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

Case Report Multifocal Buruli Ulcer Associated with Secondary Infection in HIV Positive Patient

Buruli ulcer is a chronic and infectious skin disease, caused by Mycobacterium ulcerans. It leads to large skin ulceration and sometimes bone infection which is responsible for deformities. Here, we report a case of multifocal form of Buruli ulcer associated with secondary infection in a 46-year-old human immunodeficiency virus (HIV) positive woman. The antimycobacterial drugs combined to surgery allowed curing this multifocal case and rose up two relevant issues: the susceptibility of immune reconstitution inflammatory syndrome (IRIS) occurrence and Mycobacterium dissemination. The deep immune depression, the underline biological, and clinical disorders of the patient might contribute to IRIS occurrence and Buruli ulcer dissemination. Future investigations have to be conducted on the mechanism of IRIS on set and on Mycobacterium ulcerans dissemination after ARV drugs initiation and the patient related underline clinical or biological disorders

Anticancer Activity of 2α, 3α, 19β, 23β-Tetrahydroxyurs-12-en-28-oic Acid (THA), a Novel Triterpenoid Isolated from Sinojackia sarcocarpa

BACKGROUND: Natural products represent an important source for agents of cancer prevention and cancer treatment. More than 60% of conventional anticancer drugs are derived from natural sources, particularly from plant-derived materials. In this study, 2α, 3α, 19β, 23β-tetrahydroxyurs-12-en-28-oic acid (THA), a novel triterpenoid from the leaves of Sinojackia sarcocarpa, was isolated, and its anticancer activity was investigated both in vitro and in vivo. PRINCIPAL FINDINGS: THA possessed potent tumor selected toxicity in vitro. It exhibited significantly higher cytotoxicity to the cancer cell lines A2780 and HepG2 than to IOSE144 and QSG7701, two noncancerous cell lines derived from ovary epithelium and liver, respectively. Moreover, THA showed a dose-dependent inhibitory effect on A2780 ovary tumor growth in vivo in nude mice. THA induced a dose-dependent apoptosis and G2/M cell cycle arrest in A2780 and HepG2 cells. The THA-induced cell cycle arrest was accompanied by a downregulation of Cdc2. The apoptosis induced by THA was evident by induction of DNA fragmentation, release of cytoplasmic Cytochrome c from mitochondria, activation of caspases, downregulation of Bcl-2 and upregulation of Bax. CONCLUSION: The primary data indicated that THA exhibit a high toxicity toward two cancer cells than their respective non-cancerous counterparts and has a significant anticancer activity both in vitro and in vivo. Thus, THA and/or its derivatives may have great potential in the prevention and treatment of human ovary tumors and other malignancies

Effects of vitamin D supplementation on endothelial function:a systematic review and meta-analysis of randomised clinical trials

Background: In addition to regulating calcium homoeostasis and bone health, vitamin D influences vascular and metabolic processes including endothelial function (EF) and insulin signalling. This systematic review and meta-analysis of randomised clinical trials (RCTs) were conducted to investigate the effect of vitamin D supplementation on EF and to examine whether the effect size was modified by health status, study duration, dose, route of vitamin D administration, vitamin D status (baseline and post-intervention), body mass index (BMI), age and type of vitamin D.  Methods: We searched the Medline, Embase, Cochrane Library and Scopus databases from inception until March 2015 for studies meeting the following criteria: (1) RCT with adult participants, (2) vitamin D administration alone, (3) studies that quantified EF using commonly applied methods including ultrasound, plethysmography, applanation tonometry and laser Doppler.  Results: Sixteen articles reporting data for 1177 participants were included. Study duration ranged from 4 to 52 weeks. The effect of vitamin D on EF was not significant (SMD: 0.08, 95 % CI −0.06, 0.22, p = 0.28). Subgroup analysis showed a significant improvement of EF in diabetic subjects (SMD: 0.31, 95 % CI 0.05, 0.57, p = 0.02). A non-significant trend was found for diastolic blood pressure (β = 0.02; p = 0.07) and BMI (β = 0.05; p = 0.06).  Conclusions: Vitamin D supplementation did not improve EF. The significant effect of vitamin D in diabetics and a tendency for an association with BMI may indicate a role of excess adiposity and insulin resistance in modulating the effects of vitamin D on vascular function. This remains to be tested in future studies

The HITRAN2020 Molecular Spectroscopic Database

The HITRAN database is a compilation of molecular spectroscopic parameters. It was established in the early 1970s and is used by various computer codes to predict and simulate the transmission and emission of light in gaseous media (with an emphasis on terrestrial and planetary atmospheres). The HITRAN compilation is composed of five major components: the line-by-line spectroscopic parameters required for high-resolution radiative-transfer codes, experimental infrared absorption cross-sections (for molecules where it is not yet feasible for representation in a line-by-line form), collision-induced absorption data, aerosol indices of refraction, and general tables (including partition sums) that apply globally to the data. This paper describes the contents of the 2020 quadrennial edition of HITRAN. The HITRAN2020 edition takes advantage of recent experimental and theoretical data that were meticulously validated, in particular, against laboratory and atmospheric spectra. The new edition replaces the previous HITRAN edition of 2016 (including its updates during the intervening years). All five components of HITRAN have undergone major updates. In particular, the extent of the updates in the HITRAN2020 edition range from updating a few lines of specific molecules to complete replacements of the lists, and also the introduction of additional isotopologues and new (to HITRAN) molecules: SO, CH3F, GeH4, CS2, CH3I and NF3. Many new vibrational bands were added, extending the spectral coverage and completeness of the line lists. Also, the accuracy of the parameters for major atmospheric absorbers has been increased substantially, often featuring sub-percent uncertainties. Broadening parameters associated with the ambient pressure of water vapor were introduced to HITRAN for the first time and are now available for several molecules. The HITRAN2020 edition continues to take advantage of the relational structure and efficient interface available at www.hitran.org and the HITRAN Application Programming Interface (HAPI). The functionality of both tools has been extended for the new edition

An intergenerational study of perceptions of changes in active free play among families from rural areas of Western Canada

Background: Children's engagement in active free play has declined across recent generations. Therefore, the purpose of this study was to examine perceptions of intergenerational changes in active free play among families from rural areas. We addressed two research questions: (1) How has active free play changed across three generations? (2) What suggestions do participants have for reviving active free play? Methods: Data were collected via 49 individual interviews with members of 16 families (15 grandparents, 16 parents, and 18 children) residing in rural areas/small towns in the Province of Alberta (Canada). Interview recordings were transcribed verbatim and subjected to thematic analysis guided by an ecological framework of active free play. Results: Factors that depicted the changing nature of active free play were coded in the themes of less imagination/more technology, safety concerns, surveillance, other children to play with, purposeful physical activity, play spaces/organized activities, and the good parenting ideal. Suggestions for reviving active free play were coded in the themes of enhance facilities to keep kids entertained, provide more opportunities for supervised play, create more community events, and decrease use of technology. Conclusions: These results reinforce the need to consider multiple levels of social ecology in the study of active free play, and highlight the importance of community-based initiatives to revive active free play in ways that are consistent with contemporary notions of good parentin