The concept of locally strong compactness on domains is generalized to general topological spaces. It is proved that for each distributive hypercontinuous lattice L, the space SpecL of nonunit prime elements endowed w...The concept of locally strong compactness on domains is generalized to general topological spaces. It is proved that for each distributive hypercontinuous lattice L, the space SpecL of nonunit prime elements endowed with the hull-kernel topology is locally strongly compact, and for each locally strongly compact space X, the complete lattice of all open sets O(X) is distributive hypercontinuous. For the case of distributive hyperalgebraic lattices, the similar result is given. For a sober space X, it is shown that there is an order reversing isomorphism between the set of upper-open filters of the lattice O(X) of open subsets of X and the set of strongly compact saturated subsets of X, which is analogous to the well-known Hofmann-Mislove Theorem.展开更多
By integrating topology optimization and lattice-based optimization,a novel multi-scale design method is proposed to create solid-lattice hybrid structures and thus to improve the mechanical performance as well as red...By integrating topology optimization and lattice-based optimization,a novel multi-scale design method is proposed to create solid-lattice hybrid structures and thus to improve the mechanical performance as well as reduce the structural weight.To achieve this purpose,a two-step procedure is developed to design and optimize the innovative structures.Initially,the classical topology optimization is utilized to find the optimal material layout and primary load carrying paths.Afterwards,the solid-lattice hybrid structures are reconstructed using the finite element mesh based modeling method.And lattice-based optimization is performed to obtain the optimal crosssection area of the lattice structures.Finally,two typical aerospace structures are optimized to demonstrate the effectiveness of the proposed optimization framework.The numerical results are quite encouraging since the solid-lattice hybrid structures obtained by the presented approach show remarkably improved performance when compared with traditional designs.展开更多
We use a semantical method of complete residuated lattice-valued logic to give a general- ization of fuzzy topology as a partial answer to a problem by Rosser and Turquette.
Let A be a lattice-ordered group. Gusi? showed that A can be equipped with a C-topology which makes A into a topological group. We give a generalization of Gusi?’s theorem, and reveal the very nature of a “C-group”...Let A be a lattice-ordered group. Gusi? showed that A can be equipped with a C-topology which makes A into a topological group. We give a generalization of Gusi?’s theorem, and reveal the very nature of a “C-group” of Gusi? in this paper. Moreover, we show that the C-topological groups are topological lattice-ordered groups, and prove that every archimedean lattice-ordered vector space is a T 2 topological lattice-ordered vector space under the C-topology. An easy example shows that a C-group need not be T 2. A further example demonstrates that a T 2 topological archimedean lattice-ordered group need not be C-archimedean, either.展开更多
设计满足特定需求的三维有序多孔的微桁架点阵结构,是解决航空航天领域某些构件轻量化问题的方法之一。首先,基于具有惩罚的实体各向同性材料(Solid isotropic microstructure with penalization,SIMP)拓扑优化算法,以最小柔度为目标,...设计满足特定需求的三维有序多孔的微桁架点阵结构,是解决航空航天领域某些构件轻量化问题的方法之一。首先,基于具有惩罚的实体各向同性材料(Solid isotropic microstructure with penalization,SIMP)拓扑优化算法,以最小柔度为目标,在不同载荷边界条件下进行点阵胞元的优化,随后对拓扑优化的点阵胞元进行几何重构。采用三维数值均匀化算法分析胞元在不同相对密度下的弹性矩阵及弹性模量曲面,对比4种胞元的各项力学性能;对选择性激光烧结(Selective laser sintering,SLS)增材制造技术制备的试件进行物理试验并对比试验结果,得到不同构型点阵结构胞元的力学性能。最后,以三点弯曲梁为例分析应力分布,并按照应力分布对梁结构进行Octet胞元的变密度点阵结构设计;同时设计均匀点阵结构作为对照,并通过三点弯曲试验对比变密度点阵结构与均匀点阵结构的力学性能。结果表明,优化并重构的4种胞元的三维数值均匀化模拟与压缩试验结果吻合良好;S Star Tet胞元的弹性模量最大,Octet胞元具有最高的剪切模量和较好的各向同性。相较于均匀点阵结构,变密度点阵结构的弯曲刚度和弯曲强度分别提高了162.6%和250.5%。展开更多
基金Project supported by the National Natural Science Foundation of China (Nos. 10331010, 10861007)the Foundation for the Author of National Excellent Doctoral Dissertation of China (No. 2007B14)+2 种基金the Jiangxi Provincial Natural Science Foundation of China (Nos. 0411025, 2007GZS0179)the Foundation of the Education Department of Jiangxi Province (No. GJJ08162)the Doctoral Fund of Jiangxi Normal University
文摘The concept of locally strong compactness on domains is generalized to general topological spaces. It is proved that for each distributive hypercontinuous lattice L, the space SpecL of nonunit prime elements endowed with the hull-kernel topology is locally strongly compact, and for each locally strongly compact space X, the complete lattice of all open sets O(X) is distributive hypercontinuous. For the case of distributive hyperalgebraic lattices, the similar result is given. For a sober space X, it is shown that there is an order reversing isomorphism between the set of upper-open filters of the lattice O(X) of open subsets of X and the set of strongly compact saturated subsets of X, which is analogous to the well-known Hofmann-Mislove Theorem.
