The reaction of Cd（NO_3）_2·4H_2O with 4,4？-dipyridylacetylene（4,4？-DPA） and 2-nitroterephthalic acid（2-NO_2-H_2BDC） in DMF/H_2O mixed solvent has afforded a compound {[Cd（2-NO_2-BDC）（4,4？-DPA）]·...The reaction of Cd（NO_3）_2·4H_2O with 4,4？-dipyridylacetylene（4,4？-DPA） and 2-nitroterephthalic acid（2-NO_2-H_2BDC） in DMF/H_2O mixed solvent has afforded a compound {[Cd（2-NO_2-BDC）（4,4？-DPA）]·（DMF）}_n（1）. Compound 1 has been characterized by single-crystal X-ray diffraction, powder X-ray diffraction, thermogravimetry analysis, and IR spectrum. Compound 1 crystallizes in the monoclinic system, space group P21/n, with a = 12.1488（3）, b = 14.6689（3）, c = 13.1615（3） ？, β = 111.809（3）o, V = 2177.63（9） ？~3, Z = 4, C_（23）H_（18）N_4O_7 Cd, M_r = 574.81, D_c = 1.753 g/cm^3, μ = 8.523 mm^（-1）, F（000） = 1152, the final R = 0.0411 and wR = 0.1064 for 3589 observed reflections with I 〉 2s（I）. In compound 1, the Cd（Ⅱ） ions are linked by the carboxylate groups of 2-NO_2-BDC ligands to give a two-dimensional layered structure based on the centrosymmetric dinuclear Cd_2（COO）_2 units, which are further connected by the 4,4？-DPA ligands to produce a three-dimensional framework with pcu topology. Careful examination revealed that compound 1 is a 2-fold interpenetrating framework. Furthermore, the gas adsorption properties of 1 for N_2 and CO_2 have also been investigated.展开更多
A coordination polymer [Ni（pbc）2（H2O）]n（Hpbc = 3-pyrid-4-ylbenzoic acid） has been prepared by hydrothermal synthesis and characterized by single-crystal X-ray diffraction,IR and elemental analysis.The crystal is...A coordination polymer [Ni（pbc）2（H2O）]n（Hpbc = 3-pyrid-4-ylbenzoic acid） has been prepared by hydrothermal synthesis and characterized by single-crystal X-ray diffraction,IR and elemental analysis.The crystal is of monoclinic,space group C2/c with a=19.624（5）,b=12.029（5）,c=19.452（5）A,β=104.45（5）°,C24H18NiN2O5,Mr=473.11,V=4447（2）A^3,Dc=1.413 g/cm^3,F（000）=1952,μ = 0.91 cm^-1,Z = 8,the final R=0.0424 and wR=0.0871 for 3757 reflections with I〉2σ（I）.X-ray diffraction analysis reveals that the pbc-ligands act as diconnectors to link two Ni（Ⅱ） centers and adopt two coordination modes of μ2-N,O and μ2-N,O,O to form infinite wavy nickel-carboxylate chains along the bc plane.The topological analysis of compound [Ni（pbc）2（H2O）]n reveals that it is a typical CdS framework.展开更多
We consider a parametrized family of compact G2-calibrated solvmanifolds, and construct associative (so volume-minimizing submanifolds) 3-tori with respect to the closed G2-structure. We also study the Laplacian flow ...We consider a parametrized family of compact G2-calibrated solvmanifolds, and construct associative (so volume-minimizing submanifolds) 3-tori with respect to the closed G2-structure. We also study the Laplacian flow of this closed G2 form on the solvable Lie group underlying to each of these solvmanifolds, and show long time existence of the solution.展开更多
A new coordination polymer,[Co_(2)(L)_(2)(4,4'-bipy)]_(n)·3nH_(2)O(1)based on 5-(3-methyl-5-phenyl-4H-1,2,4-tri-azol-4-yl)isophthalic acid(H_(2)L)and 4,4'-bipyridine(4,4'-bipy)has been hydrothermally ...A new coordination polymer,[Co_(2)(L)_(2)(4,4'-bipy)]_(n)·3nH_(2)O(1)based on 5-(3-methyl-5-phenyl-4H-1,2,4-tri-azol-4-yl)isophthalic acid(H_(2)L)and 4,4'-bipyridine(4,4'-bipy)has been hydrothermally synthesized and character-ized by single-crystal X-ray diffraction,XRPD,IR,and elemental analysis.Temperature-dependent magnetic sus-ceptibility and thermal degradation for 1 were also studied.The asymmetric unit of compound 1 consists of two crystallographically independent Co(II)ion,two L^(2−)ligand,one 4,4'-bipy ligand,and three lattice water molecules.The 2D triangle networks were linked by the bridging 4,4'-bipy ligand to give rise to a 2-fold interpenetrated 3D architecture.The simplest cyclic motif of the 2D networks is a triangle ring consisting of three Co(II)cations and three L^(2−)ligands.So we can define Co(II)ions as 4-connected nodes and the L^(2−)ligands as 3-connected nodes.Thus,the 3D structure can be described as a 2-fold parallel interpenetrated ins InS 3,4-conn topology.展开更多
