In this paper,the author studies the characteristic properties of stable functions between L domains. A basic notion of stable open subsets of L domain is introduced. The author shows that the two element L domains θ...In this paper,the author studies the characteristic properties of stable functions between L domains. A basic notion of stable open subsets of L domain is introduced. The author shows that the two element L domains θ={0,1} is the classifier of the category of L domains and stable functions.展开更多
The high porosity,excellent water stability and optimized supramolecular host–vip interactions of MOFs are the three key factors for their potential practical applications in many important areas including gas stor...The high porosity,excellent water stability and optimized supramolecular host–vip interactions of MOFs are the three key factors for their potential practical applications in many important areas including gas storage/separation,catalysis and so on.In this study,we designed and constructed a highly porous(3,36)-connected txt-type acylamide-functionalized metal–organic framework(HNUST-8)from a pyridine-based acylamide-linking diisophthalate and dicopper(II)-paddlewheel clusters.展开更多
In this paper, we consider a general composite convex optimization problem with a cone-convex system in locally convex Hausdorff topological vector spaces. Some Fenchel conjugate transforms for the composite convex fu...In this paper, we consider a general composite convex optimization problem with a cone-convex system in locally convex Hausdorff topological vector spaces. Some Fenchel conjugate transforms for the composite convex functions are derived to obtain the equivalent condition of the Stable Farkas Lemma, which is formulated by using the epigraph of the conjugates for the convex functions involved and turns out to be weaker than the classic Slater condition. Moreover, we get some necessary and sufficient conditions for stable duality results of the composite convex functions and present an example to illustrate that the monotonic increasing property of the outer convex function in the objective function is essential. Our main results in this paper develop some recently results.展开更多
In this paper we study the properties of the set consisting of all fixed points of a Scott continuous self-map between domains. All the results give an answer to an open problem posed by Lawson and Mislove in 1990.
文摘In this paper,the author studies the characteristic properties of stable functions between L domains. A basic notion of stable open subsets of L domain is introduced. The author shows that the two element L domains θ={0,1} is the classifier of the category of L domains and stable functions.
基金supported by the National Natural Science Foundation of China(Grant No.21401055,21371150 and 21201062)Hunan Provincial Natural Science Foundation of China(Grant No.2018JJ2113 and 2017JJ2095)State Key Laboratory of Coordination Chemistry(Grant No.SKLCC1417).
文摘The high porosity,excellent water stability and optimized supramolecular host–vip interactions of MOFs are the three key factors for their potential practical applications in many important areas including gas storage/separation,catalysis and so on.In this study,we designed and constructed a highly porous(3,36)-connected txt-type acylamide-functionalized metal–organic framework(HNUST-8)from a pyridine-based acylamide-linking diisophthalate and dicopper(II)-paddlewheel clusters.
基金Supported by the Natural Science Foundation of China(Nos.11401533,11301484,11071180,11371273,11171247)Hong Kong Polytechnic University(G-YX1Q)+1 种基金the Research Grants Council of Hong Kong(No.Poly U 5306/11E)Scientific Research Foundation of Zhejiang Agriculture and Forestry University(No.2013FR080)
文摘In this paper, we consider a general composite convex optimization problem with a cone-convex system in locally convex Hausdorff topological vector spaces. Some Fenchel conjugate transforms for the composite convex functions are derived to obtain the equivalent condition of the Stable Farkas Lemma, which is formulated by using the epigraph of the conjugates for the convex functions involved and turns out to be weaker than the classic Slater condition. Moreover, we get some necessary and sufficient conditions for stable duality results of the composite convex functions and present an example to illustrate that the monotonic increasing property of the outer convex function in the objective function is essential. Our main results in this paper develop some recently results.
基金the National Natural Science Foundation of China (Grant. No. 10071053) the SFEM of China and the Project of "Excellent Scholars Crossing Centuries" of the Education Ministry of China.
文摘In this paper we study the properties of the set consisting of all fixed points of a Scott continuous self-map between domains. All the results give an answer to an open problem posed by Lawson and Mislove in 1990.
