ≈2 μm thick. However, a decrease in the grain-boundary resistance would produce much better performance in thicker LSM–YSZ electrodes.     

Radio-frequency μSR experiments at the ISIS pulsed muon facility

This paper explores the use of pulsed radio-frequency (RF) techniques to remove the frequency limitations imposed on conventional transverse muon spin rotation (μSR) experiments at a pulsed muon source by the finite muon pulse width. The implementation of the 90° pulse technique is demonstrated by observing the free precession signal of diamagnetic muons implanted in polythene, the change in signal amplitude as a function of RF pulse length is plotted and the precise condition for a 90° pulse determined. The technique is evaluated by comparing measurements made using conventional spin rotation experiments to those employing pulsed RF methods. The potential for applying standard NMR multiple-pulse methods to the μSR experiment is considered and the use of two-pulse RF sequences (90° _x ?τ?90° _x and 90° _x ?τ?180° _x ) to form a muon spin echo demonstrated.