Multiplicity, Invariants and Tensor Product Decomposition of Tame Representations of U(\infty)

The structure of r-fold tensor products of irreducible tame representations of the inductive limit U(\infty) of unitary groups U(n) are are described, versions of contragredient representations and invariants are realized on Bargmann-Segal-Fock spaces.Comment: 48 pages, LaTeX file, to appear in J. Math. Phy

Robust active magnetic dearing control using stabilizing dynamical compensators

The robust control of active magnetic bearings, based on a linearised interval model, is considered. Through robust stability analysis, all the first-order robust stabilizing dynamical compensators for the interval system are obtained. Disturbance attenuation and minimum control effort are also addressed. The approach is applied to a high-speed flywheel supported by two active and two passive magnetic bearings. Simulation and experimental results both show that it is simple, effective, and robust

Robust magnetic bearing control using stabilizing dynamical compensators

Abstract—This paper considers the robust control of an active radial magnetic bearing system, having a homopolar, external rotor topology, which is used to support an annular fiber composite flywheel rim. A first-order dynamical compensator, which uses only position feedback information, is used for control, its design being based on a linearized one-dimensional second-order model which is treated as an interval system in order to cope with parameter uncertainties. Through robust stability analysis, a parameterization of all first-order robustly stabilizing dynamical compensators for the interval system is initially obtained. Then, by appropriate selection of the free parameters in the robust controller, the H2 norm of the disturbance-output transfer function is made arbitrarily small over the system parameter intervals, and the norm of the input–output transfer function is made arbitrarily close to a lower bound. Simulation and experimental results demonstrate both stability and performance robustness of the developed controller

Noncommutative symmetric functions and Laplace operators for classical Lie algebras

New systems of Laplace (Casimir) operators for the orthogonal and symplectic Lie algebras are constructed. The operators are expressed in terms of paths in graphs related to matrices formed by the generators of these Lie algebras with the use of some properties of the noncommutative symmetric functions associated with a matrix. The decomposition of the Sklyanin determinant into a product of quasi-determinants play the main role in the construction. Analogous decomposition for the quantum determinant provides an alternative proof of the known construction for the Lie algebra gl(N).Comment: 25 page

Performance of the Birmingham Solar-Oscillations Network (BiSON)

The Birmingham Solar-Oscillations Network (BiSON) has been operating with a full complement of six stations since 1992. Over 20 years later, we look back on the network history. The meta-data from the sites have been analysed to assess performance in terms of site insolation, with a brief look at the challenges that have been encountered over the years. We explain how the international community can gain easy access to the ever-growing dataset produced by the network, and finally look to the future of the network and the potential impact of nearly 25 years of technology miniaturisation.Comment: 31 pages, 19 figures. Accepted by Solar Physics: 2015 October 20. First online: 2015 December 7. Open Acces

Changes in the sensitivity of solar p-mode frequency shifts to activity over three solar cycles

Low-degree solar p-mode observations from the long-lived Birmingham Solar Oscillations Network (BiSON) stretch back further than any other single helioseismic data set. Results from BiSON have suggested that the response of the mode frequency to solar activity levels may be different in different cycles. In order to check whether such changes can also be seen at higher degrees, we compare the response of medium-degree solar p-modes to activity levels across three solar cycles using data from Big Bear Solar Observatory (BBSO), Global Oscillation Network Group (GONG), Michelson Doppler Imager (MDI) and Helioseismic and Magnetic Imager (HMI), by examining the shifts in the mode frequencies and their sensitivity to solar activity levels. We compare these shifts and sensitivities with those from radial modes from BiSON. We find that the medium-degree data show small but significant systematic differences between the cycles, with solar cycle 24 showing a frequency shift about 10 per cent larger than cycle 23 for the same change in activity as determined by the 10.7 cm radio flux. This may support the idea that there have been changes in the magnetic properties of the shallow subsurface layers of the Sun that have the strongest influence on the frequency shifts.Comment: 6 pages, 3 figures, accepted by MNRAS 3rd July 201

Parametrizing the time-variation of the "surface term" of stellar p-mode frequencies: application to helioseismic data

The solar-cyle variation of acoustic mode frequencies has a frequency dependence related to the inverse mode inertia. The discrepancy between model predictions and measured oscillation frequencies for solar and solar-type stellar acoustic modes includes a significant frequency-dependent term known as the surface term that is also related to the inverse mode inertia. We parametrize both the surface term and the frequency variations for low-degree solar data from Birmingham Solar-Oscillations Network (BiSON) and medium-degree data from the Global Oscillations Network Group (GONG) using the mode inertia together with cubic and inverse frequency terms. We find that for the central frequency of rotationally split multiplets the cubic term dominates both the average surface term and the temporal variation, but for the medium-degree case the inverse term improves the fit to the temporal variation. We also examine the variation of the even-order splitting coefficients for the medium-degree data and find that, as for the central frequency, the latitude-dependent frequency variation, which reflects the changing latitudinal distribution of magnetic activity over the solar cycle, can be described by the combination of a cubic and an inverse function of frequency scaled by inverse mode inertia. The results suggest that this simple parametrization could be used to assess the activity-related frequency variation in solar-like asteroseismic targets.Comment: 13 pages, 11 figures. Accepted by MNRAS 13 October 201

Faculty Productivity and Carnegie Institutional Characteristics within AEJMC Programs

This article reports the results of a content analysis of faculty vitae from eighteen ACEJMC programs drawn using stratified random sampling by Carnegie Classification. The findings indicate that faculty members differ by Carnegie Classification on research productivity, highest earned degrees, professional experience, time assignments (for research, teaching, and service), contact and credit hours, and external grants.Yeshttps://us.sagepub.com/en-us/nam/manuscript-submission-guideline

BPS Solitons in M5-Brane Worldvolume Theory with Constant Three-Form Field

We study BPS solutions for a self-dual string and a neutral string in M5-brane worldvolume theory with constant three-form field. We further generalize such solitons to superpose with a calibrated surface. We also study a traveling wave on a calibrated surface in the constant three-form field background.Comment: 12 pages, LaTeX, minor correction, added referenc

AdS/SCFT in Superspace

A discussion of the AdS/CFT correspondence in IIB is given in a superspace context. The main emphasis is on the properties of SCFT correlators on the boundary which are studied using harmonic superspace techniques. These techniques provide the easiest way of implementing the superconformal Ward identities. The Ward identities, together with analyticity, can be used to give a compelling argument in support of the non-renormalisation theorems for two- and three-point functions, and to establish the triviality of extremal and next-to-extremal correlation functions. The OPE in is also briefly discussed.Comment: 10 pages; talk given by PSH at 2nd Gursey Memorial Conference, June 200