Some conjectures about integral means of ∂f and ∂¯f

The final version of the paper appears in: "Complex Analysis and Differential Equations" 64 (1999): 91-109. Print.We discuss some conjectural inequalities concerning a problem from the calculus of variations, namely that rank 1 convex functions are quasi-convex. An affirmative answer would also give the best constants for the Beurling-Ahlfors operator that appears in the theory of quasi-conformal mappings on the plane

Disjoint minimal graphs

We prove that the number s(n) of disjoint minimal graphs supported on domains in R^n is bounded by e(n+1)^2. In the two-dimensional case we show that s(2) is at most three (the conjectured number is two).Comment: 14 page

Free Energy Minimizers for a Two--Species Model with Segregation and Liquid-Vapor Transition

We study the coexistence of phases in a two--species model whose free energy is given by the scaling limit of a system with long range interactions (Kac potentials) which are attractive between particles of the same species and repulsive between different species.Comment: 32 pages, 1 fig, plain tex, typeset twic

Predictors of Hospitalization for Injection Drug Users Seeking Care for Soft Tissue Infections

BACKGROUND: Soft tissue infections (STIs) from injection drug use are a common cause of Emergency Department visits, hospitalizations, and operating room procedures, yet little is known about factors that may predict the need for these costly medical services. OBJECTIVE: To describe a cohort of injection drug users seeking Emergency Department care for STIs and to identify risk factors associated with hospitalization. We hypothesized that participants who delayed seeking care would be hospitalized more often than those who did not. DESIGN: Cohort study using in-person structured interviews and medical record review. Logistic regression assessed the association between hospital admission and delay in seeking care as well as other demographic, clinical, and psychosocial factors. PARTICIPANTS: Injection drug users who sought Emergency Department care for STIs from May 2001 to March 2002. RESULTS: Of the 136 participants, 55 (40%) were admitted to the hospital. Delay in seeking care was not associated with hospital admission. Participants admitted for their infection were significantly more likely to be living in a shelter (P = .01) and to report being hospitalized 2 or more times in the past year (P < .01). CONCLUSIONS: We identified a subpopulation of injection drug users, mostly living in shelters, who were hospitalized frequently in the past year and who were more likely to be hospitalized for their current infections compared to others. As members of this subpopulation can be easily identified and located, they may benefit from interventions to reduce the health care utilization resulting from these infections

Medical Student Professionalism Narratives: A Thematic Analysis and Interdisciplinary Comparative Investigation

<p>Abstract</p> <p>Background</p> <p>Professionalism development is influenced by the informal and hidden curriculum. The primary objective of this study was to better understand this experiential learning in the setting of the Emergency Department (ED). Secondarily, the study aimed to explore differences in the informal curriculum between Emergency Medicine (EM) and Internal Medicine (IM) clerkships.</p> <p>Methods</p> <p>A thematic analysis was conducted on 377 professionalism narratives from medical students completing a required EM clerkship from July 2008 through May 2010. The narratives were analyzed using established thematic categories from prior research as well as basic descriptive characteristics. Chi-square analysis was used to compare the frequency of thematic categories to prior research in IM. Finally, emerging themes not fully appreciated in the established thematic categories were created using grounded theory.</p> <p>Results</p> <p>Observations involving interactions between attending physician and patient were most abundant. The narratives were coded as positive 198 times, negative 128 times, and hybrid 37 times. The two most abundant narrative themes involved <it>manifesting respect </it>(36.9%) and <it>spending time </it>(23.7%). Both of these themes were statistically more likely to be noted by students on EM clerkships compared to IM clerkships. Finally, one new theme regarding <it>cynicism </it>emerged during analysis.</p> <p>Conclusions</p> <p>This analysis describes an informal curriculum that is diverse in themes. Student narratives suggest their clinical experiences to be influential on professionalism development. Medical students focus on different aspects of professionalism depending on clerkship specialty.</p

Whitney’s extension theorem for ultradifferentiable functions of Beurling type

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/43941/1/11512_2006_Article_BF02386123.pd