Detection of tobacco smoke deposition by hyperpolarized krypton-83 MRI

Despite the importance of the tobacco smoke particulate matter in the lungs to the etiology of pulmonary disease in cigarette smokers, little is currently known about the spatial distribution of particle deposition or the persistence of the resulting deposits in humans, and no satisfactory technique currently exists to directly observe tobacco smoke condensate in airways. In this proof-of-principle work, hyperpolarized (hp) 83Kr MRI and NMR spectroscopy are introduced as probes for tobacco smoke deposition in porous media. A reduction in the hp-83Kr longitudinal (T1) relaxation of up to 95% under near-ambient humidity, pressure and temperature conditions was observed when the krypton gas was brought into contact with surfaces that had been exposed to cigarette smoke. This smoke-induced acceleration of the 83Kr self-relaxation was observed for model glass surfaces that, in some experiments, were coated with bovine lung surfactant extract. However, a similar effect was not observed with hp-(129)Xe indicating that the 83Kr sensitivity to smoke deposition was not caused by paramagnetic species but rather by quadrupolar relaxation due to high adsorption affinity for the smoke deposits. The 83Kr T1 differences between smoke-treated and untreated surfaces were sufficient to produce a strong contrast in variable flip angle FLASH hp-83Kr MRI, suggesting that hp-83Kr may be a promising contrast agent for in vivo pulmonary MRI.     

Uniqueness of isometric immersions with the same mean curvature

Motivated by the quasi-local mass problem in general relativity, we study the rigidity of isometric immersions with the same mean curvature into a warped product space. As a corollary of our main result, two star-shaped hypersurfaces in a spatial Schwarzschild or AdS-Schwarzschild manifold with nonzero mass differ only by a rotation if they are isometric and have the same mean curvature. We also prove similar results if the mean curvature condition is replaced by an ${\sigma }_2$-curvature condition.     

Duality and interpolation of anisotropic Triebel–Lizorkin spaces

We study properties of anisotropic Triebel–Lizorkin spaces associated with general expansive dilations and doubling measures on 83h78163/209_2007_216_Article_IEq1.gif" alt="$${\mathbb{R}}^n$$" align="middle" border="0"> using wavelet transforms. This paper is a continuation of (Bownik in J Geom Anal 2007, to appear, Trans Am Math Soc 358:1469–1510, 2006), where we generalized the isotropic methods of dyadic 83h78163/209_2007_216_Article_IEq2.gif" alt="$$\varphi$$" align="middle" border="0"> -transforms of Frazier and Jawerth (J Funct Anal 93:34–170, 1990) to non-isotropic settings. By working at the level of sequence spaces, we identify the duals of anisotropic Triebel–Lizorkin spaces. We also obtain several real and complex interpolation results for these spaces. The author was partially supported by the NSF grants DMS-0441817 and DMS-0653881. The author wishes to thank Michael Frazier and Dachun Yang for valuable comments and discussions on this work.     

A remark about static space times

We discuss a differential equation, whose unknowns are a function and a Riemannian metric. This equation occurs both in general relativity (static space times) and in the study of the space of Riemannian metrics on a manifold (singularities of the map from the space of metrics into the space of functions, which assigns to any metric its scalar curvature).     

Local foliations and optimal regularity of Einstein spacetimes

We investigate the local regularity of pointed spacetimes, that is, time-oriented Lorentzian manifolds in which a point and a future-oriented, unit timelike vector (an observer) are selected. Our main result covers the class of Einstein vacuum spacetimes. Under curvature and injectivity bounds only, we establish the existence of a local coordinate chart defined in a ball with definite size in which the metric coefficients have optimal regularity. The proof is based on quantitative estimates for, on one hand, a constant mean curvature (CMC) foliation by spacelike hypersurfaces defined locally near the observer and, on the other hand, the metric in local coordinates that are spatially harmonic in each CMC slice. The results and techniques in this paper should be useful in the context of general relativity for investigating the long-time behavior of solutions to the Einstein equations.     

Uniqueness results for nonlocal Hamilton-Jacobi equations

We are interested in nonlocal eikonal equations describing the evolution of interfaces moving with a nonlocal, non-monotone velocity. For these equations, only the existence of global-in-time weak solutions is available in some particular cases. In this paper, we propose a new approach for proving uniqueness of the solution when the front is expanding. This approach simplifies and extends existing results for dislocation dynamics. It also provides the first uniqueness result for a Fitzhugh-Nagumo system. The key ingredients are some new perimeter estimates for the evolving fronts as well as some uniform interior cone property for these fronts.     

Gravitational waves without gravitons

The radiation connection induced on an isotropic hypersurface of a Lorentz manifold is described. Consequences for the energy tensor in Einstein field equation are analyzed. A cosmological interpretation is proposed.