A Basis Theorem for Perfect Sets

We show that if there is a nonconstructible real, then every perfect set has a nonconstructible element, answering a question of K. Prikry. This is a specific instance of a more general theorem giving a sufficient condition on a pair M ⊂ N of models of set theory implying that every perfect set in N has an element in N which is not in M

Berezinskii-Kosterlitz-Thouless transitions in an easy-plane ferromagnetic superfluid

A two-dimensional (2D) spin-1 Bose gas exhibits two Berezenskii-Kosterlitz-Thouless (BKT) transitions in the easy-plane ferromagnetic phase. The higher temperature transition is associated with superfluidity of the mass current determined predominantly by a single spin component. The lower temperature transition is associated with superfluidity of the axial spin current, quasi-long range order of the transverse spin density and binding of polar-core spin vortices (PCVs). Above the spin BKT temperature, the component circulations that make up each PCV spatially separate, suggesting possible deconfinement analogous to quark deconfinement in high energy physics. Intercomponent interactions give rise to superfluid drag between the spin components, which we calculate analytically at zero temperature. We present the mass/spin superfluid phase diagram as a function of quadratic Zeeman energy $q$. At $q=0$ the system is in an isotropic spin phase with $\mathrm{SO}(3)$ symmetry. Here the fluid response exhibits a system size dependence, suggesting the absence of a BKT transition. Despite this, for finite systems the decay of spin correlations changes from exponential to algebraic as the temperature is decreased.Comment: 4 pages + refs, 3 figures. Interpretation of Fig. 3 results has changed since v

Intramolecular and Lattice Melting in n-Alkane Monolayers: An Analog of Melting in Lipid Bilayers

URL:http://link.aps.org/doi/10.1103/PhysRevLett.83.2362 DOI:10.1103/PhysRevLett.83.2362Molecular dynamics (MD) simulations and neutron diffraction experiments have been performed on n-dotriacontane ( n-C32D66) monolayers adsorbed on a graphite basal- plane surface. The diffraction experiments show little change in the crystalline monolayer structure up to a temperature of ~350K above which a large thermal expansion and decrease in coherence length occurs. The MD simulations provide evidence that this behavior is due to a phase transition in the monolayer in which intramolecular and translational order are lost simultaneously. This melting transition is qualitatively similar to the gel-to-fluid transition found in bilayer lipid membranes.Acknowledgment is made to the U.S. National Science Foundation under Grants No. DMR-9314235 and No. DMR-9802476, the Missouri University Research Reactor, and to the donors of The Petroleum Research Fund, administered by the ACS, for partial support of this research. We thank L. Criswell for assistance with the figures

Centrifugal melt spinning of polyvinylpyrrolidone (PVP)/triacontene copolymer fibres

Polyvinylpyrrolidone/1-triacontene (PVP/TA) copolymer fibre webs produced by centrifugal melt spinning were studied to determine the influence of jet rotation speed on morphology and internal structure as well as their potential utility as adsorbent capture media for disperse dye effluents. Fibres were produced at 72 C with jet head rotation speeds from 7000 to 15,000 r min-1. The fibres were characterised by means of SEM, XRD and DSC. Adsorption behaviour was investigated by means of an isothermal bottle point adsorption study using a commercial disperse dye, Dianix AC-E. Through centrifugal spinning nanofibers and microfibers could be produced with individual fibres as fine as 200–300 nm and mean fibre diameters of ca. 1–2 lm. The PVP/TA fibres were mechanically brittle with characteristic brittle tensile fracture regions observed at the fibre ends. DSC and XRD analyses suggested that this brittleness was linked to the graft chain crystallisation where the PVP/TA was in the form of a radial brush copolymer. In this structure, the triacontene branches interlock and form small lateral crystals around an amorphous backbone. As an adsorbent, the PVP/TA fibres were found to adsorb 35.4 mg g-1 compared to a benchmark figure of 30.0 mg g-1 for a granular-activated carbon adsorbent under the same application conditions. PVP/TA is highly hydrophobic and adsorbs disperse dyes through the strong ‘‘hydrophobic bonding’’ interaction. Such fibrous assemblies may have applications in the targeted adsorption and separation of non-polar species from aqueous or polar environments

Molecular imaging of inflammation and intraplaque vasa vasorum: A step forward to identification of vulnerable plaques?

Current developments in cardiovascular biology and imaging enable the noninvasive molecular evaluation of atherosclerotic vascular disease. Intraplaque neovascularization sprouting from the adventitial vasa vasorum has been identified as an independent predictor of intraplaque hemorrhage and plaque rupture. These intraplaque vasa vasorum result from angiogenesis, most likely under influence of hypoxic and inflammatory stimuli. Several molecular imaging techniques are currently available. Most experience has been obtained with molecular imaging using positron emission tomography and single photon emission computed tomography. Recently, the development of targeted contrast agents has allowed molecular imaging with magnetic resonance imaging, ultrasound and computed tomography. The present review discusses the use of these molecular imaging techniques to identify inflammation and intraplaque vasa vasorum to identify vulnerable atherosclerotic plaques at risk of rupture and thrombosis. The available literature on molecular imaging techniques and molecular targets associated with inflammation and angiogenesis is discussed, and the clinical applications of molecular cardiovascular imaging and the use of molecular techniques for local drug delivery are addressed