Let O be a closed geodesic polygon in S2. Maps from O into S2 are said to satisfy tangent boundary conditions if the edges of O are mapped into the geodesics which contain them. Taking O to be an octant of S2, we comp...Let O be a closed geodesic polygon in S2. Maps from O into S2 are said to satisfy tangent boundary conditions if the edges of O are mapped into the geodesics which contain them. Taking O to be an octant of S2, we compute the infimum Dirichlet energy 6（H） for continuous maps satisfying tangent boundary conditions of arbitrary homotopy type H. The expression for C（H） involves a topological invariant - the spelling length - associated with the （non-abelian） fundamental group of the n-times punctured two-sphere, π1（S2 - {s1,..., sn}, ＊）. The lower bound for C（H） is obtained from combinatorial group theory arguments, while the upper bound is obtained by constructing explicit representatives which, on all but an arbitrarily small subset of O, are alternatively locally conformal or anticonformal. For conformal and anticonformal classes （classes containing wholly conformal and anticonformal representatives respectively）, the expression for C（H） reduces to a previous result involving the degrees of a set of regular values sl,…… sn in the target 82 space. These degrees may be viewed as invariants associated with the abelianization of vr1（S2 - {s1,..., sn}, ＊）. For nonconformal classes, however, ε（H） may be strictly greater than the abelian bound. This stems from the fact that, for nonconformal maps, the number of preimages of certain regular values may necessarily be strictly greater than the absolute value of their degrees. This work is motivated by the theoretical modelling of nematic liquid crystals in confined polyhedral geometries. The results imply new lower and upper bounds for the Dirichlet energy （one-constant Oseen-Frank energy） of reflection-symmetric tangent unitvector fields in a rectangular prism.展开更多
本文概述了加勒比岛屿的林火情况。资料来自于地方管理报告和公开发布的地区性中分辨率成像光谱仪(MODIS)卫星活动火产品(active fire products)。土地管理报告的林火数量和MODIS林火信息资源管理系统数据中的起火点之间具有显著差异。...本文概述了加勒比岛屿的林火情况。资料来自于地方管理报告和公开发布的地区性中分辨率成像光谱仪(MODIS)卫星活动火产品(active fire products)。土地管理报告的林火数量和MODIS林火信息资源管理系统数据中的起火点之间具有显著差异。这些差异的原因还有待深入研究。虽然加勒比地区林火统计数据普遍缺乏,但大体观察表明:林火主要发生在干旱森林(年均降水量500～1000 mm)。这些也是人类定居点最多的地方。低地乔木和山地森林的降水量较多(每年1000mm以上),不易发生林火,但林火在特别干旱的年份也可能发生。加勒比地区大部分干旱森林生态系统属于火敏感型生态系统,但加勒比地区(古巴、多米尼加共和国和巴哈马)松林为火依赖性生态系统。在火敏感型生态系统中,通常火灾失控燃烧有利于外来入侵物种的扩散。2005～2006年,联合国粮农组织制定了加勒比地区火灾管理合作战略。这一区域战略旨在鼓励生态环境类似的国家之间密切合作,以加强加勒比地区的火灾管理网络。该战略鉴别了一系列旨在加强加勒比地区的野火管理能力的研究、培训和管理活动。展开更多
It requires approximately 800 million dollars(US)and 10 years to successfully bring a drug from the laboratory bench into the clinic(DiMasi et al.,2003).Thus,the breakthrough discovery of today will not be available i...It requires approximately 800 million dollars(US)and 10 years to successfully bring a drug from the laboratory bench into the clinic(DiMasi et al.,2003).Thus,the breakthrough discovery of today will not be available in the clinic for many years,and many dollars,after this initial discovery.One potential way to speed up this drug developmental cycle is by repurposing drugs that have been previously approved for an alternate clinical indication.With this goal in mind,Beachy and colleagues set out to identify a drug with efficacy against tumors that were dependant on the Hedgehog(HH)signaling pathway.They reported in the April issue of a leading cancer research journal that Itraconazole,a commonly used antifungal drug,can be turned against HH’s signaling function(Kim et al.,2010).It has been estimated that 25%of all human tumors may be HH dependent(Teglund et al,2010).展开更多
