Conjugacy classes of parabolic subalgebras in complex semi-simple lie algebras

For a complex semi simple Lie algebra g, Richardson's dense orbit theorem gives a map between conjugacy classes of parabolic subalgebras in g and conjugacy classes of nilpotent elements. Unfortunately, this map is not surjective, in general, and hence does not give a direct classification of the nilpotent conjugacy classes in g. Despite this, the theorem is used by Bala and Carter to produce an indirect classification of the nilpotent conjugacy classes in g. The map is not injective, either, and this thesis attempts to discover a necessary and sufficient condition for two parabolic subalgebras to give the same nilpotent conjugacy class under the above map. Springer conjectured that associated parabolics would give the same nilpotent conjugacy class. The problem was also raised in another form by Dixmier in his work concerning the distribution of nilpotent polarisable elements in g. He conjectured a generalisation of Kostant's results on the regular nilpotent elements. We prove both these conjectures correct, the method of proof being inspired by Dixmier's work. Unfortunately, the necessary and sufficient condition is clearly more complicated than this and we give two examples (one trivial, one non-trivial) of non-associated parabolics giving the same nilpotent conjugacy class under Richard son's ma

Steady State Behavior of Mechanically Perturbed Spin Glasses and Ferromagnets

A zero temperature dynamics of Ising spin glasses and ferromagnets on random graphs of finite connectivity is considered, like granular media these systems have an extensive entropy of metastable states. We consider the problem of what energy a randomly prepared spin system falls to before becoming stuck in a metastable state. We then introduce a tapping mechanism, analogous to that of real experiments on granular media, this tapping, corresponding to flipping simultaneously any spin with probability $p$, leads to stationary regime with a steady state energy $E(p)$. We explicitly solve this problem for the one dimensional ferromagnet and $\pm J$ spin glass and carry out extensive numerical simulations for spin systems of higher connectivity. The link with the density of metastable states at fixed energy and the idea of Edwards that one may construct a thermodynamics with a flat measure over metastable states is discussed. In addition our simulations on the ferromagnetic systems reveal a novel first order transition, whereas the usual thermodynamic transition on these graphs is second order.Comment: 11 pages, 7 figure

Gastrostomies Preserve but do not Increase Quality of Life for Patients and Caregivers

BACKGROUND & AIMS: Gastrostomies are widely used to provide long-term enteral nutrition to patients with neurological conditions that affect swallowing (such as following a cerebrovascular accident or for patients with motor neuron disease) or with oropharyngeal malignancies. The benefits derived from this intervention are uncertain for patients and caregivers. We conducted a prospective, multicenter cohort study to determine how gastrostomies affect health-related quality of life (HRQoL) in recipients and caregivers. METHODS: We performed a study of 100 patients who received gastrostomies (55% percutaneous endoscopic gastrostomy, 45% radiologically inserted) at 5 centers in the United Kingdom, 100 caregivers, and 200 population controls. We used the EuroQol-5D (EQ-5D, comprising a questionnaire, index, visual analogue scale) to assess HRQoL for patients and caregivers before the gastrostomy insertion and then 3 months afterward; findings were compared with those from controls. Ten patients and 10 caregivers were also interviewed after the procedure to explore quantitative findings. Findings from the EQ-5D and semi-structured interviews were integrated using a mixed methods matrix. RESULTS: Six patients died before the 3-month HRQoL reassessments. We observed no significant longitudinal changes in mean EQ-5D index scores for patients (0.70 before vs 0.710 after; P=.83) or caregivers (0.95 before vs 0.95 after; P=.32) following gastrostomy insertion. The semi-structured interviews revealed problems in managing gastrostomy tubes, social isolation, and psychological and emotional consequences that reduced HRQoL. CONCLUSIONS: We performed a mixed methods prospective study of the effects of gastrostomy feeding on HRQoL. HRQoL did not significantly improve after gastrostomy insertion for patients or caregivers. The lack of significant decrease in HRQoL after the procedure indicates that gastrostomies may help maintain HRQoL. Findings have relevance to those involved in gastrostomy insertion decisions and indicate the importance of carefully selecting patients for this intervention, despite the relative ease of insertion

The importance of long‐term experiments in agriculture: their management to ensure continued crop production and soil fertility; the Rothamsted experience

Summary Long‐term field experiments that test a range of treatments and are intended to assess the sustainability of crop production, and thus food security, must be managed actively to identify any treatment that is failing to maintain or increase yields. Once identified, carefully considered changes can be made to the treatment or management, and if they are successful yields will change. If suitable changes cannot be made to an experiment to ensure its continued relevance to sustainable crop production, then it should be stopped. Long‐term experiments have many other uses. They provide a field resource and samples for research on plant and soil processes and properties, especially those properties where change occurs slowly and affects soil fertility. Archived samples of all inputs and outputs are an invaluable source of material for future research, and data from current and archived samples can be used to develop models to describe soil and plant processes. Such changes and uses in the Rothamsted experiments are described, and demonstrate that with the appropriate crop, soil and management, acceptable yields can be maintained for many years, with either organic manure or inorganic fertilizers. Highlights Long‐term experiments demonstrate sustainability and increases in crop yield when managed to optimize soil fertility. Shifting individual response curves into coincidence increases understanding of the factors involved. Changes in inorganic and organic pollutants in archived crop and soil samples are related to inputs over time. Models describing soil processes are developed from current and archived soil data

