On Vanishing Theorems For Vector Bundle Valued p-Forms And Their Applications

Let $F: [0, \infty) \to [0, \infty)$ be a strictly increasing $C^2$ function with $F(0)=0$. We unify the concepts of $F$-harmonic maps, minimal hypersurfaces, maximal spacelike hypersurfaces, and Yang-Mills Fields, and introduce $F$-Yang-Mills fields, $F$-degree, $F$-lower degree, and generalized Yang-Mills-Born-Infeld fields (with the plus sign or with the minus sign) on manifolds. When $F(t)=t, \frac 1p(2t)^{\frac p2}, \sqrt{1+2t} -1,$ and $1-\sqrt{1-2t},$ the $F$-Yang-Mills field becomes an ordinary Yang-Mills field, $p$-Yang-Mills field, a generalized Yang-Mills-Born-Infeld field with the plus sign, and a generalized Yang-Mills-Born-Infeld field with the minus sign on a manifold respectively. We also introduce the $E_{F,g}-$energy functional (resp. $F$-Yang-Mills functional) and derive the first variational formula of the $E_{F,g}-$energy functional (resp. $F$-Yang-Mills functional) with applications. In a more general frame, we use a unified method to study the stress-energy tensors that arise from calculating the rate of change of various functionals when the metric of the domain or base manifold is changed. These stress-energy tensors, linked to $F$-conservation laws yield monotonicity formulae. A "macroscopic" version of these monotonicity inequalities enables us to derive some Liouville type results and vanishing theorems for $p-$forms with values in vector bundles, and to investigate constant Dirichlet boundary value problems for 1-forms. In particular, we obtain Liouville theorems for $F-$harmonic maps (e.g. $p$-harmonic maps), and $F-$Yang-Mills fields (e.g. generalized Yang-Mills-Born-Infeld fields on manifolds). We also obtain generalized Chern type results for constant mean curvature type equations for $p-$forms on $\Bbb{R}^m$ and on manifolds $M$ with the global doubling property by a different approach. The case $p=0$ and $M=\mathbb{R}^m$ is due to Chern.Comment: 1. This is a revised version with several new sections and an appendix that will appear in Communications in Mathematical Physics. 2. A "microscopic" approach to some of these monotonicity formulae leads to celebrated blow-up techniques and regularity theory in geometric measure theory. 3. Our unique solution of the Dirichlet problems generalizes the work of Karcher and Wood on harmonic map

Flight Development for Cryogenic Fluid Management in Support of Exploration Missions

This paper describes the results of the "Experimentation for the Maturation of Deep Space Cryogenic Refueling Technology" study. The purposes of this study were to identify cryogenic fluids management technologies requiring low gravity flight experiments to bring to technology readiness level (TRL) 5-6; to study many possible flight experiment options; and to develop near-term low-cost flight experiment concepts to mature core technologies of refueling. A total of twenty-five white papers were prepared in the course of this study. Each white paper is briefly summarized and relevant references cited. A total of 90 references are cited

Measurement of the B0-anti-B0-Oscillation Frequency with Inclusive Dilepton Events

The $B^0$-$\bar B^0$ oscillation frequency has been measured with a sample of 23 million \B\bar B pairs collected with the BABAR detector at the PEP-II asymmetric B Factory at SLAC. In this sample, we select events in which both B mesons decay semileptonically and use the charge of the leptons to identify the flavor of each B meson. A simultaneous fit to the decay time difference distributions for opposite- and same-sign dilepton events gives $\Delta m_d = 0.493 \pm 0.012{(stat)}\pm 0.009{(syst)}$ ps$^{-1}$.Comment: 7 pages, 1 figure, submitted to Physical Review Letter

Application of compact laser-driven accelerator X-ray sources for industrial imaging

X-rays generated by betatron oscillations of electrons in a laser-driven plasma accelerator were characterised and applied to imaging industrial samples. With a 125TW laser, a low divergence beam with 5.2±1.7 × 107photonsmrad−2 per pulse was produced with a synchrotron spectrum with a critical energy of 14.6±1.3keV. Radiographs were obtained of a metrology test sample, battery electrodes, and a damage site in a composite material. These results demonstrate the suitability of the source for non-destructive evaluation applications. The potential for industrial implementation of plasma accelerators is discussed

Discovery and validation of plasma proteomic biomarkers relating to brain amyloid burden by SOMAscan assay.

Plasma proteins have been widely studied as candidate biomarkers to predict brain amyloid deposition to increase recruitment efficiency in secondary prevention clinical trials for Alzheimer's disease. Most such biomarker studies are targeted to specific proteins or are biased toward high abundant proteins. 4001 plasma proteins were measured in two groups of participants (discovery group = 516, replication group = 365) selected from the European Medical Information Framework for Alzheimer's disease Multimodal Biomarker Discovery study, all of whom had measures of amyloid. A panel of proteins (n = 44), along with age and apolipoprotein E (APOE) ε4, predicted brain amyloid deposition with good performance in both the discovery group (area under the curve = 0.78) and the replication group (area under the curve = 0.68). Furthermore, a causal relationship between amyloid and tau was confirmed by Mendelian randomization. The results suggest that high-dimensional plasma protein testing could be a useful and reproducible approach for measuring brain amyloid deposition

Validation of plasma proteomic biomarkers relating to brain amyloid burden in the EMIF-Alzheimer's disease multimodal biomarker discovery cohort

We have previously investigated, discovered, and replicated plasma protein biomarkers for use to triage potential trials participants for PET or cerebrospinal fluid measures of Alzheimer's disease (AD) pathology. This study sought to undertake validation of these candidate plasma biomarkers in a large, multi-center sample collection. Targeted plasma analyses of 34 proteins with prior evidence for prediction of in vivo pathology were conducted in up to 1,000 samples from cognitively healthy elderly individuals, people with mild cognitive impairment, and in patients with AD-type dementia, selected from the EMIF-AD catalogue. Proteins were measured using Luminex xMAP, ELISA, and Meso Scale Discovery assays. Seven proteins replicated in their ability to predict in vivo amyloid pathology. These proteins form a biomarker panel that, along with age, could significantly discriminate between individuals with high and low amyloid pathology with an area under the curve of 0.74. The performance of this biomarker panel remained consistent when tested in apolipoprotein E ϵ4 non-carrier individuals only. This blood-based panel is biologically relevant, measurable using practical immunocapture arrays, and could significantly reduce the cost incurred to clinical trials through screen failure

Representational predicaments for employees: Their impact on perceptions of supervisors\u27 individualized consideration and on employee job satisfaction

A representational predicament for a subordinate vis-à-vis his or her immediate superior involves perceptual incongruence with the superior about the subordinate\u27s work or work context, with unfavourable implications for the employee. An instrument to measure the incidence of two types of representational predicament, being neglected and negative slanting, was developed and then validated through an initial survey of 327 employees. A subsequent substantive survey with a fresh sample of 330 employees largely supported a conceptual model linking being neglected and negative slanting to perceptions of low individualized consideration by superiors and to low overall job satisfaction. The respondents in both surveys were all Hong Kong Chinese. Two case examples drawn from qualitative interviews illustrate and support the conceptual model. Based on the research findings, we recommend some practical exercises to use in training interventions with leaders and subordinates. © 2013 Copyright Taylor and Francis Group, LLC