Local well-posedness for membranes in the light cone gauge

In this paper we consider the classical initial value problem for the bosonic membrane in light cone gauge. A Hamiltonian reduction gives a system with one constraint, the area preserving constraint. The Hamiltonian evolution equations corresponding to this system, however, fail to be hyperbolic. Making use of the area preserving constraint, an equivalent system of evolution equations is found, which is hyperbolic and has a well-posed initial value problem. We are thus able to solve the initial value problem for the Hamiltonian evolution equations by means of this equivalent system. We furthermore obtain a blowup criterion for the membrane evolution equations, and show, making use of the constraint, that one may achieve improved regularity estimates.Comment: 29 page

A conjecture on Exceptional Orthogonal Polynomials

Exceptional orthogonal polynomial systems (X-OPS) arise as eigenfunctions of Sturm-Liouville problems and generalize in this sense the classical families of Hermite, Laguerre and Jacobi. They also generalize the family of CPRS orthogonal polynomials. We formulate the following conjecture: every exceptional orthogonal polynomial system is related to a classical system by a Darboux-Crum transformation. We give a proof of this conjecture for codimension 2 exceptional orthogonal polynomials (X2-OPs). As a by-product of this analysis, we prove a Bochner-type theorem classifying all possible X2-OPS. The classification includes all cases known to date plus some new examples of X2-Laguerre and X2-Jacobi polynomials

Ambulatory teaching: Do approaches to learning predict the site and preceptor characteristics valued by clerks and residents in the ambulatory setting?

BACKGROUND: In a study to determine the site and preceptor characteristics most valued by clerks and residents in the ambulatory setting we wished to confirm whether these would support effective learning. The deep approach to learning is thought to be more effective for learning than surface approaches. In this study we determined how the approaches to learning of clerks and residents predicted the valued site and preceptor characteristics in the ambulatory setting. METHODS: Postal survey of all medical residents and clerks in training in Ontario determining the site and preceptor characteristics most valued in the ambulatory setting. Participants also completed the Workplace Learning questionnaire that includes 3 approaches to learning scales and 3 workplace climate scales. Multiple regression analysis was used to predict the preferred site and preceptor characteristics as the dependent variables by the average scores of the approaches to learning and perception of workplace climate scales as the independent variables. RESULTS: There were 1642 respondents, yielding a 47.3% response rate. Factor analysis revealed 7 preceptor characteristics and 6 site characteristics valued in the ambulatory setting. The Deep approach to learning scale predicted all of the learners' preferred preceptor characteristics (β = 0.076 to β = 0.234, p < .001). Valuing preceptor Direction was more strongly associated with the Surface Rational approach (β = .252, p < .001) and with the Surface Disorganized approach to learning (β = .154, p < 001) than with the Deep approach. The Deep approach to learning scale predicted valued site characteristics of Office Management, Patient Logistics, Objectives and Preceptor Interaction (p < .001). The Surface Rational approach to learning predicted valuing Learning Resources and Clinic Set-up (β = .09, p = .001; β = .197, p < .001). The Surface Disorganized approach to learning weakly negatively predicted Patient Logistics (β = -.082, p = .003) and positively the Learning Resources (β = .088, p = .003). Climate factors were not strongly predictive for any studied characteristics. Role Modeling and Patient Logistics were predicted by Supportive Receptive climate (β = .135, p < .001, β = .118, p < .001). CONCLUSION: Most site and preceptor characteristics valued by clerks and residents were predicted by their Deep approach to learning scores. Some characteristics reflecting the need for good organization and clear direction are predicted by learners' scores on less effective approaches to learning

On the vanishing electron-mass limit in plasma hydrodynamics in unbounded media

We consider the zero-electron-mass limit for the Navier-Stokes-Poisson system in unbounded spatial domains. Assuming smallness of the viscosity coefficient and ill-prepared initial data, we show that the asymptotic limit is represented by the incompressible Navier-Stokes system, with a Brinkman damping, in the case when viscosity is proportional to the electron-mass, and by the incompressible Euler system provided the viscosity is dominated by the electron mass. The proof is based on the RAGE theorem and dispersive estimates for acoustic waves, and on the concept of suitable weak solutions for the compressible Navier-Stokes system

The phosphorous necrosis of the jaws and what can we learn from the past: a comparison of "phossy" and "bisphossy" jaw

INTRODUCTION: The osteopathology of the jaws associated with bone resorption inhibitors is a current topic that engages a variety of clinical specialists. This has increased after the approval of denosumab for treatment of osteoporosis and skeletal-related events in patients with solid malignancy. Early after the first publications, there is a possible connection between phosphorous necrosis of the jaws, a dreadful industrial disease mentioned, and bisphosphonate-induced pathology. The nineteenth century was the prime time for phosphorus necrosis of match factory workers. RESULTS: This occurrence provides an interesting insight into the medical and surgical profession in the nineteenth century. There are striking parallels and repetition of current and old ideas in the approach to this "new disease." There are similar examples in case descriptions when compared with today's patients of bisphosphonate-related osteonecrosis of the jaws (BRONJ). DISCUSSION: Phosphorus necrosis was first described in Austria. Soon after this, surgeons in German-speaking countries including well-known clinicians Wegner (1872) and von Schulthess-Rechberg (1879) pioneered the analysis, preventative measures, and treatment of this disease. The tendency at this time was to approach BRONJ as a "special kind of osteomyelitis" in pretreated and metabolically different bone. Not only the treatment strategy to wait until sequestrum formation with subsequent removal and preventative measures but also the idea of focusing on the periosteum as the triggering anatomical structure may have been adopted from specialists in the nineteenth century. Therefore, phosphorous necrosis of the jaw is an excellent example of "learning from the past.

Evolution in the Brain, Evolution in the Mind: The Hierarchical Brain and the Interface between Psychoanalysis and Neuroscience

This article first aims to demonstrate the different ways the work of the English neurologist John Hughlings Jackson influenced Freud. It argues that these can be summarized in six points. It is further argued that the framework proposed by Jackson continued to be pursued by twentieth-century neuroscientists such as Papez, MacLean and Panksepp in terms of tripartite hierarchical evolutionary models. Finally, the account presented here aims to shed light on the analogies encountered by psychodynamically oriented neuroscientists, between contemporary accounts of the anatomy and physiology of the nervous system on the one hand, and Freudian models of the mind on the other. These parallels, I will suggest, are not coincidental. They have a historical underpinning, as both accounts most likely originate from a common source: John Hughlings Jackson's tripartite evolutionary hierarchical view of the brain