A novel 3D hetero-nuclear framework,namely [K_2Cd_5（Hbptc）_4（H_2O）_（12）·12H_2O]_n（1,H4 bptc = biphenyl-2,3,3？,5？-tetracarboxylic acid）,was obtained by hydrothermal reaction. X-ray singlecrystal structur...A novel 3D hetero-nuclear framework,namely [K_2Cd_5（Hbptc）_4（H_2O）_（12）·12H_2O]_n（1,H4 bptc = biphenyl-2,3,3？,5？-tetracarboxylic acid）,was obtained by hydrothermal reaction. X-ray singlecrystal structure analysis reveals that polymer 1 crystallizes in orthorhombic,space group Pbcn with a = 26.6152（13）,b = 11.7449（5）,c = 29.5923（14） ？,V = 9250.3（7） ？~3,C_（64）H_（76）Cd_5K_2O_（56）,Mr = 2381.44,Dc = 1.710 g/cm^3,μ（MoK α） = 1.323 mm^（-1）,F（000） = 4744,Z = 4,the final R = 0.0668 and wR = 0.1135 for 10613 observed reflections（I 〉 2σ（I））. Polymer 1 displays a 3D network that is built on the unprecedented heterobimetallic [Cd_3Cd_2K] molecular building block with a（3,4）-connected（6·8·8）2（6·6·82·82·126·126） topology which represents a rare 2-fold interpenetrating 3D framework topology network. The luminescence analyses reveal that polymer 1 shows obvious emission at room temperature in the solid state. In addition,it was also characterized by elemental,IR spectra and TG analyses.展开更多
Vaserstein introduced the K<sub>1</sub>-functor for the unitary groups over the associative ring with involution, studied the stabilization of unitary K<sub>1</sub> for some rings with the stab...Vaserstein introduced the K<sub>1</sub>-functor for the unitary groups over the associative ring with involution, studied the stabilization of unitary K<sub>1</sub> for some rings with the stable range condition; and particularly described the prestabilization for K<sub>1</sub>U<sup>ε</sup> of local rings. In this report, we study the prestabilization for K<sub>1</sub>U<sup>ε</sup> of a class of rings satisfying the condition Sr（R） ≤1 which is introduced by Vaserstein and Bass.展开更多
Two new 2 D → 2 D zinc(II) coordination polymers, [Zn(btre)0.5(nbdc)(H2 O)]n(1) and {[Zn(btre)0.5(Me Oip)(H2 O)2]·H2 O}n(2)(btre = 1,2-bis(1,2,4-triazol-4-yl)ethane, nbdc=3-nitro-1, 2-benzenedicarboxylate, Me Oi...Two new 2 D → 2 D zinc(II) coordination polymers, [Zn(btre)0.5(nbdc)(H2 O)]n(1) and {[Zn(btre)0.5(Me Oip)(H2 O)2]·H2 O}n(2)(btre = 1,2-bis(1,2,4-triazol-4-yl)ethane, nbdc=3-nitro-1, 2-benzenedicarboxylate, Me Oip=4-methoxybenzene-1, 3-dicarboxylate) were synthesized at room temperature condition and characterized by IR spectra, elemental analyses, single-crystal and powder X-ray diffractions. Three sets of equivalent 2 D(6, 3) networks parallel polycatenated with each other to give a 2 D → 2 D network in 1 and 2. There are strong π-π interactions and hydrogen bonding interactions between adjacent parallel polycatenated 2 D(6, 3) network in 1. Only hydrogen bonding interactions exist in 2. Thermal stabilities and luminescence of 1 and 2 were investigated.展开更多
Under investigation in this paper is a relativistic Toda lattice system with one perturbation parameterαabbreviated as RTLαsystem by Suris,which may describe the motions of particles in lattices interacting through ...Under investigation in this paper is a relativistic Toda lattice system with one perturbation parameterαabbreviated as RTLαsystem by Suris,which may describe the motions of particles in lattices interacting through an exponential interaction force.First of all,an integrable lattice hierarchy associated with an RTLαsystem is constructed,from which some relevant integrable properties such as Hamiltonian structures,Liouville integrability and conservation laws are investigated.Secondly,the discrete generalized(m,2 N-m)-fold Darboux transformation is constructed to derive multi-soliton solutions,higher-order rational and semirational solutions,and their mixed solutions of an RTLαsystem.The soliton elastic interactions and details of rational solutions are analyzed via the graphics and asymptotic analysis.Finally,soliton dynamical evolutions are investigated via numerical simulations,showing that a small noise has very little effect on the soliton propagation.These results may provide new insight into nonlinear lattice dynamics described by RTLαsystem.展开更多
