Restoration of particle number as a good quantum number in BCS theory

As shown in previous work, number projection can be carried out analytically for states defined in a quasi-particle scheme when the states are expressed in a coherent state representation. The wave functions of number-projected states are well-known in the theory of orthogonal polynomials as Schur functions. Moreover, the functions needed in pairing theory are a particularly simple class of Schur functions that are easily constructed by means of recursion relations. It is shown that complete sets of states can be projected from corresponding quasi-particle states and that such states retain many of the properties of the quasi-particle states from which they derive. It is also shown that number projection can be used to construct a complete set of orthogonal states classified by generalized seniority for any nucleus.Comment: 21 pages, 2 figures, epsf.def style file for printing figure

See No Fiduciary, Hear No Fiduciary: A Lawyer’s Knowledge Within Aiding and Abetting Fiduciary Breach Claims

Fiduciary liability for attorney conduct generally extends only to direct clients of legal services. Over the last few decades, however, the lawyer’s role has expanded. Following this trend, fiduciary liability also has expanded to allow third-party claims in certain limited circumstances. One example is the attorney aiding and abetting a client’s fiduciary breach claim. One of the key requirements for liability under this claim is the attorney’s knowledge of his client’s fiduciary relationship with the third party alleging the breach. Within those jurisdictions that have accepted the claim, there are two approaches to the knowledge element. The first is the constructive knowledge standard that permits liability if the attorney knew or reasonably should have known of the fiduciary relationship. The second approach is the actual knowledge standard that requires overt and obvious evidence of fiduciary knowledge. In addition to these standards, a third approach ignores the knowledge element entirely: the qualified immunity standard that protects attorneys against third-party liability as long as the conduct falls within an attorney-client relationship. This Note argues for the rejection of constructive knowledge and adoption of either the qualified immunity or actual knowledge standard for numerous doctrinal and policy reasons while maintaining the claim’s original policy goals

Forecasting audience increase on YouTube

User profiles constructed on Social Web platforms are often motivated by the need to maximise user reputation within a community. Subscriber, or follower, counts are an indicator of the influence and standing that the user has, where greater values indicate a greater perception or regard for what the user has to say or share. However, at present there lacks an understanding of the factors that lead to an increase in such audience levels, and how a user’s behaviour can a!ect their reputation. In this paper we attempt to fill this gap, by examining data collected from YouTube over regular time intervals. We explore the correlation between the subscriber counts and several behaviour features - extracted from both the user’s profile and the content they have shared. Through the use of a Multiple Linear Regression model we are able to forecast the audience levels that users will yield based on observed behaviour. Combining such a model with an exhaustive feature selection process, we yield statistically significant performance over a baseline model containing all features

Biomechanical motion analysis in the clinical environment : the dawn of a new era ?

Philip Rowe looks at biomechanical motion analysis and the work the department of Biomedical engineering at the University of Strathclyde, Glasgow, UK (formerly the Bioengineering Unit), has played a key role in these developments over the last 50 years

Still not getting a fair deal : the under-representation of female athletes in television news coverage of the 2006 Commonwealth Games : a thesis presented in partial fulfillment of the requirements for the degree of Master of Management in Communication Management at Massey University

This research investigates gender equity in New Zealand television news coverage of the 2006 Commonwealth Games. Using content and frame analyses, the study evaluates the prime-time news coverage of the two largest free-to-air broadcasters, TVNZ and TV3. The results demonstrate that the hegemonic masculinity of sport is still reflected and supported by New Zealand's television news media. Women athletes received just 25% of the time spent reporting on the Games with male athletes receiving 43%. This was despite women making up 46% of the New Zealand Commonwealth Games team and winning 53% of the medals, indicating that participation and success had little correlation with the media's decisions about which athletes to report on. This study also highlights differences in the framing techniques used by the media in reporting on sportsmen and sportswomen. The research found the presence of gender-marking, preferential positioning, reliance on male sources and other framing devices. The ways these were used provided further evidence of the dominant presence sportsmen have over sportswomen in the New Zealand Commonwealth Games television coverage. On a positive note, the research found no sexualisation and very little stereotyping of female athletes, techniques which have been prevalent in international studies. This thesis outlines the need for New Zealand's television news media, particularly the public service broadcaster TVNZ, to reflect on the inequality they continue to demonstrate in their coverage of sportsmen and sportswomen and to put in place active measures to increase the levels of coverage given to sportswomen by New Zealand's mainstream media

Motor control of a hub motor for electric skateboard propulsion : a thesis presented in partial fulfilment of the requirements for the degree of Masters in Engineering at Massey University, Palmerston North, New Zealand

Redacted for copyright reasons: Appendix A - Journal Article Published in IEEE International Instrumentation and Measurement Technology Conference (I2MTC 2012). Rowe, A. & Sen Gupta, G. (2012). Instrumentation and control of a high power BLDC motor for small vehicle applications.An electric powered skateboard was designed and built for testing and development of an innovative hub motor propulsion system and motor controller. The electric skateboard prototype is able to reach speeds of over 50km/h and achieve a range of over 35km on a single battery charge. The prototype weighs 8.6kg and can easily be carried by the user. This mode of transport has potential uses in recreational use, motor sports (racing), short commutes, and most notably, in ‘the last mile’ of public transport – getting to and from a train station, bus stop, etc. to the user’s final destination. Typical electric powered skateboards use external motors(s) requiring a power transmission assembly to drive the wheels. The hub motor design places the motor(s) inside the skateboard wheels and drives the wheels directly. This removes the need for power transmission assemblies therefore reductions in size, weight, cost, audible noise, and maintenance are realised. The hub motor built for this prototype has proven to be a highly feasible option over typical drive systems and further improvements to the design are discussed in this report. Advances in the processor capability of low cost microcontrollers has allowed for advanced motor control techniques to be implemented on low cost consumer level motor controllers which, until recent times, have been using the basic ‘Six-Step Control’ technique to drive Permanent Magnet Synchronous Motors. The custom built motor controllers allow for firmware to be flashed to the microcontroller. Firmware was written for the basic motor control technique, Six-Step Control and for the advanced motor control technique, ‘Field Oriented Control’ (FOC). This allowed for the two control techniques to be tested and compared using identical hardware for each. Six-Step Control drives a three phase motor by controlling the inverter output to six discrete states. The states are stepped through sequentially. This results in a square wave AC waveform. Theory shows that this is not optimal as the magnetic flux produced in the stator is not always perpendicular to the magnet poles but rather aligned to the nearest 60°. FOC addresses this by controlling the magnetic flux to always be perpendicular to the magnet poles in order to maximise torque. The inverter is essentially controlled to produce a continuously variable voltage vector output in terms of both magnitude and direction (vector control). Bench testing of the control techniques was performed using two motors coupled together with one motor driving and the other motor running as a generator. The generator motor was shown to provide a highly consistent and repeatable load on the driving motor under test and therefore comparisons could be made between the performance of the motor while controlled under Six-Step Control and FOC. This test indicated that FOC was able to drive the motor more efficiently than Six-Step Control, however the FOC implementation requires further development to achieve greater efficiency under high load demands. Furthermore, on-road testing was performed using the motor controllers in the electric skateboard prototype to compare the performance of the two control techniques in a real world application. The results from this test were inconclusive due to large variation in the results between repeated tests