The critical dimension for a 4th order problem with singular nonlinearity

We study the regularity of the extremal solution of the semilinear biharmonic equation \bi u=\f{\lambda}{(1-u)^2}, which models a simple Micro-Electromechanical System (MEMS) device on a ball B\subset\IR^N, under Dirichlet boundary conditions $u=\partial_\nu u=0$ on $\partial B$. We complete here the results of F.H. Lin and Y.S. Yang \cite{LY} regarding the identification of a "pull-in voltage" \la^*>0 such that a stable classical solution u_\la with 0 exists for \la\in (0,\la^*), while there is none of any kind when \la>\la^*. Our main result asserts that the extremal solution $u_{\lambda^*}$ is regular $(\sup_B u_{\lambda^*} <1)$ provided $N \le 8$ while $u_{\lambda^*}$ is singular ($\sup_B u_{\lambda^*} =1$) for $N \ge 9$, in which case $1-C_0|x|^{4/3}\leq u_{\lambda^*} (x) \leq 1-|x|^{4/3}$ on the unit ball, where $C_0:= (\frac{\lambda^*}{\overline{\lambda}})^{1/3}$ and $\bar{\lambda}:= {8/9} (N-{2/3}) (N- {8/3})$.Comment: 19 pages. This paper completes and replaces a paper (with a similar title) which appeared in arXiv:0810.5380. Updated versions --if any-- of this author's papers can be downloaded at this http://www.birs.ca/~nassif

Feedback Processes in Early-Type Galaxies

We present a phenomenological model of feedback in early-type galaxies that tracks the evolution of the interstellar medium gas mass, metallicity, and temperature. Modeling the star formation rate as a Schmidt law with a temperature-dependent efficiency, we find that intermittent episodes of star formation are common in moderate-size ellipticals. Our model is applicable in the case in which the thermalization time from SN is sufficiently long that spatial variations are relatively unimportant, an appropriate assumption for the empirical parameters adopted here. The departure from a standard scenario of passive evolution implies significantly younger luminosity-weighted ages for the stellar populations of low-mass galaxies at moderate redshifts, even though the more physically meaningful mass-weighted ages are changed only slightly. Secondary bursts of star formation also lead to a natural explanation of the large scatter in the NUV-optical relation observed in clusters at moderate redshift and account for the population of E+A galaxies that display a spheroidal morphology. As the late-time formation of stars in our model is due to the gradual cooling of the interstellar medium, which is heated to temperatures ~1 keV by the initial burst of supernovae, our conclusions do not rely on any environmental effects or external mechanisms. Furthermore, a simple estimate of the X-ray emission from this supernova heated gas leads to an L_X vs L_B correlation that is in good agreement with observed values. Thus feedback processes may be essential to understanding the observed properties of early-type galaxies from the optical to the X-ray.Comment: Accepted for publication in ApJ. Uses emulateapj.sty. 12 pages with 8 embedded EPS figure

The HST Survey of BL Lacertae Objects. II. Host Galaxies

We have used the HST WFPC2 camera to survey 132 BL Lac objects comprising seven complete radio-, X-ray-, and optically-selected samples. We obtained useful images for 110 targets spanning the redshift range 0 < z < 1.3. In two thirds of the BL Lac images, host galaxies are detected, including nearly all for z < 0.5 (58 of 63). The highest redshift host galaxy detected is in a BL Lac object at z=0.664. In 58 of the 72 resolved host galaxies, a de Vaucouleurs profile is significantly preferred, at >99% confidence, over a pure exponential disk; the two fits are comparable in the remaining 14 cases. These results limit the number of disk systems to at most 8% of BL Lacs (at 99% confidence), and are consistent with all BL~Lac host galaxies being ellipticals. The detected host galaxies are luminous ellipticals with a median absolute K-corrected magnitude of M_R= -23.7 +- 0.6 mag, at least one magnitude brighter than M* and comparable to brightest cluster galaxies. The galaxy morphologies are generally smooth and undisturbed, with small or negligible ellipticities (<0.2). There is no correlation between host galaxy and observed nuclear magnitude or estimated jet power corrected for beaming. If black hole mass is correlated linearly with bulge mass in general, this implies a large range in Eddington ratio. Present data strongly support the unification picture with FR I galaxies constituting the bulk of the parent population of BL Lac objects.Comment: Accepted for publication on ApJ. 38 pages, 8 figure

