Let X={X(t)∈R^(d),t∈R^(N)}be a centered space-time anisotropic Gaussian field with indices H=(H_(1),…,H_(N))∈(0,1)~N,where the components X_(i)(i=1,…,d)of X are independent,and the canonical metric√(E(X_(i)(t)-X...Let X={X(t)∈R^(d),t∈R^(N)}be a centered space-time anisotropic Gaussian field with indices H=(H_(1),…,H_(N))∈(0,1)~N,where the components X_(i)(i=1,…,d)of X are independent,and the canonical metric√(E(X_(i)(t)-X_(i)(s))^(2))^(1/2)(i=1,…,d)is commensurate with■for s=(s_(1),…,s_(N)),t=(t_(1),…,t_(N))∈R~N,α_(i)∈(0,1],and with the continuous functionγ(·)satisfying certain conditions.First,the upper and lower bounds of the hitting probabilities of X can be derived from the corresponding generalized Hausdorff measure and capacity,which are based on the kernel functions depending explicitly onγ(·).Furthermore,the multiple intersections of the sample paths of two independent centered space-time anisotropic Gaussian fields with different distributions are considered.Our results extend the corresponding results for anisotropic Gaussian fields to a large class of space-time anisotropic Gaussian fields.展开更多
In this article, we propose by using the Hausdorff distance Simpson’s rule for the triple integral of a fuzzy-valued function and the error bound of this method, one of the variables of which is fuzzy. In addition, t...In this article, we propose by using the Hausdorff distance Simpson’s rule for the triple integral of a fuzzy-valued function and the error bound of this method, one of the variables of which is fuzzy. In addition, thin δ-fine partitions are introduced. The integration domain is a quasi-fuzzy parallelipiped. A numerical example is presented in order to show the application and the significance of the method.展开更多
In this paper, the initial boundary value problem of a class of nonlinear generalized Kolmogorov-Petrovlkii-Piskunov equations is studied. The existence and uniqueness of the solution and the bounded absorption set ar...In this paper, the initial boundary value problem of a class of nonlinear generalized Kolmogorov-Petrovlkii-Piskunov equations is studied. The existence and uniqueness of the solution and the bounded absorption set are proved by the prior estimation and the Galerkin finite element method, thus the existence of the global attractor is proved and the upper bound estimate of the global attractor is obtained.展开更多
针对地表移动观测站和InSAR技术手段在矿山开采沉陷监测的局限性,利用机载激光雷达(Light Detection and Ranging,LiDAR)采集沉陷区三维点云数据,通过多时相点云构建地表数字沉陷模型(沉陷DEM),获取地表的移动变形特征。然而构建的沉陷...针对地表移动观测站和InSAR技术手段在矿山开采沉陷监测的局限性,利用机载激光雷达(Light Detection and Ranging,LiDAR)采集沉陷区三维点云数据,通过多时相点云构建地表数字沉陷模型(沉陷DEM),获取地表的移动变形特征。然而构建的沉陷DEM包含多种来源复杂且难以去除的噪声,限制了该技术在矿山开采沉陷监测的应用。提出将机载LiDAR点云直接比较的算法(Cloud to Cloud,C2C)进行矿山开采沉陷监测,以榆神矿区某工作面为研究区,将同期水准观测数据作为参考数据,并与三种主流点云插值算法构建的沉陷DEM进行对比,验证该算法的可行性和精度。结果表明,C2C算法能够快速获取高精度的沉陷值,其沉陷精度明显优于通过点云插值算法获取的计算结果,下沉曲线符合矿山开采沉陷的一般规律。该算法可以达到厘米级的精度,为矿山地表移动变形监测和生态环境修复提供了新的参考方案。展开更多
Let G be a reductive Nash group,acting on a Nash manifold X.Let Z be a G-stable closed Nash submanifold of X and denote by U the complement of Z in X.Letχbe a character of G and denote by g the complexified Lie algeb...Let G be a reductive Nash group,acting on a Nash manifold X.Let Z be a G-stable closed Nash submanifold of X and denote by U the complement of Z in X.Letχbe a character of G and denote by g the complexified Lie algebra of G.We give a sufficient condition for the natural linear map H_(k)(g,S(U)×χ)→H_k(g,S(X)×χ)between the Lie algebra homologies of Schwartz functions to be an isomorphism.For k=0,by considering the dual,we obtain the automatic extensions of g-invariant(twisted by-χ)Schwartz distributions.展开更多