The bifurcation problems of rough 2-point-loop are studied for the case ρ11＞λ11,ρ1/2＜λ1/2,ρ11ρ12＜λ11λ2, where-ρ1i＜0 and λ1i＞0 are the pair of principal eigenvalues of unperturbed system at saddle point ...The bifurcation problems of rough 2-point-loop are studied for the case ρ11＞λ11,ρ1/2＜λ1/2,ρ11ρ12＜λ11λ2, where-ρ1i＜0 and λ1i＞0 are the pair of principal eigenvalues of unperturbed system at saddle point pi, i= 1, 2. Under the transversal and nontwisted conditions, the authors obtain some results of the existence of one 1-periodic orbit, one 1-periodic and one 1-homoclinic loop, two 1-periodic orbits and one 2-fold 1-periodic orbit. Moreover, the bifurcation surfaces and the existence regions are given, and the corresponding bifurcation graph is drawn.展开更多
In this paper, a discrete KdV equation that is related to the famous continuous KdV equation is studied. First, an integrable discrete KdV hierarchy is constructed, from which several new discrete KdV equations are ob...In this paper, a discrete KdV equation that is related to the famous continuous KdV equation is studied. First, an integrable discrete KdV hierarchy is constructed, from which several new discrete KdV equations are obtained. Second, we correspond the first several discrete equations of this hierarchy to the continuous KdV equation through the continuous limit. Third, the generalized(m, 2N-m)-fold Darboux transformation of the discrete KdV equation is established based on its known Lax pair. Finally, the diverse exact solutions including soliton solutions, rational solutions and mixed solutions on non-zero seed background are obtained by applying the resulting Darboux transformation, and their asymptotic states and physical properties such as amplitude, velocity, phase and energy are analyzed. At the same time, some soliton solutions are numerically simulated to show their dynamic behaviors. The properties and results obtained in this paper may be helpful to understand some physical phenomena described by KdV equations.展开更多
基金Supported by the National Natural Science Foundation of China(No.21361011 and 21101081)the Natural Science Foundation of Jiangxi Province(No.20151BAB203002)
文摘The reaction of Cd（NO_3）_2·4H_2O with 4,4？-dipyridylacetylene（4,4？-DPA） and 2-nitroterephthalic acid（2-NO_2-H_2BDC） in DMF/H_2O mixed solvent has afforded a compound {[Cd（2-NO_2-BDC）（4,4？-DPA）]·（DMF）}_n（1）. Compound 1 has been characterized by single-crystal X-ray diffraction, powder X-ray diffraction, thermogravimetry analysis, and IR spectrum. Compound 1 crystallizes in the monoclinic system, space group P21/n, with a = 12.1488（3）, b = 14.6689（3）, c = 13.1615（3） ？, β = 111.809（3）o, V = 2177.63（9） ？~3, Z = 4, C_（23）H_（18）N_4O_7 Cd, M_r = 574.81, D_c = 1.753 g/cm^3, μ = 8.523 mm^（-1）, F（000） = 1152, the final R = 0.0411 and wR = 0.1064 for 3589 observed reflections with I 〉 2s（I）. In compound 1, the Cd（Ⅱ） ions are linked by the carboxylate groups of 2-NO_2-BDC ligands to give a two-dimensional layered structure based on the centrosymmetric dinuclear Cd_2（COO）_2 units, which are further connected by the 4,4？-DPA ligands to produce a three-dimensional framework with pcu topology. Careful examination revealed that compound 1 is a 2-fold interpenetrating framework. Furthermore, the gas adsorption properties of 1 for N_2 and CO_2 have also been investigated.