Tensionless structure of glassy phase

We study a class of homogeneous finite-dimensional Ising models which were recently shown to exhibit glassy properties. Monte Carlo simulations of a particular three-dimensional model in this class show that the glassy phase obtained under slow cooling is dominated by large scale excitations whose energy $E_l$ scales with their size $l$ as $E_l\sim l^{\Theta}$ with $\Theta\sim 1.33(5)$. Simulations suggest that in another model of this class, namely the four-spin model, energy is concentrated mainly in linear defects making also in this case domain walls tensionless. Two-dimensinal variants of these models are trivial and energy of excitations scales with the exponent $\Theta=1.05(5)$.Comment: 5 page

An ARPES view on the high-Tc problem: phonons vs spin-fluctuations

We review the search for a mediator of high-Tc superconductivity focusing on ARPES experiment. In case of HTSC cuprates, we summarize and discuss a consistent view of electronic interactions that provides natural explanation of both the origin of the pseudogap state and the mechanism for high temperature superconductivity. Within this scenario, the spin-fluctuations play a decisive role in formation of the fermionic excitation spectrum in the normal state and are sufficient to explain the high transition temperatures to the superconducting state while the pseudogap phenomenon is a consequence of a Peierls-type intrinsic instability of electronic system to formation of an incommensurate density wave. On the other hand, a similar analysis being applied to the iron pnictides reveals especially strong electron-phonon coupling that suggests important role of phonons for high-Tc superconductivity in pnictides.Comment: A summary of the ARPES part of the Research Unit FOR538, http://for538.wmi.badw.d

2007 Report of the ICES Study Group on Fisheries-Induced Adaptive Change (SGFIAC)

There is a growing body of scientific evidence indicating that fisheries can cause evolutionary responses over time periods as short as 1020 years, in particular in traits such as the onset of maturation. As these changes will most likely result in a reduction of the productivity of a fish stock, management objectives and (precautionary) reference points for sustainable exploitation need to be re-defined, and new objectives and reference points for managing fisheries-induced evolution need to be developed. Current knowledge allows for two generalisations. First, reducing harvest rates will almost always slow the rate and extent of fisheries-induced evolution in most life-history traits. Second, raising a stock's minimum size limit for exploitation well above the size range over which maturation occurs will slow down the rate of evolution in its maturation schedule. To go beyond these generic insights, "Evolutionary Impact Assessments" (EvoIAs) are proposed to quantify the effects of management measures, through the evolutionary response of specific stocks, on the utility functions defined by managers. The Study Group on Fisheries Induced Adaptive Change [SGFIAC] proposes to further develop this framework in dialogue with fisheries scientists and managers, with the aim of integrating the effects of fisheries-induced evolution into fisheries management advice. Developing EvoIAs in the context of suitable case studies is considered to be the most efficient way for making progress

Incipient Separation in Shock Wave Boundary Layer Interactions as Induced by Sharp Fin

The incipient separation induced by the shock wave turbulent boundary layer interaction at the sharp fin is the subject of present study. Existing theories for the prediction of incipient separation, such as those put forward by McCabe (1966) and Dou and Deng (1992), can have thus far only predicting the direction of surface streamline and tend to over-predict the incipient separation condition based on the Stanbrook's criterion. In this paper, the incipient separation is firstly predicted with Dou and Deng (1992)'s theory and then compared with Lu and Settles (1990)' experimental data. The physical mechanism of the incipient separation as induced by the shock wave/turbulent boundary layer interactions at sharp fin is explained via the surface flow pattern analysis. Furthermore, the reason for the observed discrepancy between the predicted and experimental incipient separation conditions is clarified. It is found that when the wall limiting streamlines behind the shock wave becomes\ aligning with one ray from the virtual origin as the strength of shock wave increases, the incipient separation line is formed at which the wall limiting streamline becomes perpendicular to the local pressure gradient. The formation of this incipient separation line is the beginning of the separation process. The effects of Reynolds number and the Mach number on incipient separation are also discussed. Finally, a correlation for the correction of the incipient separation angle as predicted by the theory is also given.Comment: 34 pages; 9 figure

Observational Constraints on the Modified Gravity Model (MOG) Proposed by Moffat: Using the Magellanic System

A simple model for the dynamics of the Magellanic Stream (MS), in the framework of modified gravity models is investigated. We assume that the galaxy is made up of baryonic matter out of context of dark matter scenario. The model we used here is named Modified Gravity (MOG) proposed by Moffat (2005). In order to examine the compatibility of the overall properties of the MS under the MOG theory, the observational radial velocity profile of the MS is compared with the numerical results using the $\chi^2$ fit method. In order to obtain the best model parameters, a maximum likelihood analysis is performed. We also compare the results of this model with the Cold Dark Matter (CDM) halo model and the other alternative gravity model that proposed by Bekenstein (2004), so called TeVeS. We show that by selecting the appropriate values for the free parameters, the MOG theory seems to be plausible to explain the dynamics of the MS as well as the CDM and the TeVeS models.Comment: 14 pages, 3 Figures, accepted in Int. J. Theor. Phy