Functional characterizations of trace spaces in Lipschitz domains

Using a factorization theorem of Douglas, we prove functional characterizations of trace spaces $H^s(\partial \Omega)$ involving a family of positive self-adjoint operators. Our method is based on the use of a suitable operator by taking the trace on the boundary $\partial \Omega$ of a bounded Lipschitz domain $\Omega \subset \mathbb R^d$ and applying Moore--Penrose pseudo-inverse properties together with a special inner product on $H^1(\Omega)$. Moreover, generalized results of the Moore--Penrose pseudo-inverse are also established.Comment: This is a preprint of a paper whose final and definite form is with 'Banach J. Math. Anal.', ISSN: 1735-8787, available at [https://projecteuclid.org/info/euclid.bjma]. Submitted 21-Aug-2018; Article accepted on 30-Nov-201

Study of the corrosion behavior of lead-free α-brass (CuZn21Si3P) and (α+β)-brass (CuZn36Pb2As) in simulated drinking water and tap water

   Corrosion behavior and quantification of Zn and Cu ions release of two types of brass, (α+β)-brass (CuZn36Pb2As) and lead-free α-brass (CuZn21Si3P) were studied in tap water (City of Rabat) and simulated drinking water. Stationary electrochemical methods of potential monitoring and polarization curves  and trans-methods showed that α-brass resists corrosion better than (α + β)-brass, This is due to the presence of elements such as Cu, Ni, Si, and Al which improve the protective performance of the oxide film, and temperature affects both alloy’s electrochemical behavior in the two mediums. It is more significant in tap water than in simulated drinking water. Inductively Coupled Plasma (ICP) spectroscopy was also used to follow the evolution of Cu2+ and Zn2+ ion concentration as a function of time and to determine dezincification factors, which are found to be greater than 1 and increase as a function of time in both media, their values are also significantly higher in drinking water than in simulated water. After a long time of exposure with agitation (28 days), SEM micrographs confirm the results obtained from the polarization and impedance curves, as well as from the ICP study. The tap water showed more corrosion than the simulated drinking water for both alloys. This may be due to the presence of solid particles in the drinking water, such as sand or limestone, which may affect substrates surface by other phenomenon as erosion

Spectral Energy Distributions of Be and Other Massive Stars

We present spectrophotometric data from 0.4 to 4.2 microns for bright, northern sky, Be stars and several other types of massive stars. Our goal is to use these data with ongoing, high angular resolution, interferometric observations to model the density structure and sky orientation of the gas surrounding these stars. We also present a montage of the H-alpha and near-infrared emission lines that form in Be star disks. We find that a simplified measurement of the IR excess flux appears to be correlated with the strength of emission lines from high level transitions of hydrogen. This suggests that the near-IR continuum and upper level line fluxes both form in the inner part of the disk, close to the star.Comment: 2010, PASP, 122, 37

Amyloid β peptides modify the expression of antioxidant repair enzymes and a potassium channel in the septohippocampal system

Alzheimer\u27s disease (AD) is a progressive, neurodegenerative brain disorder characterized by extracellular accumulations of amyloid β (Aβ) peptides, intracellular accumulation of abnormal proteins, and early loss of basal forebrain neurons. Recent studies have indicated that the conformation of Aβ is crucial for neuronal toxicity, with intermediate misfolded forms such as oligomers being more toxic than the final fibrillar forms. Our previous work shows that Aβ blocks the potassium (K(+)) currents IM and IA in septal neurons, increasing firing rates, diminishing rhythmicity and firing coherence. Evidence also suggests that oxidative stress (OS) plays a role in AD pathogenesis. Thus we wished to determine the effect of oligomeric and fibrillar forms of Aβ₁₋₄₂ on septohippocampal damage, oxidative damage, and dysfunction in AD. Oligomeric and fibrillar forms of Aβ₁₋₄₂ were injected into the CA1 region of the hippocampus in live rats. The rats were sacrificed 24 hours and 1 month after Aβ or sham injection to additionally evaluate the temporal effects. The expression levels of the K(+) voltage-gated channel, KQT-like subfamily, member 2 (KCNQ₂) and the OS-related genes superoxide dismutase 1, 8-oxoguanine DNA glycosylase, and monamine oxidase A, were analyzed in the hippocampus, medial, and lateral septum. Our results show that both forms of Aβ exhibit time-dependent differential modulation of OS and K(+) channel genes in the analyzed regions. Importantly, we demonstrate that Aβ injected into the hippocampus triggered changes in gene expression in anatomical regions distant from the injection site. Thus the Aβ effect was transmitted to anatomically separate sites, because of the functional coupling of the brain structures

