Roots of Ehrhart Polynomials of Smooth Fano Polytopes

V. Golyshev conjectured that for any smooth polytope P of dimension at most five, the roots z\in\C of the Ehrhart polynomial for P have real part equal to -1/2. An elementary proof is given, and in each dimension the roots are described explicitly. We also present examples which demonstrate that this result cannot be extended to dimension six.Comment: 10 page

Comparative Measurements of Earth and Martian Entry Environments in the NASA Langley HYMETS Facility

Arc-jet facilities play a major role in the development of heat shield materials for entry vehicles because they are capable of producing representative high-enthalpy flow environments. Arc-jet test data is used to certify material performance for a particular mission and to validate or calibrate models of material response during atmospheric entry. Materials used on missions entering Earth s atmosphere are certified in an arc-jet using a simulated air entry environment. Materials used on missions entering the Martian atmosphere should be certified in an arc-jet using a simulated Martian atmosphere entry environment, which requires the use of carbon dioxide. Carbon dioxide has not been used as a test gas in a United States arc-jet facility since the early 1970 s during the certification of materials for the Viking Missions. Materials certified for the Viking missions have been used on every entry mission to Mars since that time. The use of carbon dioxide as a test gas in an arc-jet is again of interest to the thermal protection system community for certification of new heat shield materials that can increase the landed mass capability for Mars bound missions beyond that of Viking and Pathfinder. This paper describes the modification, operation, and performance of the Hypersonic Materials Environmental Test System (HYMETS) arc-jet facility with carbon dioxide as a test gas. A basic comparison of heat fluxes, various bulk properties, and performance characteristics for various Earth and Martian entry environments in HYMETS is provided. The Earth and Martian entry environments consist of a standard Earth atmosphere, an oxygen-rich Earth atmosphere, and a simulated Martian atmosphere. Finally, a preliminary comparison of the HYMETS arc-jet facility to several European plasma facilities is made to place the HYMETS facility in a more global context of arc-jet testing capability

Presurgical tear characteristics and estimated shear modulus as predictors of repair integrity and shoulder function one year after rotator cuff repair

Background: Rotator cuff repair provides pain relief for many patients; however, retears are relatively common and affect approximately 20%-70% of patients after repair. Although magnetic resonance imaging (MRI) offers the ability to assess tissue characteristics such as tear size, retraction, and fatty infiltration, it provides little insight into the quality of the musculotendinous tissues the surgeon will encounter during surgery. However, shear wave elastography (SWE) could provide an indirect assessment of quality (ie, stiffness) by measuring the speed of shear waves propagating through tissue. The objective of this study was to determine the extent to which estimated shear modulus predicts repair integrity and functional outcomes 1 year after rotator cuff repair. Methods: Thirty-three individuals scheduled to undergo arthroscopic rotator cuff repair were enrolled in this study. Before surgery, shear modulus of the supraspinatus tendon and muscle was estimated using ultrasound SWE. MRIs were obtained before and 1 year after surgery to assess tear characteristics and repair integrity, respectively. Shoulder strength, range of motion, and patient-reported pain and function were assessed before and after surgery. Functional outcomes were compared between groups and across time using a two-factor mixed model analysis of variance. Stepwise regression with model comparison was used to investigate the extent to which MRI and shear modulus predicted repair integrity and function at 1 year after surgery. Results: At 1 year after surgery, 56.5% of patients had an intact repair. No significant differences were found in any demographic variable, presurgical tear characteristic, or shear modulus between patients with an intact repair and those with a recurrent tear. Compared with presurgical measures, patients in both groups demonstrated significant improvements at 1 year after surgery in pain (P \u3c .01), self-reported function (P \u3c .01), range of motion (P \u3c .01), and shoulder strength (P \u3c .01). In addition, neither presurgical MRI variables (P \u3e .16) nor shear modulus (P \u3e .52) was significantly different between groups at 1 year after surgery. Finally, presurgical shear modulus generally did not improve the prediction of functional outcomes above and beyond that provided by MRI variables alone (P \u3e .22). Conclusion: Although SWE remains a promising modality for many clinical applications, this study found that SWE-estimated shear modulus did not predict repair integrity or functional outcomes at 1 year after surgery, nor did it add to the prediction of outcomes above and beyond that provided by traditional presurgical MRI measures of tear characteristics. Therefore, it appears that further research is needed to fully understand the clinical utility of SWE for musculoskeletal tissue and its potential use for predicting outcomes after surgical rotator cuff repair

Nordic Post-Graduate Sustainable Design and Engineering Research from a Supervisor Perspective

The multi- and interdisciplinary field of sustainable product innovation is rapidly expanding as an arena for scientific research. Universities in Nordic countries can be considered as an exponent of this type of research, with active research groups in, among others, Göteborg, Helsinki, Lund, Lyngby, Linköping and Trondheim. In the context of a Nordforsk funded project, seven second generation PhD supervisors from these universities, who have been active in this field for many years, discuss funding, publication, research traditions, education and supervision practices related to PhD research in this field. A number of recommendations to improve current practices are made, including the mapping currently existing differences in different academic institutions, studying the cross-over learning effects between academica and non-academic partners, and the development of ‘quality indicators’ of research in the SPI domain