Self-shrinkers with a rotational symmetry

In this paper we present a new family of non-compact properly embedded, self-shrinking, asymptotically conical, positive mean curvature ends $\Sigma^n\subseteq\mathbb{R}^{n+1}$ that are hypersurfaces of revolution with circular boundaries. These hypersurface families interpolate between the plane and half-cylinder in $\mathbb{R}^{n+1}$, and any rotationally symmetric self-shrinking non-compact end belongs to our family. The proofs involve the global analysis of a cubic-derivative quasi-linear ODE. We also prove the following classification result: a given complete, embedded, self-shrinking hypersurface of revolution $\Sigma^n$ is either a hyperplane $\mathbb{R}^{n}$, the round cylinder $\mathbb{R}\times S^{n-1}$ of radius $\sqrt{2(n-1)}$, the round sphere $S^n$ of radius $\sqrt{2n}$, or is diffeomorphic to an $S^1\times S^{n-1}$ (i.e. a "doughnut" as in [Ang], which when $n=2$ is a torus). In particular for self-shrinkers there is no direct analogue of the Delaunay unduloid family. The proof of the classification uses translation and rotation of pieces, replacing the method of moving planes in the absence of isometries.Comment: Trans. Amer. Math. Soc. (2011), to appear; 23 pages, 1 figur

Extraction of aqueous gold sols with styrene/2-vinylpyridine block copolymers in toluene

Polymers containing small noble-metal particles are of interest for catalysis and in the generation of optically tunable composites. The currently used process results in materials which are often difficult to process. A method is presented here for the direct transfer of small gold particles from an aqueous sol into a non-aqueous polymer solution (e.g. a block copolymer, see Figure) facilitating the formation of films

Zircon dissolution in a ductile shear zone, Monte Rosa granite gneiss, northern Italy

The sizes, distributions and shapes of zircon grains within variably deformed granite gneiss from the western Alps have been studied. Zircon shows numerous indicators of a metamorphic response in both the host gneiss and a 5 cm wide continuous ductile shear zone, within which the zircon grain sizes range from <1 µm to >50 µm. However, the very fine grain sizes are virtually absent from grain boundaries. Within this zone, zircons consistently have more rounded and embayed margins, which are interpreted as evidence of dissolution in response to fluid influx during shearing. Zircons are preferentially located near metamorphic muscovite in both the host gneiss and the shear zone and tend to show the poorest crystal shape, indicating that fluids linked to the formation and presence of muscovite may enhance both the crystallization of zircon and its subsequent dissolution. Larger zircon crystals typically show a brittle response to deformation when adjacent to phyllosilicates, with fractures consistently perpendicular to the (001) mica cleavage. The variety of metamorphic behaviour observed for zircon indicates that it may be highly reactive in sub-solidus mid-crustal metamorphic environments

Diffuse Galactic antimatter from faint thermonuclear supernovae in old stellar populations

Our Galaxy hosts the annihilation of a few $\times 10^{43}$ low-energy positrons every second. Radioactive isotopes capable of supplying such positrons are synthesised in stars, stellar remnants, and supernovae. For decades, however, there has been no positive identification of a main stellar positron source leading to suggestions that many positrons originate from exotic sources like the Galaxy's central super-massive black hole or dark matter annihilation. %, but such sources would not explain the recently-detected positron signal from the extended Galactic disk. Here we show that a single type of transient source, deriving from stellar populations of age 3-6 Gyr and yielding ~0.03 $M_\odot$ of the positron emitter $^{44}$Ti, can simultaneously explain the strength and morphology of the Galactic positron annihilation signal and the solar system abundance of the $^{44}$Ti decay product $^{44}$Ca. This transient is likely the merger of two low-mass white dwarfs, observed in external galaxies as the sub-luminous, thermonuclear supernova known as SN1991bg-like.Comment: 28 pages main text with 4 figures in preprint style; 26 pages of Supplementary Informatio

Transfusion strategies in bleeding critically ill adults : A clinical practice guideline from the European Society of Intensive Care Medicine: Endorsement by the Scandinavian Society of Anaesthesiology and Intensive Care Medicine

The Clinical Practice Committee of the Scandinavian Society of Anaesthesiology and Intensive Care Medicine endorses the clinical practice guideline Transfusion strategies in bleeding critically ill adults: a clinical practice guideline from the European Society of Intensive Care Medicine. This trustworthy clinical practice guideline serves as a useful decision aid for Nordic anaesthesiologists caring for critically ill patients with bleeding.Non peer reviewe

Surviving sepsis campaign : International guidelines for management of sepsis and septic shock in adults 2021-endorsement by the Scandinavian society of anaesthesiology and intensive care medicine

The Clinical Practice Committee of the Scandinavian Society of Anaesthesiology and Intensive Care Medicine endorses the clinical practice guideline Surviving sepsis campaign: international guidelines for management of sepsis and septic shock 2021. The guideline serves as a useful bedside decision aid for clinicians managing adults with suspected and confirmed septic shock and sepsis-associated organ dysfunction.Non peer reviewe