Uniqueness of convex ancient solutions to mean curvature flow in higher dimensions

In this paper, we consider noncompact ancient solutions to the mean curvature flow in $\mathbb{R}^{n+1}$ ($n \geq 3$) which are strictly convex, uniformly two-convex, and noncollapsed. We prove that such an ancient solution is a rotationally symmetric translating soliton.Comment: In this paper, we extend the result in arxiv:1711.00823 to higher dimensions, assuming uniform two-convexit

Static flow on complete noncompact manifolds I: short-time existence and asymptotic expansions at conformal infinity

In this paper, we study short-time existence of static flow on complete noncompact asymptotically static manifolds from the point of view that the stationary points of the evolution equations can be interpreted as static solutions of the Einstein vacuum equations with negative cosmological constant. For a static vacuum $(M^n,g,V),$ we also compute the asymptotic expansions of $g$ and $V$ at conformal infinity.Comment: 25 page

Elaboration and Characterization of Recycled PP/Clay Nanocomposites

In this paper, the elaboration and characterization of recycled polypropylene/Tunisian clay nanocomposites has been investigated. When recycled, polypropylene polymer is degraded and has poorer mechanical and rheological properties. To overcome this problem, we proposed to incorporate Tunisian clay nanoparticles in recycled polypropylene (rPP) matrix. The incorporation of Tunisian clay was performed in molten state using maleic anhydride grafted polypropylene (PP-g-MA) as compatibilizer. The dispersion of clay in rPP polymer was evaluated by scanning electron microscopy and Fourier transformed infrared spectroscopy. Thus, Tunisian clay was more dispersed in nanocomposites with the increase of Tunisian clay loading. In dead, the incorporation of silicate layers gave rise to a considerable increase of the static viscosity demonstrating the reinforcing effect of Tunisian clay nanofillers on rPP matrix. However, the increasing trend of morphological and rheological properties is lower when the clay content exceeds 5%

Mouse Papillomavirus L1 and L2 Are Dispensable for Viral Infection and Persistence at Both Cutaneous and Mucosal Tissues.

Papillomavirus L1 and L2, the major and minor capsid proteins, play significant roles in viral assembly, entry, and propagation. In the current study, we investigate the impact of L1 and L2 on viral life cycle and tumor growth with a newly established mouse papillomavirus (MmuPV1) infection model. MmuPV1 L1 knockout, L2 knockout, and L1 plus L2 knockout mutant genomes (designated as L1ATGko-4m, L2ATGko, and L1-L2ATGko respectively) were generated. The mutants were examined for their ability to generate lesions in athymic nude mice. Viral activities were examined by qPCR, immunohistochemistry (IHC), in situ hybridization (ISH), and transmission electron microscopy (TEM) analyses. We demonstrated that viral DNA replication and tumor growth occurred at both cutaneous and mucosal sites infected with each of the mutants. Infections involving L1ATGko-4m, L2ATGko, and L1-L2ATGko mutant genomes generally resulted in smaller tumor sizes compared to infection with the wild type. The L1 protein was absent in L1ATGko-4m and L1-L2ATGko mutant-treated tissues, even though viral transcripts and E4 protein expression were robust. Therefore, L1 is not essential for MmuPV1-induced tumor growth, and this finding parallels our previous observations in the rabbit papillomavirus model. Very few viral particles were detected in L2ATGko mutant-infected tissues. Interestingly, the localization of L1 in lesions induced by L2ATGko was primarily cytoplasmic rather than nuclear. The findings support the hypothesis that the L2 gene influences the expression, location, transport, and assembly of the L1 protein in vivo

Factors Affecting European Farmers’Participation in Biodiversity Policies

This article reports the major findings from an interdisciplinary research project that synthesises key insights into farmers’ willingness and ability to co-operate with biodiversity policies. The results of the study are based on an assessment of about 160 publications and research reports from six EU member states and from international comparative research.We developed a conceptual framework to systematically review the existent literature relevant for our purposes. This framework provides a common structure for analysing farmers’ perspectives regarding the introduction into farming practices of measures relevant to biodiversity. The analysis is coupled and contrasted with a survey of experts. The results presented above suggest that it is important to view support for practices oriented towards biodiversity protection not in a static sense – as a situation determined by one or several influencing factors – but rather as a process marked by interaction. Financial compensation and incentives function as a necessary, though clearly not sufficient condition in this process