Response to comment on 'Amphibian fungal panzootic causes catastrophic and ongoing loss of biodiversity'

Lambert et al. question our retrospective and holistic epidemiological assessment of the role of chytridiomycosis in amphibian declines. Their alternative assessment is narrow and provides an incomplete evaluation of evidence. Adopting this approach limits understanding of infectious disease impacts and hampers conservation efforts. We reaffirm that our study provides unambiguous evidence that chytridiomycosis has affected at least 501 amphibian species

PRIMA subretinal wireless photovoltaic microchip implantation in non-human primate and feline models

Purpose To evaluate the surgical technique for subretinal implantation of two sizes of PRIMA photovoltaic wireless microchip in two animal models, and refine these surgical procedures for human trials. Methods Cats and Macaca fascicularis primates with healthy retina underwent vitrectomy surgery and were implanted with subretinal wireless photovoltaic microchip at the macula/central retina. The 1.5mm PRIMA chip was initially studied in feline eyes. PRIMA implant (2mm,1.5mm sizes) arrays were studied in primates. Feasibility of subretinal chip implantation was evaluated with a newly-developed surgical technique, with surgical complications and adverse events recorded. Results The 1.5mm implant was placed in the central retina of 11 feline eyes, with implantation duration 43-106 days. The 1.5mm implant was correctly positioned into central macula of 11 primate eyes, with follow-up periods of minimum 6 weeks (n = 11), 2 years (n = 2), and one eye for 3 years. One primate eye underwent multi-chip 1.5mm implantation using two 1.5mm chips. The 2mm implant was delivered to 4 primate eyes. Optical coherence tomography confirmed correct surgical placement of photovoltaic arrays in the subretinal space in all 26 eyes. Intraoperative complications in primate eyes included retinal tear, macular hole, retinal detachment, and vitreous hemorrhage that resolved spontaneously. Postoperatively, there was no case of significant ocular inflammation in the 1.5mm implant group. Conclusions We report subretinal implantation of 1.5mm and 2mm photovoltaic arrays in the central retina of feline and central macula of primate eyes with a low rate of device-related complications. The in vivo PRIMA implantation technique has been developed and refined for use for a 2mm PRIMA implant in ongoing human trials

The James Webb Space Telescope Mission

Twenty-six years ago a small committee report, building on earlier studies, expounded a compelling and poetic vision for the future of astronomy, calling for an infrared-optimized space telescope with an aperture of at least $4m$. With the support of their governments in the US, Europe, and Canada, 20,000 people realized that vision as the $6.5m$ James Webb Space Telescope. A generation of astronomers will celebrate their accomplishments for the life of the mission, potentially as long as 20 years, and beyond. This report and the scientific discoveries that follow are extended thank-you notes to the 20,000 team members. The telescope is working perfectly, with much better image quality than expected. In this and accompanying papers, we give a brief history, describe the observatory, outline its objectives and current observing program, and discuss the inventions and people who made it possible. We cite detailed reports on the design and the measured performance on orbit.Comment: Accepted by PASP for the special issue on The James Webb Space Telescope Overview, 29 pages, 4 figure

Mortality and pulmonary complications in patients undergoing surgery with perioperative SARS-CoV-2 infection: an international cohort study

