Rationality of moduli of vector bundles on curves

The moduli space M(r,d) of stable, rank r, degree d vector bundles on a smooth projective curve of genus g>1 is shown to be birational to M(h,0) x A, where h=hcf(r,d) and A is affine space of dimension (r^2-h^2)(g-1). The birational isomorphism is compatible with fixing determinants in M(r,d) and M(h,0) and we obtain as a corollary that the moduli space of bundles of rank r and fixed determinant of degree d is rational, when r and d are coprime. A key ingredient in the proof is the use of a naturally defined Brauer class for the function field of M(r,d).Comment: 21 pages, Latex2e (with AMS packages

Amplitude and frequency control of a vibratory pile driver

Abstract—This paper describes the digital control of a vibratory pile driver in which the vibration is generated via two tandem pairs of electrically driven, geared, contra-rotating eccentrics. Experimental results are included to show the controller-induced system dynamics for a variety of load condtions, and to highlight the fact that, if the relative phase of the eccentric pairs is not controlled, the natural tendency at high excitation frequency is for the pile driver to operate with a low vibration amplitude. An analytical technique for identifying the system parameters is presented, and analytical performance predictions are compared with experimental results. Analysis of the power flow in the system shows that, although significant power transfer occurs between the two electrical drives, the net power dissipation during pile driving is relatively low

Reduction of cogging torque in interior-magnet brushless machines

An investigation into the cogging torque in a four-pole interior-magnet brushless machines having either a six-slot stator and a short-pitched nonoverlapping winding or a 12-slot stator and a full-pitched overlapping winding is described. It is shown by finite-element analyses and measurements that, by appropriately defining the pole-arc to pole-pitch ratio, the optimal pole-arc to pole-pitch ratio for minimum cogging torque, which has been derived for surface-mounted magnet machines, is equally applicable to interior-magnet machines

Design of robust current tracking control for active power filters

The paper describes a design methodology for robust current-tracking control of active power filters using quantitative feedback theory (QFT). The design aim is to address system issues of power quality and power factor correction in a double-sided converter (rectifierhverter combination) subject to parametric uncertainty, non-linear dynamic behavior and exogenous disturbances. The paper includes simulation results to demonstrate the dynamic performance attributes afforded to the resulting closed-loop control system, and to verify the design procedure

Drive systems for operation on deep-sea ROVs

Power systems for thruster actuators and other auxiliaries employed on work-class deep-sea ROVs subject to 300bar ambient pressures, are considered. Emphasis on 3×3 matrix converters for thrusters and 3×2 matrix converters for system auxiliaries, is given, along with experimental results showing operation during pressure cycling consistent with typical operational duties

Chemistry and valency spectra of Chromite in SNC meteorites

Shergottite chromite core mantle sources were Al-poor, Fe-rich, low Fe^{3+}/Fe^{2+}, fO_{2} 1 to 4 unit

Frontier exploration and the North Atlantic Igneous Province : new insights from a 2.6 km offshore volcanic sequence in the NE Faroe–Shetland Basin

Acknowledgements and Funding This work was funded by Chevron. The authors would like to acknowledge the Chevron West of Shetlands team along with the Joint Venture partners OMV, Faroe Petroleum and Indemitsu for access to data along with permission to publish this study. PGS is thanked for access to the Corona Ridge Regional Geostreamer (CRRG) data and permission to publish the seismic line. The paper was improved thanks to insightful reviews by S. M. Jones and A. Saunders, which substantially improved an earlier draft. J. Still and F. Thompson gave invaluable technical support at the University of Aberdeen, and K. Wall helped with real-time cuttings analysis.Peer reviewedPostprin

Structural Instability of the Core

Let σ be a q-rule, where any coalition of size q, from the society of size n, is decisive. Let w(n,q)=2q-n+1 and let W be a smooth ‘policy space’ of dimension w. Let U〖(W)〗^N be the space of all smooth profiles on W, endowed with the Whitney topology. It is shown that there exists an ‘instability dimension’ w*(σ) with 2≦w*(σ)≦w(n,q) such that: 1. (i) if w≧w*(σ), and W has no boundary, then the core of σ is empty for a dense set of profiles in U(W)N (i.e., almost always), 2. (ii) if w≧w*(σ)+1, and W has a boundary, then the core of σ is empty, almost always, 3. (iii) if w≧w*(σ)+1, then the cycle set is dense in W, almost always, 4. (iv) if w≧w*(σ)+2 then the cycle set is also path connected, almost always. The method of proof is first of all to show that if a point belongs to the core, then certain generalized symmetry conditions in terms of ‘pivotal’ coalitions of size 2q-n must be satisfied. Secondly, it is shown that these symmetry conditions can almost never be satisfied when either W has empty boundary and is of dimension w(n,q) or when W has non-empty boundary and is of dimension w(n,q)+1

Generalized symmetry conditions at a core point

Previous analyses have shown that if a point is to be a core of a majority rule voting game in Euclidean space, when preferences are smooth, then the utility gradients at the point must satisfy certain restrictive symmetry conditions. In this paper, these results are generalized to the case of an arbitrary voting rule, and necessary and sufficient conditions, expressed in terms of the utility gradients of "pivotal" coalitions, are obtained