Projective homogeneous varieties birational to quadrics

We will consider an explicit birational map between a quadric and the projective variety X(J) of traceless rank one elements in a simple reduced Jordan algebra J. X(J) is a homogeneous G-variety for the automorphism group G=Aut(J). We will show that the birational map is a blow up followed by a blow down. This will allow us to use the blow up formula for motives together with Vishik's work on the motives of quadrics to give a motivic decomposition of X(J).Comment: 20 pages, 1 figur

The use of ASBOs against young people in England and Wales: lessons from Scotland

The Anti-Social Behaviour Order (ASBO) is one of the best known measures used to tackle anti-social behaviour. In keeping with the popular conception, the order is frequently used against young people. Of all ASBOs issued in England and Wales up to the end of 2005, roughly 40% were imposed on under-18s. This paper begins with a brief outline of the three principles at the heart of the celebrated Scottish children’s hearings system. With reference to these principles, and to the provisions which govern the use of the order against 12–15 year olds north of the border, the paper then discusses five areas of concern about the use of ASBOs against young people in England and Wales: the readiness to resort to ASBOs; the forum for ASBO applications; the terms of ASBOs; publicising the details of ASBOs; and custodial net-widening. The paper ends by suggesting reforms to the ASBO regime in England and Wales insofar as it is used against young people.<br/

Working Health Services Scotland: a four-year evaluation

Background: Working Health Service Scotland (WHSS) supports the self-employed and employees of small and medium-sized enterprises (SMEs) in Scotland with a health condition affecting their ability to work, who are either absent or at risk of becoming absent due to it. Aims: To evaluate the impact on health and work outcomes of WHSS clients over a 4-year period. Methods: Data were collected at enrolment, entry, discharge and follow-up at 3 and 6 months after discharge. Clients completed up to three validated health questionnaires at entry and discharge—EuroQol five dimensions (EQ-5D) and visual analogue scale (VAS); Hospital Anxiety and Depression Scale (HADS); and Canadian Occupational Performance Measure (COPM). Results: A total of 13463 referrals occurred in the 4-year period; 11748 (87%) were eligible and completed entry assessment and 60% of the latter completed discharge paperwork. The majority of referrals were due to musculoskeletal conditions (84%) while 12% were referred with mental health conditions. Almost a fifth (18%) of cases were absent at entry and back at work at discharge. Work days lost while in WHSS was associated with age, length of absence prior to entering WHSS, primary health condition and time in programme. All health measures showed significant improvements from entry to discharge. Improvement in general health was sustained at 3- and 6-month follow-up. Conclusions: The WHSS evaluation findings indicate that participation was associated with positive changes to health and return-to-work. The extent of the positive change in health measures and work ability can be highly important economically for employees and employers

Estimating the Undercoverage of a Sampling Frame due to Reporting Delays

One of the imperfections of a sampling frame is miscoverage caused by delays in recording real- life events that change the eligibility of population units. For example, new units generally appear on the frame some time after they came into existence and units that have ceased to exist are not removed from the frame immediately. We provide methodology for predicting the undercoverage due to delays in reporting new units. The approach presented here is novel in a business survey context, and is equally applicable to overcoverage due to delays in reporting the closure of units. As a special case, we also predict the number of new-born units per month. The methodology is applied to the principal business register in the UK, maintained by the Office for National Statistics. <br/

Competition Stress Leads to a Blunting of the Cortisol Awakening Response in Elite Rowers

Background: Anticipation of forthcoming demands is often met with biological up-regulation, for example, levels of the stress hormone cortisol are typically elevated immediately prior to an anticipated event. Similarly, the cortisol awakening response (CAR), a surge in cortisol in the period following waking, is elevated on days of anticipated demand and this is viewed as an adaptive response in the preparation for challenge. This study assessed the effects of competition as an anticipated challenge in elite rowers. Methods: Elite rowers (N = 8) were assessed during two training and two competition weekends. Each assessment involved the measurement of self-reported competitive (cognitive and somatic) anxiety and salivary diurnal cortisol across 2 days representing a preparation day prior to either a training or competition day. Competitive anxiety was measured each morning and saliva samples were provided immediately upon waking and 30 min post waking (CAR) and before bed. Results: Self-reported cognitive and somatic anxiety levels were significantly greater during the competition phase compared with training. Additionally, levels of cognitive anxiety were greater on the day of competition compared with the preparation day. CAR magnitude was significantly reduced during the competition phase compared with training; however, there were no differences between preparation and event days. Conclusions: Reduced or blunted CARs are typically observed in chronically stressed populations and are characteristic of burnout and fatigue. While an increased CAR during competition may represent an adaptive response to challenge, blunted CARs and the concomitant increases in competitive anxiety observed here indicate maladaptive responding during a period where maximized functioning is critical

The role of languages in organization internationalisation

It has been suggested that British firms may be losing out on valuable export sales because of their lack of language skills. The information presented in the article provides an insight into the role of language training and its relationship to export growth. The authors conclude that an external presence of UK firms is likely to depend to a great extent on strategic planning for language training

Lattice Diagram Polynomials and Extended Pieri Rules

The lattice cell in the ${i+1}^{st}$ row and ${j+1}^{st}$ column of the positive quadrant of the plane is denoted $(i,j)$. If $\mu$ is a partition of $n+1$, we denote by $\mu/ij$ the diagram obtained by removing the cell $(i,j)$ from the (French) Ferrers diagram of $\mu$. We set $\Delta_{\mu/ij}=\det \| x_i^{p_j}y_i^{q_j} \|_{i,j=1}^n$, where $(p_1,q_1),... ,(p_n,q_n)$ are the cells of $\mu/ij$, and let ${\bf M}_{\mu/ij}$ be the linear span of the partial derivatives of $\Delta_{\mu/ij}$. The bihomogeneity of $\Delta_{\mu/ij}$ and its alternating nature under the diagonal action of $S_n$ gives ${\bf M}_{\mu/ij}$ the structure of a bigraded $S_n$-module. We conjecture that ${\bf M}_{\mu/ij}$ is always a direct sum of $k$ left regular representations of $S_n$, where $k$ is the number of cells that are weakly north and east of $(i,j)$ in $\mu$. We also make a number of conjectures describing the precise nature of the bivariate Frobenius characteristic of ${\bf M}_{\mu/ij}$ in terms of the theory of Macdonald polynomials. On the validity of these conjectures, we derive a number of surprising identities. In particular, we obtain a representation theoretical interpretation of the coefficients appearing in some Macdonald Pieri Rules.Comment: 77 pages, Te