Existence of immersed spheres minimizing curvature functionals in compact 3-manifolds

We study curvature functionals for immersed 2-spheres in a compact, three-dimensional Riemannian manifold M. Under the assumption that the sectional curvature of M is strictly positive, we prove the existence of a smoothly immersed sphere minimizing the L^{2} integral of the second fundamental form. Assuming instead that the sectional curvature is less than or equal to 2, and that there exists a point in M with scalar curvature bigger than 6, we obtain a smooth 2-sphere minimizing the integral of 1/4|H|^{2} +1, where H is the mean curvature vector

Respiratory Insufficiency Correlated Strongly with Mortality of Rodents Infected with West Nile Virus

West Nile virus (WNV) disease can be fatal for high-risk patients. Since WNV or its antigens have been identified in multiple anatomical locations of the central nervous system of persons or rodent models, one cannot know where to investigate the actual mechanism of mortality without careful studies in animal models. In this study, depressed respiratory functions measured by plethysmography correlated strongly with mortality. This respiratory distress, as well as reduced oxygen saturation, occurred beginning as early as 4 days before mortality. Affected medullary respiratory control cells may have contributed to the animals' respiratory insufficiency, because WNV antigen staining was present in neurons located in the ventrolateral medulla. Starvation or dehydration would be irrelevant in people, but could cause death in rodents due to lethargy or loss of appetite. Animal experiments were performed to exclude this possibility. Plasma ketones were increased in moribund infected hamsters, but late-stage starvation markers were not apparent. Moreover, daily subcutaneous administration of 5% dextrose in physiological saline solution did not improve survival or other disease signs. Therefore, infected hamsters did not die from starvation or dehydration. No cerebral edema was apparent in WNV- or sham-infected hamsters as determined by comparing wet-to-total weight ratios of brains, or by evaluating blood-brain-barrier permeability using Evans blue dye penetration into brains. Limited vasculitis was present in the right atrium of the heart of infected hamsters, but abnormal electrocardiograms for several days leading up to mortality did not occur. Since respiratory insufficiency was strongly correlated with mortality more than any other pathological parameter, it is the likely cause of death in rodents. These animal data and a poor prognosis for persons with respiratory insufficiency support the hypothesis that neurological lesions affecting respiratory function may be the primary cause of human WNV-induced death

Topological and geometrical restrictions, free-boundary problems and self-gravitating fluids

Let (P1) be certain elliptic free-boundary problem on a Riemannian manifold (M,g). In this paper we study the restrictions on the topology and geometry of the fibres (the level sets) of the solutions f to (P1). We give a technique based on certain remarkable property of the fibres (the analytic representation property) for going from the initial PDE to a global analytical characterization of the fibres (the equilibrium partition condition). We study this analytical characterization and obtain several topological and geometrical properties that the fibres of the solutions must possess, depending on the topology of M and the metric tensor g. We apply these results to the classical problem in physics of classifying the equilibrium shapes of both Newtonian and relativistic static self-gravitating fluids. We also suggest a relationship with the isometries of a Riemannian manifold.Comment: 36 pages. In this new version the analytic representation hypothesis is proved. Please address all correspondence to D. Peralta-Sala

Section Extension from Hyperbolic Geometry of Punctured Disk and Holomorphic Family of Flat Bundles

The construction of sections of bundles with prescribed jet values plays a fundamental role in problems of algebraic and complex geometry. When the jet values are prescribed on a positive dimensional subvariety, it is handled by theorems of Ohsawa-Takegoshi type which give extension of line bundle valued square-integrable top-degree holomorphic forms from the fiber at the origin of a family of complex manifolds over the open unit 1-disk when the curvature of the metric of line bundle is semipositive. We prove here an extension result when the curvature of the line bundle is only semipositive on each fiber with negativity on the total space assumed bounded from below and the connection of the metric locally bounded, if a square-integrable extension is known to be possible over a double point at the origin. It is a Hensel-lemma-type result analogous to Artin's application of the generalized implicit function theorem to the theory of obstruction in deformation theory. The motivation is the need in the abundance conjecture to construct pluricanonical sections from flatly twisted pluricanonical sections. We also give here a new approach to the original theorem of Ohsawa-Takegoshi by using the hyperbolic geometry of the punctured open unit 1-disk to reduce the original theorem of Ohsawa-Takegoshi to a simple application of the standard method of constructing holomorphic functions by solving the d-bar equation with cut-off functions and additional blowup weight functions

Light-weighting of automotive and aerospace transport

The automotive and aerospace industries are keen to reduce their environmental impact and so have looked to move to lightweight materials. This creates issues in terms of joining, using and disposing of dissimilar materials. Oxford Brookes has therefore worked with national and multi-national companies in the adhesive, materials, automotive and aerospace industries to try to solve these problems. This has resulted in high quality research publications, innovative test equipment, improved numerical methods, novel designs, design guidelines, manufacturing procedures, British Standards, patents, commercial products and further funding. The impact of the work has global safety, environmental and economic benefits with multi-national aerospace and automotive companies implementing the results in current developments

Humanized Monoclonal Antibody against West Nile Virus Envelope Protein Administered after Neuronal Infection Protects against Lethal Encephalitis in Hamsters

