Based on the construction of reference e le ment and bilinear transformation, a quasi-Wilson element for arbitrary narrow q uadrilateral is presented. Using the interpolation Theorem for narrow quadrilate ral isoparam...Based on the construction of reference e le ment and bilinear transformation, a quasi-Wilson element for arbitrary narrow q uadrilateral is presented. Using the interpolation Theorem for narrow quadrilate ral isoparametric finite element and related methods, the bounds of interpolatio n error for arbitrary narrow quadrilateral quasi-Wilson element are obtained in case when the condition ρ K/h K≥σ 0】0 is not satisfied, where h K is the diameter of the element K and ρ K is the diameter of an ins cribed circle in K. The interpolation error is O(h2 K) in the L2( K)-norm and O(h K) in the H1(K) -norm provided that the in terpolated function belongs to H2(K).展开更多
We perform molecular dynamics simulations for water confined between two smooth hydrophobic walls and observe two crystalline structures with one being first reported. Both of these structures obey the ice rule. The n...We perform molecular dynamics simulations for water confined between two smooth hydrophobic walls and observe two crystalline structures with one being first reported. Both of these structures obey the ice rule. The novel ice phase is a flat hexagonal-rhombic trilayer ice, obtained under 1 GPa load at wall separation of 1.0 nm. In this structure, the water molecules in the two layers next to one of the walls （outer layers） and in the middle layer form hexagonal rings and rhombic rings, respectively. For a molecule in the outer layers, three of its four hydrogen bonds are in the same layer, and the other one hydrogen bond connects to the middle layer. For a molecule in the middle layer, only two of its four hydrogen-bonds are located in the same layer, and the other two connect to two different outer layers. Despite their different motifs, the area densities of the three layers are almost equal. The other structure is a flat hexagonal bilayer ice produced at wall separation of 0.8 nm under lateral pressure of 100 MPa, analogous to a system demonstrated by Koga et al [Phys. Rev. Lett. 79, 5262 （1997）]. Both first-order and continuous phase transitions take place in these simulations.展开更多
L（ s, t）-labeling is a variation of graph coloring which is motivated by a special kind of the channel assignment problem. Let s and t be any two nonnegative integers. An L （s, t）-labeling of a graph G is an assig...L（ s, t）-labeling is a variation of graph coloring which is motivated by a special kind of the channel assignment problem. Let s and t be any two nonnegative integers. An L （s, t）-labeling of a graph G is an assignment of integers to the vertices of G such that adjacent vertices receive integers which differ by at least s, and vertices that are at distance of two receive integers which differ by at least t. Given an L（s, t） -labeling f of a graph G, the L（s, t） edge span of f, βst （ G, f） = max { ｜f（u） -f（v）｜： （ u, v） ∈ E（G） } is defined. The L（ s, t） edge span of G, βst（G）, is minβst（G,f）, where the minimum runs over all L（s, t）-labelings f of G. Let T be any tree with a maximum degree of △≥2. It is proved that if 2s≥t≥0, then βst（T） =（ [△/2 ] - 1）t ＋s; if 0≤2s 〈 t and △ is even, then βst（T） = [ （△ - 1） t/2 ] ; and if 0 ≤2s 〈 t and △ is odd, then βst（T） = （△ - 1） t/2 ＋ s. Thus, the L（s, t） edge spans of the Cartesian product of two paths and of the square lattice are completely determined.展开更多
In this paper we investigate the existence of positive solution for a class of fourth_order superlinear semipositone eigenvalue problems. This class of problems usually describes the deformation of the elastic beam wh...In this paper we investigate the existence of positive solution for a class of fourth_order superlinear semipositone eigenvalue problems. This class of problems usually describes the deformation of the elastic beam whose both end_points are fixed.展开更多
文摘Based on the construction of reference e le ment and bilinear transformation, a quasi-Wilson element for arbitrary narrow q uadrilateral is presented. Using the interpolation Theorem for narrow quadrilate ral isoparametric finite element and related methods, the bounds of interpolatio n error for arbitrary narrow quadrilateral quasi-Wilson element are obtained in case when the condition ρ K/h K≥σ 0】0 is not satisfied, where h K is the diameter of the element K and ρ K is the diameter of an ins cribed circle in K. The interpolation error is O(h2 K) in the L2( K)-norm and O(h K) in the H1(K) -norm provided that the in terpolated function belongs to H2(K).
基金ACKNOWLEDGMENTS This work was supported by the National Natural Science Foundation of China （No.20603032, No.20733004, No.21121003, No.91021004, and No.20933006）, by the Ministry of Science and Technology of China （No.2011CB921400）, the National Excellent DoctoralDissertation of China （No.200736）, the Fundamental Research Funds for the Central Universities （No.WK2340000006, No.WK2060140005, and No.WK2060030012）, and the USTC-HP HPC Project.
文摘We perform molecular dynamics simulations for water confined between two smooth hydrophobic walls and observe two crystalline structures with one being first reported. Both of these structures obey the ice rule. The novel ice phase is a flat hexagonal-rhombic trilayer ice, obtained under 1 GPa load at wall separation of 1.0 nm. In this structure, the water molecules in the two layers next to one of the walls （outer layers） and in the middle layer form hexagonal rings and rhombic rings, respectively. For a molecule in the outer layers, three of its four hydrogen bonds are in the same layer, and the other one hydrogen bond connects to the middle layer. For a molecule in the middle layer, only two of its four hydrogen-bonds are located in the same layer, and the other two connect to two different outer layers. Despite their different motifs, the area densities of the three layers are almost equal. The other structure is a flat hexagonal bilayer ice produced at wall separation of 0.8 nm under lateral pressure of 100 MPa, analogous to a system demonstrated by Koga et al [Phys. Rev. Lett. 79, 5262 （1997）]. Both first-order and continuous phase transitions take place in these simulations.
基金The National Natural Science Foundation of China(No10671033)Southeast University Science Foundation ( NoXJ0607230)
文摘L（ s, t）-labeling is a variation of graph coloring which is motivated by a special kind of the channel assignment problem. Let s and t be any two nonnegative integers. An L （s, t）-labeling of a graph G is an assignment of integers to the vertices of G such that adjacent vertices receive integers which differ by at least s, and vertices that are at distance of two receive integers which differ by at least t. Given an L（s, t） -labeling f of a graph G, the L（s, t） edge span of f, βst （ G, f） = max { ｜f（u） -f（v）｜： （ u, v） ∈ E（G） } is defined. The L（ s, t） edge span of G, βst（G）, is minβst（G,f）, where the minimum runs over all L（s, t）-labelings f of G. Let T be any tree with a maximum degree of △≥2. It is proved that if 2s≥t≥0, then βst（T） =（ [△/2 ] - 1）t ＋s; if 0≤2s 〈 t and △ is even, then βst（T） = [ （△ - 1） t/2 ] ; and if 0 ≤2s 〈 t and △ is odd, then βst（T） = （△ - 1） t/2 ＋ s. Thus, the L（s, t） edge spans of the Cartesian product of two paths and of the square lattice are completely determined.
文摘In this paper we investigate the existence of positive solution for a class of fourth_order superlinear semipositone eigenvalue problems. This class of problems usually describes the deformation of the elastic beam whose both end_points are fixed.
