Given an open bounded subset Ω of ℝ^(n) we consider the eigenvalue problem{Δu-(■u,■V)=-λvu,u>0inΩ,u=0 onδΩ,where V is a given function defined inΩandλV is the relevant eigenvalue.We determine sufficient c...Given an open bounded subset Ω of ℝ^(n) we consider the eigenvalue problem{Δu-(■u,■V)=-λvu,u>0inΩ,u=0 onδΩ,where V is a given function defined inΩandλV is the relevant eigenvalue.We determine sufficient conditions on V such that ifΩis convex,the solution u is log-concave.We also determine sufficient conditions ensuring that λ_(V),as a function of the setΩ,verifies a convexity inequality with respect to the Minkowski addition of sets.展开更多
为解决现有大场景三维地理信息系统(geographic information system,GIS)平台中道路建筑信息模型(building information modeling,BIM)模型与倾斜实景模型融合展示中存在的坐标基准不统一问题,提出一种道路BIM模型与倾斜实景地理坐标高...为解决现有大场景三维地理信息系统(geographic information system,GIS)平台中道路建筑信息模型(building information modeling,BIM)模型与倾斜实景模型融合展示中存在的坐标基准不统一问题,提出一种道路BIM模型与倾斜实景地理坐标高精度匹配方法。针对道路带状分布特征及道路养护需求,首先对模型进行分段处理;然后根据道路路面及资产设施模型的特征点分布设计构建一种空间距离加权的最小二乘坐标匹配参数拟合方法,重点解决各分段路面的精准接边难题。选取真实道路数据展开实验,验证该坐标匹配方法,通过所提方法可以有效解决道路模型与倾斜实景模型匹配产生偏差的问题,匹配后二者之间的精度达到毫米级,满足道路交通设施数字化管养和动态更新的需要。展开更多
基金supported by the project Disuguaglianze analitiche e geometriche,funded by the Gruppo per Analisi Matematica la Probabilitàe le loro Applicazioni.
文摘Given an open bounded subset Ω of ℝ^(n) we consider the eigenvalue problem{Δu-(■u,■V)=-λvu,u>0inΩ,u=0 onδΩ,where V is a given function defined inΩandλV is the relevant eigenvalue.We determine sufficient conditions on V such that ifΩis convex,the solution u is log-concave.We also determine sufficient conditions ensuring that λ_(V),as a function of the setΩ,verifies a convexity inequality with respect to the Minkowski addition of sets.
文摘为解决现有大场景三维地理信息系统(geographic information system,GIS)平台中道路建筑信息模型(building information modeling,BIM)模型与倾斜实景模型融合展示中存在的坐标基准不统一问题,提出一种道路BIM模型与倾斜实景地理坐标高精度匹配方法。针对道路带状分布特征及道路养护需求,首先对模型进行分段处理;然后根据道路路面及资产设施模型的特征点分布设计构建一种空间距离加权的最小二乘坐标匹配参数拟合方法,重点解决各分段路面的精准接边难题。选取真实道路数据展开实验,验证该坐标匹配方法,通过所提方法可以有效解决道路模型与倾斜实景模型匹配产生偏差的问题,匹配后二者之间的精度达到毫米级,满足道路交通设施数字化管养和动态更新的需要。