基金supported by the Natural Science Foundation of Shandong Province (No Y2007F68)
文摘A coordination polymer [Ni（pbc）2（H2O）]n（Hpbc = 3-pyrid-4-ylbenzoic acid） has been prepared by hydrothermal synthesis and characterized by single-crystal X-ray diffraction,IR and elemental analysis.The crystal is of monoclinic,space group C2/c with a=19.624（5）,b=12.029（5）,c=19.452（5）A,β=104.45（5）°,C24H18NiN2O5,Mr=473.11,V=4447（2）A^3,Dc=1.413 g/cm^3,F（000）=1952,μ = 0.91 cm^-1,Z = 8,the final R=0.0424 and wR=0.0871 for 3757 reflections with I〉2σ（I）.X-ray diffraction analysis reveals that the pbc-ligands act as diconnectors to link two Ni（Ⅱ） centers and adopt two coordination modes of μ2-N,O and μ2-N,O,O to form infinite wavy nickel-carboxylate chains along the bc plane.The topological analysis of compound [Ni（pbc）2（H2O）]n reveals that it is a typical CdS framework.
文摘We consider a parametrized family of compact G2-calibrated solvmanifolds, and construct associative (so volume-minimizing submanifolds) 3-tori with respect to the closed G2-structure. We also study the Laplacian flow of this closed G2 form on the solvable Lie group underlying to each of these solvmanifolds, and show long time existence of the solution.
基金This work was supported by the National Natural Science Foundation of China(Nos.21071083 and 20771062).
文摘A new coordination polymer,[Co_(2)(L)_(2)(4,4'-bipy)]_(n)·3nH_(2)O(1)based on 5-(3-methyl-5-phenyl-4H-1,2,4-tri-azol-4-yl)isophthalic acid(H_(2)L)and 4,4'-bipyridine(4,4'-bipy)has been hydrothermally synthesized and character-ized by single-crystal X-ray diffraction,XRPD,IR,and elemental analysis.Temperature-dependent magnetic sus-ceptibility and thermal degradation for 1 were also studied.The asymmetric unit of compound 1 consists of two crystallographically independent Co(II)ion,two L^(2−)ligand,one 4,4'-bipy ligand,and three lattice water molecules.The 2D triangle networks were linked by the bridging 4,4'-bipy ligand to give rise to a 2-fold interpenetrated 3D architecture.The simplest cyclic motif of the 2D networks is a triangle ring consisting of three Co(II)cations and three L^(2−)ligands.So we can define Co(II)ions as 4-connected nodes and the L^(2−)ligands as 3-connected nodes.Thus,the 3D structure can be described as a 2-fold parallel interpenetrated ins InS 3,4-conn topology.
基金supported by the National Natural Science Foundation of China(No.21273101 and 21302082)the Program for Science&Technology Innovation Talents in Universities of Henan Province(2014HASTIT014,14IRTSTHN008 and 164100510012)the Tackle Key Problem of Science and Technology Project of Henan Province(No.142102310483)
文摘A novel 3D hetero-nuclear framework,namely [K_2Cd_5（Hbptc）_4（H_2O）_（12）·12H_2O]_n（1,H4 bptc = biphenyl-2,3,3？,5？-tetracarboxylic acid）,was obtained by hydrothermal reaction. X-ray singlecrystal structure analysis reveals that polymer 1 crystallizes in orthorhombic,space group Pbcn with a = 26.6152（13）,b = 11.7449（5）,c = 29.5923（14） ？,V = 9250.3（7） ？~3,C_（64）H_（76）Cd_5K_2O_（56）,Mr = 2381.44,Dc = 1.710 g/cm^3,μ（MoK α） = 1.323 mm^（-1）,F（000） = 4744,Z = 4,the final R = 0.0668 and wR = 0.1135 for 10613 observed reflections（I 〉 2σ（I））. Polymer 1 displays a 3D network that is built on the unprecedented heterobimetallic [Cd_3Cd_2K] molecular building block with a（3,4）-connected（6·8·8）2（6·6·82·82·126·126） topology which represents a rare 2-fold interpenetrating 3D framework topology network. The luminescence analyses reveal that polymer 1 shows obvious emission at room temperature in the solid state. In addition,it was also characterized by elemental,IR spectra and TG analyses.