Some new directions in infinite-combinatorial topology

We give a light introduction to selection principles in topology, a young subfield of infinite-combinatorial topology. Emphasis is put on the modern approach to the problems it deals with. Recent results are described, and open problems are stated. Some results which do not appear elsewhere are also included, with proofs.Comment: Small update

Prediction of inter-particle adhesion force from surface energy and surface roughness

Fine powder flow is a topic of great interest to industry, in particular for the pharmaceutical industry; a major concern being their poor flow behavior due to high cohesion. In this study, cohesion reduction, produced via surface modification, at the particle scale as well as bulk scale is addressed. The adhesion force model of Derjaguin-Muller-Toporov (DMT) was utilized to quantify the inter-particle adhesion force of both pure and surface modified fine aluminum powders (∼8 μm in size). Inverse Gas Chromatography was utilized for the determination of surface energy of the samples, and Atomic Force Microscopy was utilized to evaluate surface roughness of the powders. Surface modification of the original aluminum powders was done for the purpose of reduction in cohesiveness and improvement in flowability, employing either silane surface treatment or dry mechanical coating of nano-particles on the surface of original powders. For selected samples, the AFM was utilized for direct evaluation of the particle pull-off force. The results indicated that surface modification reduced the surface energy and altered the surface nano-roughness, resulting in drastic reduction of the inter-particle adhesion force. The particle bond number values were computed based on either the inter-particle adhesion force from the DMT model or the inter-particle pull-off force obtained from direct AFM measurements. Surface modification resulted in two to three fold reductions in the Bond number. In order to examine the influence of the particle scale property such as the Bond number on the bulk-scale flow characterization, Angle of Repose measurements were done and showed good qualitative agreements with the Bond number and acid/base surface characteristics of the powders. The results indicate a promising method that may be used to predict flow behavior of original (cohesive) and surface modified (previously cohesive) powders utilizing very small samples

Bifurcation and local rigidity of homogeneous solutions to the Yamabe problem on spheres

We study existence and non-existence of constant scalar curvature metrics conformal and arbitrarily close to homogeneous metrics on spheres, using variational techniques. This describes all critical points of the Hilbert-Einstein functional on such conformal classes, near homogeneous metrics. Both bifurcation and local rigidity type phenomena are obtained for 1-parameter families of U(n+1), Sp(n+1) and Spin(9)-homogeneous metrics.Comment: LaTeX2e, 18 pages, 1 figure, revised version. To appear in Calc. Var. and PDE

The diagnostic accuracy of high b-value diffusion- and T2-weighted imaging for the detection of prostate cancer: a meta-analysis

Purpose: This study aims to investigate the role of diffusion-weighted imaging (DWI) and T2-weighted imaging (T2WI) in combination for the detection of prostate cancer, specifically assessing the role of high b-values (> 1000 s/mm2), with a systematic review and meta-analysis of the existing published data.  Methods: The electronic databases MEDLINE, EMBASE, and OpenSIGLE were searched between inception and September 1, 2017. Eligible studies were those that reported the sensitivity and specificity of DWI and T2WI for the diagnosis of prostate cancer by visual assessment using a histopathologic reference standard. The QUADAS-2 critical appraisal tool was used to assess the quality of included studies. A meta-analysis with pooling of sensitivity, specificity, likelihood, and diagnostic odds ratios was undertaken, and a summary receiver-operating characteristics (sROC) curve was constructed. Predetermined subgroup analysis was also performed.  Results: Thirty-three studies were included in the final analysis, evaluating 2949 patients. The pooled sensitivity and specificity were 0.69 (95% CI 0.68–0.69) and 0.84 (95% CI 0.83–0.85), respectively, and the sROC AUC was 0.84 (95% CI 0.81–0.87). Subgroup analysis showed significantly better sensitivity with high b-values (> 1000 s/mm2). There was high statistical heterogeneity between studies.  Conclusion: The diagnostic accuracy of combined DWI and T2WI is good with high b-values (> 1000 s/mm2) seeming to improve overall sensitivity while maintaining specificity. However, further large-scale studies specifically looking at b-value choice are required before a categorical recommendation can be made