Humans infected with West Nile virus (WNV) may clinically present with symptoms that are suggestive of neurological infection. Nearly all treatments of WNV disease have been effective in animal models only if administered before or soon after viral challenge. Here, we evaluated whether a potent neutralizing anti-WNV humanized monoclonal antibody (MAb), hE16, could improve the course of disease in a hamster model when administered after the virus had infected neurons in the brain. Five days after viral injection, WNV was detected in the brains of hamsters by cytopathic assay, quantitative reverse-transcription polymerase chain reaction, and immunohistochemical staining of WNV envelope in neurons. Notably, 80%–90% of the hamsters treated 5 days after viral injection by intraperitoneal injection with hE16 survived the disease, compared with 37% of the placebo-treated hamsters (P \u3c= .001). The hamsters that received hE16 directly in the brain also exhibited markedly improved survival rates, compared with those in the placebo-treated hamsters. In prospective experiments, hamsters with high levels of infectious WNV in their cerebrospinal fluid were also protected by hE16 when administered 5 days after viral injection. These experiments suggest that humanized MAbs with potent neutralizing activity are a possible treatment for human patients after WNV has infected neurons in the central nervous system

Exploratory study of complexant concentrate waste processing

The purpose of this exploratory study, conducted by Pacific Northwest Laboratory for Westinghouse Hanford Company, was to determine the effect of applying advanced chemical separations technologies to the processing and disposal of high-level wastes (HLW) stored in underground tanks. The major goals of this study were to determine (1) if the wastes can be partitioned into a small volume of HLW plus a large volume of low-level waste (LLW), and (2) if the activity in the LLW can be lowered enough to meet NRC Class LLW criteria. This report presents the results obtained in a brief scouting study of various processes for separating radionuclides from Hanford complexant concentrate (CC) waste

Zika Virus Associated Pathology and Antigen Presence in the Testicle in the Absence of Sexual Transmission During Subacute to Chronic Infection in a Mouse Model

Zika virus (ZIKV) is an arboviral infection that has been shown to be sexually transmitted. The study outlined herein aims to determine if accessory sex glands and epididymal epithelial cells are sources of viral persistence in subacute and chronic ZIKV infection, and if infection of these organs is important in sexual transmission during long-term (chronic) infection. Male interferon type I receptor knockout (Ifnar−/−) mice were challenged with ZIKV and reproductive tissues were harvested 14 and 35 days post infection (DPI) for inoculation studies and 14, 35 and 70 DPI for histopathology. Artificial insemination fluid derived from epididymal flush and seminal plasma from the prostate and seminal vesicle was obtained from ZIKV inoculated and sham-infected males. Naïve interferon type I and II receptor knockout (AG129) female mice were pre-treated with progesterone and inoculated intravaginally with artificial insemination fluid from ZIKV-infected males. ZIKV RNA was detected in the artificial insemination fluid generated from epididymal flush or seminal plasma from ZIKV infected males at 14 and 35 DPI. ZIKV antigens were only detected in seminiferous tubules at 14 DPI. Epididymal epithelial cells did not show ZIKV antigen immunoreactivity at 14, 35 or 70 DPI. Severe fibrosing orchitis (end stage orchitis) was observed at 35 and 70 DPI. Mild inflammation and peri-tubular fibrosis were observed in the epididymis following clearance of virus. Viral RNA was not detected by PCR in whole blood samples of females from any intravaginal experimental group and only detected in 20% of subcutaneously inoculated animals (derived from 1 experimentally infected male) at 35 DPI. While ZIKV RNA and antigens can be detected in the male reproductive tract at 14 DPI and RNA can also be detected at 35 DPI, intravaginal inoculation of artificial insemination fluid from these time-points failed to result in viremia in naïve females inoculated intravaginally. These studies support the hypothesis that epididymal epithelial cells are critical to sexual transmission in immunocompromised mice. Additionally, acute but not chronic male reproductive tract infection with ZIKV results in infectious virus capable of being sexually transmitted in mice

The Cauchy problems for Einstein metrics and parallel spinors

We show that in the analytic category, given a Riemannian metric $g$ on a hypersurface $M\subset \Z$ and a symmetric tensor $W$ on $M$, the metric $g$ can be locally extended to a Riemannian Einstein metric on $Z$ with second fundamental form $W$, provided that $g$ and $W$ satisfy the constraints on $M$ imposed by the contracted Codazzi equations. We use this fact to study the Cauchy problem for metrics with parallel spinors in the real analytic category and give an affirmative answer to a question raised in B\"ar, Gauduchon, Moroianu (2005). We also answer negatively the corresponding questions in the smooth category.Comment: 28 pages; final versio

Ginzburg-Landau model with small pinning domains

We consider a Ginzburg-Landau type energy with a piecewise constant pinning term $a$ in the potential $(a^2 - |u|^2)^2$. The function $a$ is different from 1 only on finitely many disjoint domains, called the {\it pinning domains}. These pinning domains model small impurities in a homogeneous superconductor and shrink to single points in the limit $\v\to0$; here, \v is the inverse of the Ginzburg-Landau parameter. We study the energy minimization in a smooth simply connected domain $\Omega \subset \mathbb{C}$ with Dirichlet boundary condition $g$ on \d \O, with topological degree {\rm deg}_{\d \O} (g) = d >0. Our main result is that, for small \v, minimizers have $d$ distinct zeros (vortices) which are inside the pinning domains and they have a degree equal to 1. The question of finding the locations of the pinning domains with vortices is reduced to a discrete minimization problem for a finite-dimensional functional of renormalized energy. We also find the position of the vortices inside the pinning domains and show that, asymptotically, this position is determined by {\it local renormalized energy} which does not depend on the external boundary conditions.Comment: 39 page