The cross-dimensional dynamical systems have received increasing research attention in recent years.This paper characterizes the structure features of the cross-dimensional vector space.Specifically,it is proved that ...The cross-dimensional dynamical systems have received increasing research attention in recent years.This paper characterizes the structure features of the cross-dimensional vector space.Specifically,it is proved that the completion of cross-dimensional vector space is an infinite-dimensional separable Hilbert space.Hence,it means that one can isometrically and linearly embed the crossdimensional vector space into theℓ^(2),which is known as the space of square summable sequences.This result will be helpful in the modeling and analyzing the dynamics of cross-dimensional dynamical systems.展开更多
new coordination polymer {[Zn(CF3COO)2(C5H5ON)]·H2O}n was synthesized based on the reaction of zinc(Ⅱ) trifluoroacetate and 3-hydroxypyridine(C5H5ON) in methanol medium for the first time. The structure of the c...new coordination polymer {[Zn(CF3COO)2(C5H5ON)]·H2O}n was synthesized based on the reaction of zinc(Ⅱ) trifluoroacetate and 3-hydroxypyridine(C5H5ON) in methanol medium for the first time. The structure of the coordination polymer was confirmed by IR, 1H NMR, elemental analysis and thermal analysis. The crystal structure of the coordination polymer was also determined by X-ray single crystal diffraction. The crystal belongs to monoclinic system with space group P21/m, and crystallographic data of the coordination polymer are: a= 0.863 1(4) nm, b=0.717 7(3) nm, c=1.116 4(5) nm, α=γ=90°, β=107.542(6)°, V=0.659 4(5) nm3; Dc=2.037 g·cm-3; Z=2; F(000)=400; μ=1.969 mm-1. Zinc(Ⅱ) atom lies at the center of an octahedron formed by the coordination of zinc atom and six O atoms which come from four different trifluoroacetate ions and two different 3-hydroxypyridine molecules where each trifluoroacetate ion and 3-hydroxypyridine are coordinated to two different zinc ions to form coordination polymer. CCDC: 253909.展开更多
The μ-oxygen-bis[tri(p-fluorobenzyl)tin] was synthesized. The structure were characterized by elementary analysis, IR and 1H NMR and the crystal structure were determined by X-ray single crystal diffraction. The crys...The μ-oxygen-bis[tri(p-fluorobenzyl)tin] was synthesized. The structure were characterized by elementary analysis, IR and 1H NMR and the crystal structure were determined by X-ray single crystal diffraction. The crystal of the title compound belongs to rhombohedral with space group R, a=1.346 4(4), b=1.346 4(4), c=1.772 9(7) nm, α=90°, β=90°, γ=120°, Z=3, V=2.783 2(15) nm3, Dc=1.625 g·cm-3, μ(Mo Kα)=1.408 mm-1, S=1.088, F(000)=1 350, R1=0.027 5, wR2=0.065 9. In compound, the tin atom has a distorted tetrahedral coordination configuration. CCDC: 257079.展开更多
Diorganotin(Ⅳ) compound [(p-CNC6H4CH2)2Sn(C9H7N3O3)(H2O)]2 was synthesized by the reaction of tri-p-cyanobenzyltin chloride with Schiff base ligand pyruvic acid isonicotinyl hydrazone. The compound was characterized ...Diorganotin(Ⅳ) compound [(p-CNC6H4CH2)2Sn(C9H7N3O3)(H2O)]2 was synthesized by the reaction of tri-p-cyanobenzyltin chloride with Schiff base ligand pyruvic acid isonicotinyl hydrazone. The compound was characterized by elemental analysis, IR, 1H NMR. The crystal structure was determined by X-ray single crystal diffraction. The crystal belongs to monoclinic space group C2/c, with a=3.143 1(3) nm, b=0.989 99(10) nm, c=1.785 68(18) nm, β=114.908 0(13)°, V=5.039 6(9) nm3, Z=4, μ=1.054 mm-1, Dc=1.513 Mg·m-3, F(000)=2 304, R=0.042 8, wR=0.090 3, GOF=0.997. In this compound, the Sn atom exists in a distorted octahedral coordination environment in which one water molecule, one tridentate pyruvic acid isonicotinyl hydrazone ligand, and two trans p-cyanobenzyl groups coordinate to each Sn center, the angle of the axial C10-Sn1-C18 is 166.1(2)°. Two molecules form a weak-bridged dimmer with weak interactions of Sn...O bonding and hydrogen bonds. CCDC: 270796.展开更多
N-(m-ferrocenylphenyl)-formamide has been synthesized by the reaction of m-ferrocenyl-aniline with DMF, and characterized by elements analysis, IR, 1H NMR, and X-ray structure determination. The crystallized was in th...N-(m-ferrocenylphenyl)-formamide has been synthesized by the reaction of m-ferrocenyl-aniline with DMF, and characterized by elements analysis, IR, 1H NMR, and X-ray structure determination. The crystallized was in the monoclinic, P21/c space group, with a=0.140 94(3) nm, b=0.102 87(2) nm, c=0.100 26(2) nm, β=104.85(3)° and final R indices [I>2σ(I)] R1=0.072 7, wR2=0.184 5. An infinite one-dimensional chain is formed by intermolecular hydrogen bonding N-H...O. Cyclic voltammetry was studied comparing with the parent compound (m-ferrocenylaniline). CCDC: 243511.展开更多