Background: The impact of severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) on postoperative recovery needs to be understood to inform clinical decision making during and after the COVID-19 pandemic. This study reports 30-day mortality and pulmonary complication rates in patients with perioperative SARS-CoV-2 infection. Methods: This international, multicentre, cohort study at 235 hospitals in 24 countries included all patients undergoing surgery who had SARS-CoV-2 infection confirmed within 7 days before or 30 days after surgery. The primary outcome measure was 30-day postoperative mortality and was assessed in all enrolled patients. The main secondary outcome measure was pulmonary complications, defined as pneumonia, acute respiratory distress syndrome, or unexpected postoperative ventilation. Findings: This analysis includes 1128 patients who had surgery between Jan 1 and March 31, 2020, of whom 835 (74·0%) had emergency surgery and 280 (24·8%) had elective surgery. SARS-CoV-2 infection was confirmed preoperatively in 294 (26·1%) patients. 30-day mortality was 23·8% (268 of 1128). Pulmonary complications occurred in 577 (51·2%) of 1128 patients; 30-day mortality in these patients was 38·0% (219 of 577), accounting for 81·7% (219 of 268) of all deaths. In adjusted analyses, 30-day mortality was associated with male sex (odds ratio 1·75 [95% CI 1·28–2·40], p\textless0·0001), age 70 years or older versus younger than 70 years (2·30 [1·65–3·22], p\textless0·0001), American Society of Anesthesiologists grades 3–5 versus grades 1–2 (2·35 [1·57–3·53], p\textless0·0001), malignant versus benign or obstetric diagnosis (1·55 [1·01–2·39], p=0·046), emergency versus elective surgery (1·67 [1·06–2·63], p=0·026), and major versus minor surgery (1·52 [1·01–2·31], p=0·047). Interpretation: Postoperative pulmonary complications occur in half of patients with perioperative SARS-CoV-2 infection and are associated with high mortality. Thresholds for surgery during the COVID-19 pandemic should be higher than during normal practice, particularly in men aged 70 years and older. Consideration should be given for postponing non-urgent procedures and promoting non-operative treatment to delay or avoid the need for surgery. Funding: National Institute for Health Research (NIHR), Association of Coloproctology of Great Britain and Ireland, Bowel and Cancer Research, Bowel Disease Research Foundation, Association of Upper Gastrointestinal Surgeons, British Association of Surgical Oncology, British Gynaecological Cancer Society, European Society of Coloproctology, NIHR Academy, Sarcoma UK, Vascular Society for Great Britain and Ireland, and Yorkshire Cancer Research

Use of micro CHP plants to support the local operation of electric heat pumps

Fig. 1. Global distribution of chytridiomycosis-associated amphibian species declines. Bar plots indicate the number (N) of declined species, grouped by continental area and classified by decline severity. Brazilian species are plotted separately from all other South American species (South America W); Mesoamerica includes Central America, Mexico, and the Caribbean Islands; and Oceania includes Australia and New Zealand. No declines have been reported in Asia. n, total number of declines by region. [Photo credits (clockwise from top left): Anaxyrus boreas, C. Brown, U.S. Geological Survey; Atelopus varius, B.G.; Salamandra salamandra, D. Descouens, Wikimedia Commons; Telmatobius sanborni, I.D.l.R; Cycloramphus boraceiensis, L.F.T.; Cardioglossa melanogaster, M.H.; and Pseudophryne corroboree, C. Doughty

Why Should We Preserve Fishless High Mountain Lakes?

High mountain lakes are originally fishless, although many have had introductions of non-native fish species, predominantly trout, and recently also minnows introduced by fishermen that use them as live bait. The extent of these introductions is general and substantial often involving many lakes over mountain ranges. Predation on native fauna by introduced fish involves profound ecological changes since fish occupy a higher trophic level that was previously inexistent. Fish predation produces a drastic reduction or elimination of autochthonous animal groups, such as amphibians and large macroinvertebrates in the littoral, and crustaceans in the plankton. These strong effects raise concerns for the conservation of high mountain lakes. In terms of individual species, those adapted to live in larger lakes have suffered a higher decrease in the size of their metapopulation. This ecological problem is discussed from a European perspective providing examples from two study areas: the Pyrenees and the Western Italian Alps. Species-specific studies are urgently needed to evaluate the conservation status of the more impacted species, together with conservation measures at continental and regional scales, through regulation, and at local scale, through restoration actions, aimed to stop further invasive species expansions and to restore the present situation. At different high mountain areas of the world, there have been restoration projects aiming to return lakes to their native fish-free status. In these areas autochthonous species that disappeared with the introduction of fish are progressively recovering their initial distribution when nearby fish-free lakes and ponds are available