By coincidence degree,the existence of solution to the boundary value problem of a generalized Liénard equationa(t)x'+F(x,x′)x′+g(x)=e(t), x(0)=x(2π),x′(0)=x′(2π)is proved,where a∈C 1[0,2π],a(t)>...By coincidence degree,the existence of solution to the boundary value problem of a generalized Liénard equationa(t)x'+F(x,x′)x′+g(x)=e(t), x(0)=x(2π),x′(0)=x′(2π)is proved,where a∈C 1[0,2π],a(t)>0(0≤t≤2π),a(0)=a(2π),F(x,y)=f(x)+α|y| β,α>0,β>0 are all constants,f∈C(R,R),e∈C[0,2π]. An example is given as an application.展开更多
The reaction of triphenylphosphine with AgNO3 yielded an unusual nitrate anion bridging one-dimensional infinite chain [Ag(PPh3)NO3] in which the silver(I) atom is three-coordinated by one P atom of triphenylphosphine...The reaction of triphenylphosphine with AgNO3 yielded an unusual nitrate anion bridging one-dimensional infinite chain [Ag(PPh3)NO3] in which the silver(I) atom is three-coordinated by one P atom of triphenylphosphine and two O atoms of two bridging nitrate anions to form a scalene triangle. The complex [Ag(PPh3)NO3] crystallizes in the monoclinic system, space group P21/c with a = 10.281(2), b = 18.596(5), c = 9.180(2) , = 90.60(1), V = 1755.1(7) 3, Z = 4, Mr = 432.15, Dc = 1.635 g/cm3, F(000) = 864 and = 1.254 mm-1. The final R = 0.0606 and wR = 0.1400 for 2188 observed reflections with I > 2(I) out of 3057 unique ones (Rint = 0.0539). IR and elemental analysis of the complex are characterized.展开更多
The reaction of MoO2(acac)2 with 2-amino-6-methyl-pyridine (amp) in the mixed solvent of DMF (N,N-dimethylformamide) and water affords the title complex [H-amp]4- [Mo8O26(DMF)2]2H2O which was characterized by elementa...The reaction of MoO2(acac)2 with 2-amino-6-methyl-pyridine (amp) in the mixed solvent of DMF (N,N-dimethylformamide) and water affords the title complex [H-amp]4- [Mo8O26(DMF)2]2H2O which was characterized by elemental analysis, IR spectroscopy and single-crystal X-ray diffraction analysis with the following crystallographic data: C30H54Mo8N10O30, Mr = 1802.35, monoclinic, P21/n, a = 8.631(1), b = 24.260(3), c = 13.351(2) ? b = 104.688(3), V = 2704.2(7) 3, Z = 2, Dc = 2.213 g/cm3, m =1.890 mm-1 and F(000) = 1760. The final R = 0.0281 and wR = 0.0620 for 4935 observed reflections with I > 2s(I). X-ray structure analysis has confirmed the existence of g-[Mo8O26]4- anion in the molecule. Eight MoO6 distorted octahedra share edges with short terminal MoO bonds from 1.691(3) to 1.749(2) ? medium bonds from 1.868(2) to 1.965(2) ?and long bonds from 2.059(2) to 2.450(2) ? In the terminal site there exist two DMF ligands bound to the Mo atom through O atoms with the MoODMF bond length of 2.166(3) ? affording a bond strength of 0.433. A three-dimensional network structure was formed through hydrogen bonds.展开更多
In this paper, a periodic Holling Ⅱ predator-prey model with impulsive effect is investigated. By applying the Floquet theory of linear periodic impulsive equation,some sufficient conditions are obtained for the line...In this paper, a periodic Holling Ⅱ predator-prey model with impulsive effect is investigated. By applying the Floquet theory of linear periodic impulsive equation,some sufficient conditions are obtained for the linear stability and instability of trivial and semi-trivial periodic solutions. Moreover, we use standard bifurcation theory to show the existence of coexistence states which arise near the semi-trivial periodic solution. As an application, we also examine some special case of the system to confirm our main results.展开更多
文摘By coincidence degree,the existence of solution to the boundary value problem of a generalized Liénard equationa(t)x'+F(x,x′)x′+g(x)=e(t), x(0)=x(2π),x′(0)=x′(2π)is proved,where a∈C 1[0,2π],a(t)>0(0≤t≤2π),a(0)=a(2π),F(x,y)=f(x)+α|y| β,α>0,β>0 are all constants,f∈C(R,R),e∈C[0,2π]. An example is given as an application.
基金NNSFC (No. 20001007 20131020) and Natural Science Foundation of the Chinese Academy of Sciences (KJCX2-H3) and Fujian Province (2000F006)
文摘The reaction of triphenylphosphine with AgNO3 yielded an unusual nitrate anion bridging one-dimensional infinite chain [Ag(PPh3)NO3] in which the silver(I) atom is three-coordinated by one P atom of triphenylphosphine and two O atoms of two bridging nitrate anions to form a scalene triangle. The complex [Ag(PPh3)NO3] crystallizes in the monoclinic system, space group P21/c with a = 10.281(2), b = 18.596(5), c = 9.180(2) , = 90.60(1), V = 1755.1(7) 3, Z = 4, Mr = 432.15, Dc = 1.635 g/cm3, F(000) = 864 and = 1.254 mm-1. The final R = 0.0606 and wR = 0.1400 for 2188 observed reflections with I > 2(I) out of 3057 unique ones (Rint = 0.0539). IR and elemental analysis of the complex are characterized.
基金This work was supported by the Natural Science Foundation and the Youth Science Foundation of Guangxi province
文摘The reaction of MoO2(acac)2 with 2-amino-6-methyl-pyridine (amp) in the mixed solvent of DMF (N,N-dimethylformamide) and water affords the title complex [H-amp]4- [Mo8O26(DMF)2]2H2O which was characterized by elemental analysis, IR spectroscopy and single-crystal X-ray diffraction analysis with the following crystallographic data: C30H54Mo8N10O30, Mr = 1802.35, monoclinic, P21/n, a = 8.631(1), b = 24.260(3), c = 13.351(2) ? b = 104.688(3), V = 2704.2(7) 3, Z = 2, Dc = 2.213 g/cm3, m =1.890 mm-1 and F(000) = 1760. The final R = 0.0281 and wR = 0.0620 for 4935 observed reflections with I > 2s(I). X-ray structure analysis has confirmed the existence of g-[Mo8O26]4- anion in the molecule. Eight MoO6 distorted octahedra share edges with short terminal MoO bonds from 1.691(3) to 1.749(2) ? medium bonds from 1.868(2) to 1.965(2) ?and long bonds from 2.059(2) to 2.450(2) ? In the terminal site there exist two DMF ligands bound to the Mo atom through O atoms with the MoODMF bond length of 2.166(3) ? affording a bond strength of 0.433. A three-dimensional network structure was formed through hydrogen bonds.
基金This research is supported by the National Natural Science Foundation of China (10171106).
文摘In this paper, a periodic Holling Ⅱ predator-prey model with impulsive effect is investigated. By applying the Floquet theory of linear periodic impulsive equation,some sufficient conditions are obtained for the linear stability and instability of trivial and semi-trivial periodic solutions. Moreover, we use standard bifurcation theory to show the existence of coexistence states which arise near the semi-trivial periodic solution. As an application, we also examine some special case of the system to confirm our main results.