MOST detects corotating bright spots on the mid-O type giant {\xi} Persei

We have used the MOST (Microvariability and Oscillations of STars) microsatellite to obtain four weeks of contiguous high-precision broadband visual photometry of the O7.5III(n)((f)) star {\xi} Persei in November 2011. This star is well known from previous work to show prominent DACs (Discrete Absorption Components) on time-scales of about 2 d from UV spectroscopy and NRP (Non Radial Pulsation) with one (l = 3) p-mode oscillation with a period of 3.5 h from optical spectroscopy. Our MOST-orbit (101.4 min) binned photometry fails to reveal any periodic light variations above the 0.1 mmag 3-sigma noise level for periods of hours, while several prominent Fourier peaks emerge at the 1 mmag level in the two-day period range. These longer-period variations are unlikely due to pulsations, including gravity modes. From our simulations based upon a simple spot model, we deduce that we are seeing the photometric modulation of several co-rotating bright spots on the stellar surface. In our model, the starting times (random) and lifetimes (up to several rotations) vary from one spot to another yet all spots rotate at the same period of 4.18 d, the best-estimated rotation period of the star. This is the first convincing reported case of co-rotating bright spots on an O star, with important implications for drivers of the DACs (resulting from CIRs - Corotating Interaction Regions) with possible bright-spot generation via a breakout at the surface of a global magnetic field generated by a subsurface convection zone.Comment: 9 pages, 4 figures, 2 tables, MNRAS in pres

Effects of a Composite Endomycorrhizal Inoculum on Olive Cuttings under the Greenhouse Conditions

This study was carried out in a nursery to evaluate the impact of mycorrhizal fungi on the cutting's root growth, and root colonization of a Moroccan olive variety ‘Picholine Marocaine' under greenhouse conditions during 2 years of cultivation. The results revealed that the inoculation with a composite inoculum of arbuscular mycorrhizal fungi (AMF) stimulated an early root formation and high development of vegetative shoots in inoculated cuttings respectively, 35 days (50 days in the control plots) and 40 days (60 days in the control plots) after their culture. The progressive establishment of mycorrhizal symbiosis in the roots of the inoculated plants showed that the root and vegetative masses were respectively 24 g and 19.5 g two years after inoculation. The average height and the leave's number of the inoculated plants relative to the control were respectively s 42/ 12 cm and 145/12. The newly formed roots were mycorrhizal and present different structures characteristic of AMF: arbuscules, vesicles, hyphae and spores, whose frequency and intensity reached 90% and 75% two years after cuttings cultivation. The arbuscular and vesicular contents and the number of spores were 67%, 96% and 212 spores/ 100 g of soil respectively. The fourteen species of mycorrhizal fungi isolated from the rhizosphere belong to 4 genera (Glomus, Acaulospora, Gigaspora, and Scutellospora) and three families (Glomaceae, Acaulosporaceae and Gigasporacea).The Glomus genus was the most dominant (65%) followed by the Gigaspora genus (22%). Glomus intraradices, Gigaspora sp.2, Glomus versiformes are the most abundant species, their frequency of occurrence are respectively 30%, 21% and 16%

Probing the Inner Disk Emission of the Herbig Ae Stars HD 163296 and HD 190073

This is the author accepted manuscript. The final version is available from American Astronomical Society / IOP Publishing via the DOI in this record.The physical processes occurring within the inner few astronomical units of proto-planetary disks surrounding Herbig Ae stars are crucial to setting the environment in which the outer planet-forming disk evolves and put critical constraints on the processes of accretion and planet migration. We present the most complete published sample of high angular resolution H- and K-band observations of the stars HD 163296 and HD 190073, including 30 previously unpublished nights of observations of the former and 45 nights of the latter with the CHARA long-baseline interferometer, in addition to archival VLTI data. We confirm previous observations suggesting significant near-infrared emission originates within the putative dust evaporation front of HD 163296 and show this is the case for HD 190073 as well. The H- and K-band sizes are the same within (3±3)% for HD 163296 and within (6±10)% for HD 190073. The radial surface brightness profiles for both disks are remarkably Gaussian-like with little or no sign of the sharp edge expected for a dust evaporation front. Coupled with spectral energy distribution analysis, our direct measurements of the stellar flux component at H and K bands suggest that HD 190073 is much younger (<400 kyr) and more massive (~5.6 M⊙) than previously thought, mainly as a consequence of the new Gaia distance (891 pc).JDM and BRS acknowledge support from NSF-AST 1506540 and AA acknowledges support from NSF-AST 1311698. CLD, AK, and SK acknowledge support from the ERC Starting Grant “ImagePlanetFormDiscs” (Grant Agreement No. 639889), STFC Rutherford fellowship/grant (ST/J004030/1, ST/K003445/1) and Philip Leverhulme Prize (PLP2013-110). FB acknowledges support from NSF-AST 1210972 and 1445935. MS acknowledges support by the NASA Origins of Solar Systems grant NAG5-9475, and NASA Astrophysics Data Program contract NNH05CD30C. The CHARA Array is supported by the National Science Foundation under Grant No. AST-1211929, AST-1636624, and AST-1715788. Institutional support has been provided from the GSU College of Arts and Sciences and the GSU Office of the Vice President for Research and Economic Development