In this paper, we study the integral solution operators for the -equations on pseudoconvex domains. As a generalization of [1] for the -dequations on pseudoconvex domains with boundary of class C∞, we obtain the ex...In this paper, we study the integral solution operators for the -equations on pseudoconvex domains. As a generalization of [1] for the -dequations on pseudoconvex domains with boundary of class C∞, we obtain the explicit integral operator solutions of C -form for the -equations on pseudoconvex open sets with boundary of Ck (k≥0) and the sup-norm estimates of which solutions have similar as that [1] in form.展开更多
This paper presents the matrix representation for extension of inverse of restriction of a linear operator to a subspace, on the basis of which we establish useful representations in operator and matrix form for the g...This paper presents the matrix representation for extension of inverse of restriction of a linear operator to a subspace, on the basis of which we establish useful representations in operator and matrix form for the generalized inverse A(T,S)^(2) and give some of their applications.展开更多
In this paper,a new numerical method based on a new expanded mixed scheme and the characteristic method is developed and discussed for Sobolev equation with convection term.The hyperbolic part d(x)∂u/∂t+c(x,t)·∇u...In this paper,a new numerical method based on a new expanded mixed scheme and the characteristic method is developed and discussed for Sobolev equation with convection term.The hyperbolic part d(x)∂u/∂t+c(x,t)·∇u is handled by the characteristic method and the diffusion term∇·(a(x,t)∇u+b(x,t)∇ut)is approximated by the new expanded mixed method,whose gradient belongs to the simple square integrable(L^(2)(Ω))^(2)space instead of the classical H(div;Ω)space.For a priori error estimates,some important lemmas based on the new expanded mixed projection are introduced.An optimal priori error estimates in L^(2)-norm for the scalar unknown u and a priori error estimates in(L^(2))^(2)-norm for its gradientλ,and its fluxσ(the coefficients times the negative gradient)are derived.In particular,an optimal priori error estimate in H1-norm for the scalar unknown u is obtained.展开更多
基金supported by the National Natural Science Foundation of China under Grant No.61673129the Key Programs in Shaanxi Province of China under Grant No.2021JZ-12Science and the Technology Bureau Project of Yulin under Grant Nos.2019-89-2 and 2019-89-4。
文摘The cross-dimensional dynamical systems have received increasing research attention in recent years.This paper characterizes the structure features of the cross-dimensional vector space.Specifically,it is proved that the completion of cross-dimensional vector space is an infinite-dimensional separable Hilbert space.Hence,it means that one can isometrically and linearly embed the crossdimensional vector space into theℓ^(2),which is known as the space of square summable sequences.This result will be helpful in the modeling and analyzing the dynamics of cross-dimensional dynamical systems.
文摘new coordination polymer {[Zn(CF3COO)2(C5H5ON)]·H2O}n was synthesized based on the reaction of zinc(Ⅱ) trifluoroacetate and 3-hydroxypyridine(C5H5ON) in methanol medium for the first time. The structure of the coordination polymer was confirmed by IR, 1H NMR, elemental analysis and thermal analysis. The crystal structure of the coordination polymer was also determined by X-ray single crystal diffraction. The crystal belongs to monoclinic system with space group P21/m, and crystallographic data of the coordination polymer are: a= 0.863 1(4) nm, b=0.717 7(3) nm, c=1.116 4(5) nm, α=γ=90°, β=107.542(6)°, V=0.659 4(5) nm3; Dc=2.037 g·cm-3; Z=2; F(000)=400; μ=1.969 mm-1. Zinc(Ⅱ) atom lies at the center of an octahedron formed by the coordination of zinc atom and six O atoms which come from four different trifluoroacetate ions and two different 3-hydroxypyridine molecules where each trifluoroacetate ion and 3-hydroxypyridine are coordinated to two different zinc ions to form coordination polymer. CCDC: 253909.