基金supported by a Royal Commission for the Exhibition of 1851 Research Fellowship between 2006-2008supported by Award No.KUK-C1-013-04, made by King Abdullah University of Science and Technology (KAUST) to the Oxford Centre for Collaborative Applied Mathematics
文摘Let O be a closed geodesic polygon in S2. Maps from O into S2 are said to satisfy tangent boundary conditions if the edges of O are mapped into the geodesics which contain them. Taking O to be an octant of S2, we compute the infimum Dirichlet energy 6（H） for continuous maps satisfying tangent boundary conditions of arbitrary homotopy type H. The expression for C（H） involves a topological invariant - the spelling length - associated with the （non-abelian） fundamental group of the n-times punctured two-sphere, π1（S2 - {s1,..., sn}, ＊）. The lower bound for C（H） is obtained from combinatorial group theory arguments, while the upper bound is obtained by constructing explicit representatives which, on all but an arbitrarily small subset of O, are alternatively locally conformal or anticonformal. For conformal and anticonformal classes （classes containing wholly conformal and anticonformal representatives respectively）, the expression for C（H） reduces to a previous result involving the degrees of a set of regular values sl,…… sn in the target 82 space. These degrees may be viewed as invariants associated with the abelianization of vr1（S2 - {s1,..., sn}, ＊）. For nonconformal classes, however, ε（H） may be strictly greater than the abelian bound. This stems from the fact that, for nonconformal maps, the number of preimages of certain regular values may necessarily be strictly greater than the absolute value of their degrees. This work is motivated by the theoretical modelling of nematic liquid crystals in confined polyhedral geometries. The results imply new lower and upper bounds for the Dirichlet energy （one-constant Oseen-Frank energy） of reflection-symmetric tangent unitvector fields in a rectangular prism.
文摘本文概述了加勒比岛屿的林火情况。资料来自于地方管理报告和公开发布的地区性中分辨率成像光谱仪(MODIS)卫星活动火产品(active fire products)。土地管理报告的林火数量和MODIS林火信息资源管理系统数据中的起火点之间具有显著差异。这些差异的原因还有待深入研究。虽然加勒比地区林火统计数据普遍缺乏,但大体观察表明:林火主要发生在干旱森林(年均降水量500～1000 mm)。这些也是人类定居点最多的地方。低地乔木和山地森林的降水量较多(每年1000mm以上),不易发生林火,但林火在特别干旱的年份也可能发生。加勒比地区大部分干旱森林生态系统属于火敏感型生态系统,但加勒比地区(古巴、多米尼加共和国和巴哈马)松林为火依赖性生态系统。在火敏感型生态系统中,通常火灾失控燃烧有利于外来入侵物种的扩散。2005～2006年,联合国粮农组织制定了加勒比地区火灾管理合作战略。这一区域战略旨在鼓励生态环境类似的国家之间密切合作,以加强加勒比地区的火灾管理网络。该战略鉴别了一系列旨在加强加勒比地区的野火管理能力的研究、培训和管理活动。
文摘It requires approximately 800 million dollars(US)and 10 years to successfully bring a drug from the laboratory bench into the clinic(DiMasi et al.,2003).Thus,the breakthrough discovery of today will not be available in the clinic for many years,and many dollars,after this initial discovery.One potential way to speed up this drug developmental cycle is by repurposing drugs that have been previously approved for an alternate clinical indication.With this goal in mind,Beachy and colleagues set out to identify a drug with efficacy against tumors that were dependant on the Hedgehog(HH)signaling pathway.They reported in the April issue of a leading cancer research journal that Itraconazole,a commonly used antifungal drug,can be turned against HH’s signaling function(Kim et al.,2010).It has been estimated that 25%of all human tumors may be HH dependent(Teglund et al,2010).
