Abstract The existence of n positive solutions for a class of third-order three-point boundary value problems is investigated, where n is an arbitrary natural number. The main tool is Krasnosel'skii fixed point th...Abstract The existence of n positive solutions for a class of third-order three-point boundary value problems is investigated, where n is an arbitrary natural number. The main tool is Krasnosel'skii fixed point theorem on the cone.展开更多
The existing state and partitioning of rare earth （RE） on weathered ores in Longnan County（LN）, Xingfeng County（XF） and Ninghua County（NH） were characterized systematically by standard geological analytical me...The existing state and partitioning of rare earth （RE） on weathered ores in Longnan County（LN）, Xingfeng County（XF） and Ninghua County（NH） were characterized systematically by standard geological analytical methods. It is found that RE in the weathered rare earth ores exist as four phases： （a） water soluble, （b） ion-exchangeable, （c） colloidal sediment （oxides）, （d） minerals, in which mainly as ion exchangeable phase, accounting for nearly 80% of total RE, with about 20% in the form of colloid sediment phase and mineral phase, but very little as aqueous soluble phase. These rare earth partitioning were mainly chosen mid-heavy RE elements, occupying above 60%, but not equal in the four phases. The mid-heavy RE elements were primarily enriched in the ion exchangeable phase up to 40%, while the containment of cerium dioxide is below 2 %. The cerium deficiency occurs in the ion exchangeable phase in weathered ore. It results from that the Ce^3＋ is oxidized into Ce^4＋ and changes into CeO2. For LN ore, the containment of Y is high in weathered ore because Y-minerals are abundant in original rock.展开更多
该文从数学上描述了配电系统的N-1安全性,给出了安全域(distribution system security region,DSSR)的严格数学定义,并首次证明DSSR的存在性。首先,从数学上描述了配电系统运行的状态空间与正常运行方式下的约束条件。其次,为描述N-1安...该文从数学上描述了配电系统的N-1安全性,给出了安全域(distribution system security region,DSSR)的严格数学定义,并首次证明DSSR的存在性。首先,从数学上描述了配电系统运行的状态空间与正常运行方式下的约束条件。其次,为描述N-1安全性及安全程度,提出了安全函数的概念,并给出一个具体的安全函数,并证明其具有连续和单调减的重要性质。再从数学上将N-1安全性描述为安全函数满足某个预定临界值的问题。然后,给出了更严格的DSSR数学定义:DSSR是所有安全工作点的集合,该集合具有封闭的边界,边界内部均为安全工作点,外部均为不安全工作点。最后,从数学上证明了对于任意给定配电网,其DSSR一定存在。文中工作对揭示配电网安全域的数学本质具有重要意义,为未来智能配电系统安全高效的运行及规划技术奠定理论基础。展开更多
文摘Abstract The existence of n positive solutions for a class of third-order three-point boundary value problems is investigated, where n is an arbitrary natural number. The main tool is Krasnosel'skii fixed point theorem on the cone.
文摘The existing state and partitioning of rare earth （RE） on weathered ores in Longnan County（LN）, Xingfeng County（XF） and Ninghua County（NH） were characterized systematically by standard geological analytical methods. It is found that RE in the weathered rare earth ores exist as four phases： （a） water soluble, （b） ion-exchangeable, （c） colloidal sediment （oxides）, （d） minerals, in which mainly as ion exchangeable phase, accounting for nearly 80% of total RE, with about 20% in the form of colloid sediment phase and mineral phase, but very little as aqueous soluble phase. These rare earth partitioning were mainly chosen mid-heavy RE elements, occupying above 60%, but not equal in the four phases. The mid-heavy RE elements were primarily enriched in the ion exchangeable phase up to 40%, while the containment of cerium dioxide is below 2 %. The cerium deficiency occurs in the ion exchangeable phase in weathered ore. It results from that the Ce^3＋ is oxidized into Ce^4＋ and changes into CeO2. For LN ore, the containment of Y is high in weathered ore because Y-minerals are abundant in original rock.
文摘该文从数学上描述了配电系统的N-1安全性,给出了安全域(distribution system security region,DSSR)的严格数学定义,并首次证明DSSR的存在性。首先,从数学上描述了配电系统运行的状态空间与正常运行方式下的约束条件。其次,为描述N-1安全性及安全程度,提出了安全函数的概念,并给出一个具体的安全函数,并证明其具有连续和单调减的重要性质。再从数学上将N-1安全性描述为安全函数满足某个预定临界值的问题。然后,给出了更严格的DSSR数学定义:DSSR是所有安全工作点的集合,该集合具有封闭的边界,边界内部均为安全工作点,外部均为不安全工作点。最后,从数学上证明了对于任意给定配电网,其DSSR一定存在。文中工作对揭示配电网安全域的数学本质具有重要意义,为未来智能配电系统安全高效的运行及规划技术奠定理论基础。