高比例可再生能源的接入给微电网的稳定运行带来的巨大挑战,传统随机优化和鲁棒优化方法在处理不确定性方面仍存在一定的局限性。综合考虑风电、负荷的双重不确定性,采用分布鲁棒优化方法,构建了基于豪斯多夫(Hausdorff)距离的微电网两...高比例可再生能源的接入给微电网的稳定运行带来的巨大挑战,传统随机优化和鲁棒优化方法在处理不确定性方面仍存在一定的局限性。综合考虑风电、负荷的双重不确定性,采用分布鲁棒优化方法,构建了基于豪斯多夫(Hausdorff)距离的微电网两阶段分布鲁棒优化调度模型,第一阶段利用场景预测信息,制定包含储能充放电计划、购售电计划的预调度方案,第二阶段基于各典型场景信息制定微电网各单元出力调整计划;然后采用列与约束生成算法(columns and constraints generation,CCG)进行迭代求解,得到最恶劣概率分布下运行成本最低的调度方案;最后,通过算例仿真分析验证了所提方法的有效性,所得到的决策方案兼顾了经济性和安全性。展开更多
基金supported by the National Natural Science Foundation of China(12371150,11971432)the Natural Science Foundation of Zhejiang Province(LY21G010003)+2 种基金the Management Project of"Digital+"Discipline Construction of Zhejiang Gongshang University(SZJ2022A012,SZJ2022B017)the Characteristic&Preponderant Discipline of Key Construction Universities in Zhejiang Province(Zhejiang Gongshang University-Statistics)the Scientific Research Projects of Universities in Anhui Province(2022AH050955)。
文摘Let X={X(t)∈R^(d),t∈R^(N)}be a centered space-time anisotropic Gaussian field with indices H=(H_(1),…,H_(N))∈(0,1)~N,where the components X_(i)(i=1,…,d)of X are independent,and the canonical metric√(E(X_(i)(t)-X_(i)(s))^(2))^(1/2)(i=1,…,d)is commensurate with■for s=(s_(1),…,s_(N)),t=(t_(1),…,t_(N))∈R~N,α_(i)∈(0,1],and with the continuous functionγ(·)satisfying certain conditions.First,the upper and lower bounds of the hitting probabilities of X can be derived from the corresponding generalized Hausdorff measure and capacity,which are based on the kernel functions depending explicitly onγ(·).Furthermore,the multiple intersections of the sample paths of two independent centered space-time anisotropic Gaussian fields with different distributions are considered.Our results extend the corresponding results for anisotropic Gaussian fields to a large class of space-time anisotropic Gaussian fields.
文摘In this article, we propose by using the Hausdorff distance Simpson’s rule for the triple integral of a fuzzy-valued function and the error bound of this method, one of the variables of which is fuzzy. In addition, thin δ-fine partitions are introduced. The integration domain is a quasi-fuzzy parallelipiped. A numerical example is presented in order to show the application and the significance of the method.
文摘In this paper, the initial boundary value problem of a class of nonlinear generalized Kolmogorov-Petrovlkii-Piskunov equations is studied. The existence and uniqueness of the solution and the bounded absorption set are proved by the prior estimation and the Galerkin finite element method, thus the existence of the global attractor is proved and the upper bound estimate of the global attractor is obtained.
文摘针对地表移动观测站和InSAR技术手段在矿山开采沉陷监测的局限性,利用机载激光雷达(Light Detection and Ranging,LiDAR)采集沉陷区三维点云数据,通过多时相点云构建地表数字沉陷模型(沉陷DEM),获取地表的移动变形特征。然而构建的沉陷DEM包含多种来源复杂且难以去除的噪声,限制了该技术在矿山开采沉陷监测的应用。提出将机载LiDAR点云直接比较的算法(Cloud to Cloud,C2C)进行矿山开采沉陷监测,以榆神矿区某工作面为研究区,将同期水准观测数据作为参考数据,并与三种主流点云插值算法构建的沉陷DEM进行对比,验证该算法的可行性和精度。结果表明,C2C算法能够快速获取高精度的沉陷值,其沉陷精度明显优于通过点云插值算法获取的计算结果,下沉曲线符合矿山开采沉陷的一般规律。该算法可以达到厘米级的精度,为矿山地表移动变形监测和生态环境修复提供了新的参考方案。
基金the Fundamental Research Funds for the Central Universities(JUSRP121045)the NSF of Jiangsu Province(BK20221057)。
文摘Let G be a reductive Nash group,acting on a Nash manifold X.Let Z be a G-stable closed Nash submanifold of X and denote by U the complement of Z in X.Letχbe a character of G and denote by g the complexified Lie algebra of G.We give a sufficient condition for the natural linear map H_(k)(g,S(U)×χ)→H_k(g,S(X)×χ)between the Lie algebra homologies of Schwartz functions to be an isomorphism.For k=0,by considering the dual,we obtain the automatic extensions of g-invariant(twisted by-χ)Schwartz distributions.
文摘高比例可再生能源的接入给微电网的稳定运行带来的巨大挑战,传统随机优化和鲁棒优化方法在处理不确定性方面仍存在一定的局限性。综合考虑风电、负荷的双重不确定性,采用分布鲁棒优化方法,构建了基于豪斯多夫(Hausdorff)距离的微电网两阶段分布鲁棒优化调度模型,第一阶段利用场景预测信息,制定包含储能充放电计划、购售电计划的预调度方案,第二阶段基于各典型场景信息制定微电网各单元出力调整计划;然后采用列与约束生成算法(columns and constraints generation,CCG)进行迭代求解,得到最恶劣概率分布下运行成本最低的调度方案;最后,通过算例仿真分析验证了所提方法的有效性,所得到的决策方案兼顾了经济性和安全性。
