一维问题的一种积分形式的流量重构算法

1引言我们考虑如下一维二阶椭圆边界值问题(-(β(x)p′)(x))′=f(x),x∈(a,b) p(a)=p(b)=0(1))其中β=β(x)是一恒正函数,且β∈H~1(a,b),f∈L~2(a,b)．事实上,在此条件下,我们可保证p∈H~2(a,b)(见[1],[2])．(1)之弱形式为：求p∈H_0~1(a,b)使得a(p,q)=(f,q),(?)q∈H_0~1(a,b),(2)其中a(p,q)=(?)_a~bβp′q′dx,(f,g)=(?)_a~bfqdx．给定(a,b)的一个分割α=x_0＜x_1＜…＜x_(n-1)＜x_n=b,令h=(?)(x_i-x_(i-1)),(?)_i表示通常相应于节点x_i的形状函数,即(?)_i是连续的分段线性函数且满足(?)_i(x_k)=δ_(ik),这里δ_(ik)=(?)i,k=0,1,…,n．又记V_h~0=span{(?)_1,(?)_2,…,(?)_(n-1)),取V_h~0作为p的逼近空间,则求解(1)的标准有限元格式为：求ph∈V_h~0使得     

p-Laplace方程正解的存在性和多重性

这篇文章讨论边值问题-(| u′|p-2u′)′=λf(t ,u) ,t∈(0,1) ,p >1,u(0) =u(1) =0,其中f(t ,u)≥-M( M是正常数) ,对(t ,u)∈0,1×0,∞) .我们利用度理论和锥上的不动点定理得到方程存在两个正解.     

一维链配位聚合物[Mn(acacen){N(CN)2}]n的合成、结构和性质的研究(英)

The manganese(Ⅲ) complex [Mn(acacen){N(CN)₂}]_n [H₂acacen=bis(acetylacetone)ethylenediimine] has been synthesized and the structure has been determined. The complex forms a one-dimensional chain structure via the bidentate bridge ligand μ_1,5-[N(CN)₂]^- linking [Mn(acacen)] moiety. The magnetic property of the compound (75～300 K) shows the existence of an antiferromagnetic exchange interaction among paramagnetic centers along the chain. CCDC: 244940.     

氢键连接的一维镍和镍铜异金属配合物的合成与性质

合成了1,2-二硫代草酸根(以下简记为Dto)桥联的4个一维镍和镍铜异金属配合物: (Me₆[14]二烯N₄)Ni₂(Dto)₂ (1), (Me₆[14]二烯N₄)CuNi(Dto)₂ (2), (Me₆[14]烷N4)Ni₂(Dto)₂ (3)和(Me₆[14]烷N₄)CuNi(Dto)₂ (4), 进行了元素分析、红外光谱、紫外-可见光谱和电子顺磁共振谱的表征. 得到了配合物3的晶体结构, 晶体属单斜晶系, C2/c空间群; 晶胞参数: a = 2.2425(4) , b = 1.0088(2), c = 1.4665(3) nm, b = 125.32(3)°; Z = 4; 最终偏离因子R = 0.076, R_w = 0.079. 配合物中Ni(1)与2个Dto配位, 具有平面四方型配位环境, Ni(2)处于大环配体的中心; Dto的2个硫原子与Ni(1)配位, O(1)与Ni(2)形成弱的配位键, O(2)与大环配体上的N(2)形成氢键, 这是一种未见文献报道的新的Dto配位形式.     

一维链状锰(Ⅱ)三氮唑配合物的合成，结构与磁性质(英)

A novel one-dimensional chain manganese(Ⅱ) compound [Mn(trz)₂Cl][phthH], (trz=1,2,4-triazole, phthH=hydrogen phthalate), 1, was synthesized and structurally characterized. It crystallizes in monoclinic system, space group P2 /c with a=1.381 1(11) nm, b=0.815 5(7) nm, c=0.735 4(6) nm, β=94.667(15)°, V=0.825 5(12) nm³. It consists of one dimensional cationic manganese(Ⅱ) chain and uncoordinated hydrogen phthalate anions. The manganese(Ⅱ) ions are bridged with two 1,2,4-traizoles and one chloride anion along the cationic chain, in which the weak antiferromagnetic exchange occurs between manganese(Ⅱ) atoms. CCDC: 267461.     

