On unbounded bodies with finite mass: asymptotic behaviour

There is introduced a class of barotropic equations of state (EOS) which become polytropic of index $n = 5$ at low pressure. One then studies asymptotically flat solutions of the static Einstein equations coupled to perfect fluids having such an EOS. It is shown that such solutions, in the same manner as the vacuum ones, are conformally smooth or analytic at infinity, when the EOS is smooth or analytic, respectively.Comment: 6 page

Analysis of optical flow models in the framework of calculus of variations

In image sequence analysis, variational optical flow computations require the solution of a parameter dependent optimization problem with a data term and a regularizer. In this paper we study existence and uniqueness of the optimizers. Our studies rely on quasiconvex functionals on the spaces W¹,P(Ω, IRd), with p > 1, BV(Ω, IRd), BD(&Omeag;). The methods that are covered by our results include several existing techniques. Experiments are presented that illustrate the behavior of these approaches

The impact of the mixing properties within the Antarctic stratospheric vortex on ozone loss in spring

Calculations of equivalent length from an artificial advected tracer provide new insight into the isentropic transport processes occurring within the Antarctic stratospheric vortex. These calculations show two distinct regions of approximately equal area: a strongly mixed vortex core and a broad ring of weakly mixed air extending out to the vortex boundary. This broad ring of vortex air remains isolated from the core between late winter and midspring. Satellite measurements of stratospheric H2O confirm that the isolation lasts until at least mid-October. A three-dimensional chemical transport model simulation of the Antarctic ozone hole quantifies the ozone loss within this ring and demonstrates its isolation. In contrast to the vortex core, ozone loss in the weakly mixed broad ring is not complete. The reasons are twofold. First, warmer temperatures in the broad ring prevent continuous polar stratospheric cloud (PSC) formation and the associated chemical processing (i.e., the conversion of unreactive chlorine into reactive forms). Second, the isolation prevents ozone-rich air from the broad ring mixing with chemically processed air from the vortex core. If the stratosphere continues to cool, this will lead to increased PSC formation and more complete chemical processing in the broad ring. Despite the expected decline in halocarbons, sensitivity studies suggest that this mechanism will lead to enhanced ozone loss in the weakly mixed region, delaying the future recovery of the ozone hole

An optimal gap theorem

By solving the Cauchy problem for the Hodge-Laplace heat equation for $d$-closed, positive $(1, 1)$-forms, we prove an optimal gap theorem for K\"ahler manifolds with nonnegative bisectional curvature which asserts that the manifold is flat if the average of the scalar curvature over balls of radius $r$ centered at any fixed point $o$ is a function of $o(r^{-2})$. Furthermore via a relative monotonicity estimate we obtain a stronger statement, namely a `positive mass' type result, asserting that if $(M, g)$ is not flat, then $\liminf_{r\to \infty} \frac{r^2}{V_o(r)}\int_{B_o(r)}\mathcal{S}(y)\, d\mu(y)>0$ for any $o\in M$

Time-Independent Gravitational Fields

This article reviews, from a global point of view, rigorous results on time independent spacetimes. Throughout attention is confined to isolated bodies at rest or in uniform rotation in an otherwise empty universe. The discussion starts from first principles and is, as much as possible, self-contained.Comment: 47 pages, LaTeX, uses Springer cl2emult styl

Endpoint Estimates for N-dimensional Hardy Operators and Their Commutators

In this paper, it is proved that the higher dimensional Hardy operator is bounded from Hardy space to Lebesgue space. The endpoint estimate for the commutator generated by Hardy operator and (central) BMO function is also discussed.Comment: 8 page

Multidimensional Conservation Laws: Overview, Problems, and Perspective

Some of recent important developments are overviewed, several longstanding open problems are discussed, and a perspective is presented for the mathematical theory of multidimensional conservation laws. Some basic features and phenomena of multidimensional hyperbolic conservation laws are revealed, and some samples of multidimensional systems/models and related important problems are presented and analyzed with emphasis on the prototypes that have been solved or may be expected to be solved rigorously at least for some cases. In particular, multidimensional steady supersonic problems and transonic problems, shock reflection-diffraction problems, and related effective nonlinear approaches are analyzed. A theory of divergence-measure vector fields and related analytical frameworks for the analysis of entropy solutions are discussed.Comment: 43 pages, 3 figure

The masterpieces of John Forbes Nash Jr.

In this set of notes I follow Nash’s four groundbreaking works on real algebraic manifolds, on isometric embeddings of Riemannian manifolds and on the continuity of solutions to parabolic equations. My aim has been to stay as close as possible to Nash’s original arguments, but at the same time present them with a more modern language and notation. Occasionally I have also provided detailed proofs of the points that Nash leaves to the reader

A preliminary randomized double blind placebo-controlled trial of intravenous immunoglobulin for Japanese encephalitis in Nepal

BACKGROUND: Japanese encephalitis (JE) virus (JEV) is a mosquito-borne flavivirus found across Asia that is closely related to West Nile virus. There is no known antiviral treatment for any flavivirus. Results from in vitro studies and animal models suggest intravenous immunoglobulin (IVIG) containing virus-specific neutralizing antibody may be effective in improving outcome in viral encephalitis. IVIG's anti-inflammatory properties may also be beneficial. METHODOLOGY/PRINCIPAL FINDINGS: We performed a pilot feasibility randomized double-blind placebo-controlled trial of IVIG containing anti-JEV neutralizing antibody (ImmunoRel, 400mg/kg/day for 5 days) in children with suspected JE at two sites in Nepal; we also examined the effect on serum neutralizing antibody titre and cytokine profiles. 22 children were recruited, 13 of whom had confirmed JE; 11 received IVIG and 11 placebo, with no protocol violations. One child (IVIG group) died during treatment and two (placebo) subsequently following hospital discharge. Overall, there was no difference in outcome between treatment groups at discharge or follow up. Passive transfer of anti-JEV antibody was seen in JEV negative children. JEV positive children treated with IVIG had JEV-specific neutralizing antibody titres approximately 16 times higher than those treated with placebo (p=0.2), which was more than could be explained by passive transfer alone. IL-4 and IL-6 were higher in the IVIG group. CONCLUSIONS/SIGNIFICANCE: A trial of IVIG for JE in Nepal is feasible. IVIG may augment the development of neutralizing antibodies in JEV positive patients. IVIG appears an appealing option for JE treatment that warrants further study. TRIAL REGISTRATION: ClinicalTrials.gov NCT01856205