文摘The μ-oxygen-bis[tri(p-fluorobenzyl)tin] was synthesized. The structure were characterized by elementary analysis, IR and 1H NMR and the crystal structure were determined by X-ray single crystal diffraction. The crystal of the title compound belongs to rhombohedral with space group R, a=1.346 4(4), b=1.346 4(4), c=1.772 9(7) nm, α=90°, β=90°, γ=120°, Z=3, V=2.783 2(15) nm3, Dc=1.625 g·cm-3, μ(Mo Kα)=1.408 mm-1, S=1.088, F(000)=1 350, R1=0.027 5, wR2=0.065 9. In compound, the tin atom has a distorted tetrahedral coordination configuration. CCDC: 257079.
文摘Diorganotin(Ⅳ) compound [(p-CNC6H4CH2)2Sn(C9H7N3O3)(H2O)]2 was synthesized by the reaction of tri-p-cyanobenzyltin chloride with Schiff base ligand pyruvic acid isonicotinyl hydrazone. The compound was characterized by elemental analysis, IR, 1H NMR. The crystal structure was determined by X-ray single crystal diffraction. The crystal belongs to monoclinic space group C2/c, with a=3.143 1(3) nm, b=0.989 99(10) nm, c=1.785 68(18) nm, β=114.908 0(13)°, V=5.039 6(9) nm3, Z=4, μ=1.054 mm-1, Dc=1.513 Mg·m-3, F(000)=2 304, R=0.042 8, wR=0.090 3, GOF=0.997. In this compound, the Sn atom exists in a distorted octahedral coordination environment in which one water molecule, one tridentate pyruvic acid isonicotinyl hydrazone ligand, and two trans p-cyanobenzyl groups coordinate to each Sn center, the angle of the axial C10-Sn1-C18 is 166.1(2)°. Two molecules form a weak-bridged dimmer with weak interactions of Sn...O bonding and hydrogen bonds. CCDC: 270796.
文摘N-(m-ferrocenylphenyl)-formamide has been synthesized by the reaction of m-ferrocenyl-aniline with DMF, and characterized by elements analysis, IR, 1H NMR, and X-ray structure determination. The crystallized was in the monoclinic, P21/c space group, with a=0.140 94(3) nm, b=0.102 87(2) nm, c=0.100 26(2) nm, β=104.85(3)° and final R indices [I>2σ(I)] R1=0.072 7, wR2=0.184 5. An infinite one-dimensional chain is formed by intermolecular hydrogen bonding N-H...O. Cyclic voltammetry was studied comparing with the parent compound (m-ferrocenylaniline). CCDC: 243511.
文摘In this paper, we study the integral solution operators for the -equations on pseudoconvex domains. As a generalization of [1] for the -dequations on pseudoconvex domains with boundary of class C∞, we obtain the explicit integral operator solutions of C -form for the -equations on pseudoconvex open sets with boundary of Ck (k≥0) and the sup-norm estimates of which solutions have similar as that [1] in form.
基金This research is supported by the Natural Science Foundation of the Educational Committee of Jiang Su Province.
文摘This paper presents the matrix representation for extension of inverse of restriction of a linear operator to a subspace, on the basis of which we establish useful representations in operator and matrix form for the generalized inverse A(T,S)^(2) and give some of their applications.
基金supported by the National Natural Science Fund of China(11061021)the Scientific Research Projection of Higher Schools of Inner Mongolia(NJZZ12011,NJZY13199)+1 种基金the Natural Science Fund of Inner Mongolia Province(2012MS0108,2012MS0106)the Program of Higher-level talents of Inner Mongolia University(125119,30105-125132).
文摘In this paper,a new numerical method based on a new expanded mixed scheme and the characteristic method is developed and discussed for Sobolev equation with convection term.The hyperbolic part d(x)∂u/∂t+c(x,t)·∇u is handled by the characteristic method and the diffusion term∇·(a(x,t)∇u+b(x,t)∇ut)is approximated by the new expanded mixed method,whose gradient belongs to the simple square integrable(L^(2)(Ω))^(2)space instead of the classical H(div;Ω)space.For a priori error estimates,some important lemmas based on the new expanded mixed projection are introduced.An optimal priori error estimates in L^(2)-norm for the scalar unknown u and a priori error estimates in(L^(2))^(2)-norm for its gradientλ,and its fluxσ(the coefficients times the negative gradient)are derived.In particular,an optimal priori error estimate in H1-norm for the scalar unknown u is obtained.