一维链状冠醚配合物:[{Na(18-C-6)}2(H2O)]n[M(SCN)4]n(M=Pd、Pt)的合成与结构

The reactions of 18-crown-6 with Na₂[M(SCN)₄] (M= Pd,Pt) were studied and the complex 1 [{Na(18-C-6)}₂(H₂O)]_n[Pd(SCN)₄]_n and complex 2 [{Na(18-C-6)}₂(H₂O)]_n[Pt(SCN)₄]_n were characterized by ele-mental analysis, IR and X-ray diffraction analysis. The complexes belong to monoclinic, space group P2₁/n with cell dimensions, 1:a=1.05734(7),b=1.42250(10),c=1.47762(10) nm,β=107.5330(10)°,V=2.1192(2)nm³,Z=2,D_calcd=1.460g·cm^-3,F(000)=964,R₁=0.0406,wR₂=0.1264 and 2:a=1.05985(19),b=1.4237(3),c=1.4744(3) nm,β=107. 096(3)°, V=2.1264(7)nm³,Z=2,D_calcd=1.690g·cm^-3,F(000)=1028,R₁=0.0292,wR₂=0.0859. In the solid state, the complexes 1 and 2 show an one-dimensional chain of [{Na(18-C-6)}₂(H₂O)]²⁺ complex cations and [M(SCN)₄]^2- (M=Pd,Pt) complex anions bridged by Na-N in-teractions.     

Dawson结构杂多化合物(C_5H_6N)_(4.5)H_(1.5)(P_2W_(18)O_(62))·1.5H_2O的水热合成及晶体结构

用水热合成方法制备了Dawson结构杂多化合物(C5H6N)4.5H1.5(P2W18O62).1.5H2O,通过红外光谱和X射线单晶衍射对其进行了表征.结果表明,该化合物属于单斜晶系,C2/m空间群.a=2.6970(3)nm,b=1.39730(16)nm,c=2.0777(2)nm,β=102.33(0)°,V=7.64927(364)nm3,Z=4,R=0.0412,wR2=0.1016.标题化合物阴离子通过质子化的吡啶分子在氢键作用下形成了一维无限链状结构.     

Horseshoe effect and topological entropy of one-dimensional maps

Abstract. In this paper, for any continuous function     

硫化聚乙炔结构对其电子性能的影响

本文用硫原子和共轭多烯的复合物模拟硫化聚乙炔结构,并采用一维紧束缚的LCAO-SCF-MO法,探讨了硫化聚乙炔结构对其电子性能的影响,揭示出影响的原因,确定了最佳结构,为实验合成提供了理论依据。     

一维梯状配合物{[Cu2(4,4''-bpy)3(p-Ab)2(H2O)2]·(NO3)2·4H2O}n的晶体结构

合成了一维分子梯状配合物{[Cu2(4,4'-bpy)3(p-Ab)2(H2O)2]·(NO3) 2·4H2O}n(4,4'-bpy=4,4'-联吡啶,p-Ab-=对氨基苯甲酸根离子),该配合物晶体属单斜晶系,P2(1)/c空间群,晶胞参数:a=1.110 7(5) nm,b=1.550 4(3) nm,c=1.450 9(3) nm,β=104.81(3)°,V=2.415 5(12) nm3,Z=2.铜离子周围有3个氧原子和3个氮原子与之配位,其中2个氧原子由对氨基苯甲酸的螯合氧原子提供,另一个氧原子由配位水提供,3个氮原子分别由三个4,4'-联吡啶提供.这六个原子在铜离子周围形成一个畸变的八面体配位环境.配体对氨基苯甲酸只有一种配位形式--双齿螯合,第二配体4,4'-联吡啶的两个氮原子均参与配位,将配合物组装成一维分子梯结构.