A Probabilistic proof of the breakdown of Besov regularity in LL-shaped domains

{We provide a probabilistic approach in order to investigate the smoothness of the solution to the Poisson and Dirichlet problems in $L$-shaped domains. In particular, we obtain (probabilistic) integral representations for the solution. We also recover Grisvard's classic result on the angle-dependent breakdown of the regularity of the solution measured in a Besov scale

Eggshell membrane: A possible new natural therapeutic for joint and connective tissue disorders. Results from two open-label human clinical studies

Kevin J Ruff1, Dale P DeVore2, Michael D Leu3, Mark A Robinson41ESM Technologies, LLC, Carthage, MO, USA; 2Membrell, LLC, Carthage, MO, USA; 3Private Practice, Jenks, OK, USA; 4Robinson Family Health Center, Carthage, MO, USABackground: Natural Eggshell Membrane (NEM®) is a novel dietary supplement that contains naturally occurring glycosaminoglycans and proteins essential for maintaining healthy joint and connective tissues. Two single center, open-label human clinical studies were conducted to evaluate the efficacy and safety of NEM® as a treatment for pain and inflexibility associated with joint and connective tissue disorders. Methods: Eleven (single-arm trial) and 28 (double-arm trial) patients received oral NEM® 500 mg once daily for four weeks. The primary outcome measure was to evaluate the change in general pain associated with the treatment joints/areas (both studies). In the single-arm trial, range of motion (ROM) and related ROM-associated pain was also evaluated. The primary treatment response endpoints were at seven and 30 days. Both clinical assessments were performed on the intent-to-treat (ITT) population within each study.Results: Single-arm trial: Supplementation with NEM® produced a significant treatment response at seven days for flexibility (27.8% increase; P = 0.038) and at 30 days for general pain (72.5% reduction; P = 0.007), flexibility (43.7% increase; P = 0.006), and ROM-associated pain (75.9% reduction; P = 0.021). Double-arm trial: Supplementation with NEM® produced a significant treatment response for pain at seven days for both treatment arms (X: 18.4% reduction; P = 0.021. Y: 31.3% reduction; P = 0.014). There was no clinically meaningful difference between treatment arms at seven days, so the Y arm crossed over to the X formulation for the remainder of the study. The significant treatment response continued through 30 days for pain (30.2% reduction; P = 0.0001). There were no adverse events reported during either study and the treatment was reported to be well tolerated by study participants. Conclusions: Natural Eggshell Membrane (NEM®) is a possible new effective and safe therapeutic option for the treatment of pain and inflexibility associated with joint and connective tissue (JCT) disorders. Supplementation with NEM®, 500 mg taken once daily, significantly reduced pain, both rapidly (seven days) and continuously (30 days). It also showed clinically meaningful results from a brief responder analysis, demonstrating that significant proportions of treated patients may be helped considerably from NEM® supplementation. The Clinical Trial Registration numbers for these trials are: NCT00750230 and NCT00750854.Keywords: arthritis, pain, stiffness, eggshell membrane, joint, connective tissue, complimentary, alternativ

Future Prospects: Deep Imaging of Galaxy Outskirts using Telescopes Large and Small

The Universe is almost totally unexplored at low surface brightness levels. In spite of great progress in the construction of large telescopes and improvements in the sensitivity of detectors, the limiting surface brightness of imaging observations has remained static for about forty years. Recent technical advances have at last begun to erode the barriers preventing progress. In this Chapter we describe the technical challenges to low surface brightness imaging, describe some solutions, and highlight some relevant observations that have been undertaken recently with both large and small telescopes. Our main focus will be on discoveries made with the Dragonfly Telephoto Array (Dragonfly), which is a new telescope concept designed to probe the Universe down to hitherto unprecedented low surface brightness levels. We conclude by arguing that these discoveries are probably only scratching the surface of interesting phenomena that are observable when the Universe is explored at low surface brightness levels.Comment: 27 pages, 10 figures, Invited review, Book chapter in "Outskirts of Galaxies", Eds. J. H. Knapen, J. C. Lee and A. Gil de Paz, Astrophysics and Space Science Library, Springer, in pres

Anisotropic smoothness classes : from finite element approximation to image models

We propose and study quantitative measures of smoothness which are adapted to anisotropic features such as edges in images or shocks in PDE's. These quantities govern the rate of approximation by adaptive finite elements, when no constraint is imposed on the aspect ratio of the triangles, the simplest examples of such quantities are based on the determinant of the hessian of the function to be approximated. Since they are not semi-norms, these quantities cannot be used to define linear function spaces. We show that they can be well defined by mollification when the function to be approximated has jump discontinuities along piecewise smooth curves. This motivates for using them in image processing as an alternative to the frequently used record variation semi-norm which does not account for the geometric smoothness of the edges.Comment: 24 pages, 2 figure

Precision Tests of the Standard Model

30 páginas, 11 figuras, 11 tablas.-- Comunicación presentada al 25º Winter Meeting on Fundamental Physics celebrado del 3 al 8 de MArzo de 1997 en Formigal (España).Precision measurements of electroweak observables provide stringent tests of the Standard Model structure and an accurate determination of its parameters. An overview of the present experimental status is presented.This work has been supported in part by CICYT (Spain) under grant No. AEN-96-1718.Peer reviewe

Sparse Deterministic Approximation of Bayesian Inverse Problems

We present a parametric deterministic formulation of Bayesian inverse problems with input parameter from infinite dimensional, separable Banach spaces. In this formulation, the forward problems are parametric, deterministic elliptic partial differential equations, and the inverse problem is to determine the unknown, parametric deterministic coefficients from noisy observations comprising linear functionals of the solution. We prove a generalized polynomial chaos representation of the posterior density with respect to the prior measure, given noisy observational data. We analyze the sparsity of the posterior density in terms of the summability of the input data's coefficient sequence. To this end, we estimate the fluctuations in the prior. We exhibit sufficient conditions on the prior model in order for approximations of the posterior density to converge at a given algebraic rate, in terms of the number $N$ of unknowns appearing in the parameteric representation of the prior measure. Similar sparsity and approximation results are also exhibited for the solution and covariance of the elliptic partial differential equation under the posterior. These results then form the basis for efficient uncertainty quantification, in the presence of data with noise

Structure and Dynamics of the Sun's Open Magnetic Field

The solar magnetic field is the primary agent that drives solar activity and couples the Sun to the Heliosphere. Although the details of this coupling depend on the quantitative properties of the field, many important aspects of the corona - solar wind connection can be understood by considering only the general topological properties of those regions on the Sun where the field extends from the photosphere out to interplanetary space, the so-called open field regions that are usually observed as coronal holes. From the simple assumptions that underlie the standard quasi-steady corona-wind theoretical models, and that are likely to hold for the Sun, as well, we derive two conjectures on the possible structure and dynamics of coronal holes: (1) Coronal holes are unique in that every unipolar region on the photosphere can contain at most one coronal hole. (2) Coronal holes of nested polarity regions must themselves be nested. Magnetic reconnection plays the central role in enforcing these constraints on the field topology. From these conjectures we derive additional properties for the topology of open field regions, and propose several observational predictions for both the slowly varying and transient corona/solar wind.Comment: 26 pages, 6 figure