基金supported by National Key Research and Development Program(No.2017YFB1102800)Key Project of NSFC(Nos.51790171 and 51761145111)NSFC for Excellent Young Scholars(No.11722219)。
文摘By integrating topology optimization and lattice-based optimization,a novel multi-scale design method is proposed to create solid-lattice hybrid structures and thus to improve the mechanical performance as well as reduce the structural weight.To achieve this purpose,a two-step procedure is developed to design and optimize the innovative structures.Initially,the classical topology optimization is utilized to find the optimal material layout and primary load carrying paths.Afterwards,the solid-lattice hybrid structures are reconstructed using the finite element mesh based modeling method.And lattice-based optimization is performed to obtain the optimal crosssection area of the lattice structures.Finally,two typical aerospace structures are optimized to demonstrate the effectiveness of the proposed optimization framework.The numerical results are quite encouraging since the solid-lattice hybrid structures obtained by the presented approach show remarkably improved performance when compared with traditional designs.
基金supported by the National Foundation for Distionguished Young Scholars(Grant No:69725004)Rrsearch and Development Project of High-Technology(Grant No:863-306-ZT06-04-3)+1 种基金Foundation of Natural Sciences(Grant No:6982001) of ChinaFOK Ying-Tung Edu
文摘We use a semantical method of complete residuated lattice-valued logic to give a general- ization of fuzzy topology as a partial answer to a problem by Rosser and Turquette.
基金supported by the Fund of Elitist Development of Beijing (Grant No. 20071D1600600412)the Scientific Research Foundation for the Returned Overseas Chinese Scholars,State Education Ministry
文摘Let A be a lattice-ordered group. Gusi? showed that A can be equipped with a C-topology which makes A into a topological group. We give a generalization of Gusi?’s theorem, and reveal the very nature of a “C-group” of Gusi? in this paper. Moreover, we show that the C-topological groups are topological lattice-ordered groups, and prove that every archimedean lattice-ordered vector space is a T 2 topological lattice-ordered vector space under the C-topology. An easy example shows that a C-group need not be T 2. A further example demonstrates that a T 2 topological archimedean lattice-ordered group need not be C-archimedean, either.
文摘设计满足特定需求的三维有序多孔的微桁架点阵结构,是解决航空航天领域某些构件轻量化问题的方法之一。首先,基于具有惩罚的实体各向同性材料(Solid isotropic microstructure with penalization,SIMP)拓扑优化算法,以最小柔度为目标,在不同载荷边界条件下进行点阵胞元的优化,随后对拓扑优化的点阵胞元进行几何重构。采用三维数值均匀化算法分析胞元在不同相对密度下的弹性矩阵及弹性模量曲面,对比4种胞元的各项力学性能;对选择性激光烧结(Selective laser sintering,SLS)增材制造技术制备的试件进行物理试验并对比试验结果,得到不同构型点阵结构胞元的力学性能。最后,以三点弯曲梁为例分析应力分布,并按照应力分布对梁结构进行Octet胞元的变密度点阵结构设计;同时设计均匀点阵结构作为对照,并通过三点弯曲试验对比变密度点阵结构与均匀点阵结构的力学性能。结果表明,优化并重构的4种胞元的三维数值均匀化模拟与压缩试验结果吻合良好;S Star Tet胞元的弹性模量最大,Octet胞元具有最高的剪切模量和较好的各向同性。相较于均匀点阵结构,变密度点阵结构的弯曲刚度和弯曲强度分别提高了162.6%和250.5%。