The H-band Emitting Region of the Luminous Blue Variable P Cygni: Spectrophotometry and Interferometry of the Wind

This is the final version of the article. Available from American Astronomical Society / IOP Publishing via the DOI in this record.We present the first high angular resolution observations in the near-infrared H band (1.6 μm) of the luminous blue variable star P Cygni. We obtained six-telescope interferometric observations with the CHARA Array and the MIRC beam combiner. These show that the spatial flux distribution is larger than expected for the stellar photosphere. A two-component model for the star (uniform disk) plus a halo (two-dimensional Gaussian) yields an excellent fit of the observations, and we suggest that the halo corresponds to flux emitted from the base of the stellar wind. This wind component contributes about 45% of the H-band flux and has an angular FWHM = 0.96 mas, compared to the predicted stellar diameter of 0.41 mas. We show several images reconstructed from the interferometric visibilities and closure phases, and they indicate a generally spherical geometry for the wind. We also obtained near-infrared spectrophotometry of P Cygni from which we derive the flux excess compared to a purely photospheric spectral energy distribution. The H-band flux excess matches that from the wind flux fraction derived from the two-component fits to the interferometry. We find evidence of significant near-infrared flux variability over the period from 2006 to 2010 that appears similar to the variations in the Hα emission flux from the wind.We acknowledge with thanks the variable star observations from the AAVSO International Database contributed by observers worldwide and used in this research. Support for Ritter Astrophysical Research Center during the time of the observations was provided by the National Science Foundation Program for Research and Education with Small Telescopes (NSF-PREST) under grant AST-0440784 (N.D.M.). This work was also supported by the National Science Foundation under grants AST-0606861 and AST-1009080 (D.R.G.). N.D.R. gratefully acknowledges his current CRAQ postdoctoral fellowship. We are grateful for the insightful comments of A. F. J. Moffat that improved portions of the paper, discussions with Paco Najarro and Luc Dessart about spectroscopic modeling of P Cygni, and support of the MIRC 6 telescope beam combiner by Ettore Pedretti. Institutional support has been provided by the GSU College of Arts and Sciences and by the Research Program Enhancement fund of the Board of Regents of the University System of Georgia, administered through the GSU Office of the Vice President for Research. Operational funding for the CHARA Array is provided by the GSU College of Arts and Sciences, by the National Science Foundation through grants AST-0606958 and AST-0908253, by the W. M. Keck Foundation, and by the NASA Exoplanet Science Institute. We thank the Mount Wilson Institute for providing infrastructure support at Mount Wilson Observatory. The CHARA Array, operated by Georgia State University, was built with funding provided by the National Science Foundation, Georgia State University, the W. M. Keck Foundation, and the David and Lucile Packard Foundation. This research was conducted in part using the Mimir instrument, jointly developed at Boston University and Lowell Observatory and supported by NASA, NSF, and the W. M. Keck Foundation. J.D.M. acknowledges University of Michigan and NSF AST-0707927 for support of MIRC construction and observations. D.P.C. acknowledges support under NSF AST-0907790 to Boston University. We gratefully acknowledge all of this support. This research has made use of the SIMBAD database operated at CDS, Strasbourg, France

Protein Pattern Formation

Protein pattern formation is essential for the spatial organization of many intracellular processes like cell division, flagellum positioning, and chemotaxis. A prominent example of intracellular patterns are the oscillatory pole-to-pole oscillations of Min proteins in \textit{E. coli} whose biological function is to ensure precise cell division. Cell polarization, a prerequisite for processes such as stem cell differentiation and cell polarity in yeast, is also mediated by a diffusion-reaction process. More generally, these functional modules of cells serve as model systems for self-organization, one of the core principles of life. Under which conditions spatio-temporal patterns emerge, and how these patterns are regulated by biochemical and geometrical factors are major aspects of current research. Here we review recent theoretical and experimental advances in the field of intracellular pattern formation, focusing on general design principles and fundamental physical mechanisms.Comment: 17 pages, 14 figures, review articl