文摘Vaserstein introduced the K<sub>1</sub>-functor for the unitary groups over the associative ring with involution, studied the stabilization of unitary K<sub>1</sub> for some rings with the stable range condition; and particularly described the prestabilization for K<sub>1</sub>U<sup>ε</sup> of local rings. In this report, we study the prestabilization for K<sub>1</sub>U<sup>ε</sup> of a class of rings satisfying the condition Sr（R） ≤1 which is introduced by Vaserstein and Bass.
基金Supported by the National Natural Science Foundation of China(21271035)the Natural Science Foundation of Anhui Province(KJ2016A512)the Key Projects of Anhui Province University Outstanding Youth Talent Support Program(gxyqZD2016372)
文摘Two new 2 D → 2 D zinc(II) coordination polymers, [Zn(btre)0.5(nbdc)(H2 O)]n(1) and {[Zn(btre)0.5(Me Oip)(H2 O)2]·H2 O}n(2)(btre = 1,2-bis(1,2,4-triazol-4-yl)ethane, nbdc=3-nitro-1, 2-benzenedicarboxylate, Me Oip=4-methoxybenzene-1, 3-dicarboxylate) were synthesized at room temperature condition and characterized by IR spectra, elemental analyses, single-crystal and powder X-ray diffractions. Three sets of equivalent 2 D(6, 3) networks parallel polycatenated with each other to give a 2 D → 2 D network in 1 and 2. There are strong π-π interactions and hydrogen bonding interactions between adjacent parallel polycatenated 2 D(6, 3) network in 1. Only hydrogen bonding interactions exist in 2. Thermal stabilities and luminescence of 1 and 2 were investigated.
基金supported by National Natural Science Foundation of China (Grant No. 12 071 042)Beijing Natural Science Foundation (Grant No. 1 202 006)。
文摘Under investigation in this paper is a relativistic Toda lattice system with one perturbation parameterαabbreviated as RTLαsystem by Suris,which may describe the motions of particles in lattices interacting through an exponential interaction force.First of all,an integrable lattice hierarchy associated with an RTLαsystem is constructed,from which some relevant integrable properties such as Hamiltonian structures,Liouville integrability and conservation laws are investigated.Secondly,the discrete generalized(m,2 N-m)-fold Darboux transformation is constructed to derive multi-soliton solutions,higher-order rational and semirational solutions,and their mixed solutions of an RTLαsystem.The soliton elastic interactions and details of rational solutions are analyzed via the graphics and asymptotic analysis.Finally,soliton dynamical evolutions are investigated via numerical simulations,showing that a small noise has very little effect on the soliton propagation.These results may provide new insight into nonlinear lattice dynamics described by RTLαsystem.
基金This work was supported by the National Natural Science Foundation of China(Grant No.10071022)the Shanghai Priority Academic Discipline.
文摘The bifurcation problems of rough 2-point-loop are studied for the case ρ11＞λ11,ρ1/2＜λ1/2,ρ11ρ12＜λ11λ2, where-ρ1i＜0 and λ1i＞0 are the pair of principal eigenvalues of unperturbed system at saddle point pi, i= 1, 2. Under the transversal and nontwisted conditions, the authors obtain some results of the existence of one 1-periodic orbit, one 1-periodic and one 1-homoclinic loop, two 1-periodic orbits and one 2-fold 1-periodic orbit. Moreover, the bifurcation surfaces and the existence regions are given, and the corresponding bifurcation graph is drawn.
基金supported by the National Natural Science Foundation of China (Grant No. 12071042)the Beijing Natural Science Foundation (Grant No. 1202006)。
文摘In this paper, a discrete KdV equation that is related to the famous continuous KdV equation is studied. First, an integrable discrete KdV hierarchy is constructed, from which several new discrete KdV equations are obtained. Second, we correspond the first several discrete equations of this hierarchy to the continuous KdV equation through the continuous limit. Third, the generalized(m, 2N-m)-fold Darboux transformation of the discrete KdV equation is established based on its known Lax pair. Finally, the diverse exact solutions including soliton solutions, rational solutions and mixed solutions on non-zero seed background are obtained by applying the resulting Darboux transformation, and their asymptotic states and physical properties such as amplitude, velocity, phase and energy are analyzed. At the same time, some soliton solutions are numerically simulated to show their dynamic behaviors. The properties and results obtained in this paper may be helpful to understand some physical phenomena described by KdV equations.
