Notes on Automorphisms of Prime Rings

Let R be a prime ring, L a noncentral Lie ideal and σ a nontrivial automorphism of R such that usσ(u)ut= 0 for all u ∈ L, where s, t are fixed non-negative integers. If either char R s + t or char R = 0, then R satisfies s4, the standard identity in four variables. We also examine the identity(σ([x, y])-[x, y])n=0 for all x, y ∈ I, where I is a nonzero ideal of R and n is a fixed positive integer. If either char R n or char R = 0, then R is commutative.     

镉(Ⅱ)磺基水杨酸配合物的合成、结构和荧光性质

配体2,2′-联吡啶(bipy)、磺基水杨酸(H2hssal)和镉盐反应合成了配合物[Cd(hssal)(bipy)(H2O)2]·H2O(1),用单晶X-射线和元素分析对生成的晶体进行了表征,结构研究发现该晶体属于单斜晶系P21/c空间群。Cd(Ⅱ)采取八面体配位几何构型,磺基水杨酸作为二齿桥联配体连结不同的Cd(Ⅱ)原子形成一维链结构,一维链被O-H…O氢键连接形成二维层,再进一步由O-H…O氢键将二维层联结在一起形成三维结构。研究了配合物1的荧光性质。CCDC:772715。     

Interior and boundary continuity of the solution of the singular equation (β(u))t=Lu

We extend some results of DiBenedetto and Vespri (Arch. Rational Mech. Anal 132(3) (1995) 247) proving the interior and boundary continuity of bounded solutions of the singular equation $\text{(β(u))}{}_{\mathrm{t}}\text{=}\text{L}\text{u}$ where $\text{L}$ is a second order elliptic operator with bounded measurable coefficients that depend both on space and time in a proper way.     

Synthesis, Structure and Properties of a Strontium（Ⅱ） Complex with 2, 3-Pyrazinedicarboxylic Acid

Complex [Sr2(pdc)2(H2O)7]·H2O(1, H2 pdc=2,3-pyrazinedicarboxylic acid) has been synthesized and characterized by single-crystal X-ray diffraction studies and FT-IR. Structural determination reveals that there are two crystallographically independent strontium ions in 1. The coordination geometry of Sr(1) is a nine-coordinated distorted monocapped tetragonal antiprism, while Sr(2) is a nine-coordinated distorted monocapped tetragonal prism. The ligand pdc 2- takes two different connecting modes and links Sr(Ⅱ) centers to generate a 2D layer structure. The 2D layers are linked through O-H···O and O-H···N hydrogen bonds to form a 3D framework structure. Thermal stability and luminescent properties of complex 1 are investigated. 1 belongs to the monoclinic system, space group P21/n with a=10.7182(10), b=7.0377(6), c=29.225(3) , β=95.7170(10)o, Z=4, V=2193.5(3) 3 , M r=651.56, D c=1.973 g/cm 3 , F(000)=1296, μ=4.951 mm -1 , the final R=0.0318 and wR=0.0726 for 3938 observed reflections with I > 2σ(I).     

On the spectral spread of bicyclic graphs with given girth

The spectral spread of a graph is defined to be the difference between the largest and the least eigenvalue of the adjacency matrix of the graph. A graph G is said to be bicyclic, if G is connected and |E(G)| = |V(G)|+ 1. Let B(n, g) be the set of bicyclic graphs on n vertices with girth g. In this paper some properties about the least eigenvalues of graphs are given, by which the unique graph with maximal spectral spread in B(n, g) is determined.     

铜(Ⅱ)与2-吡啶酸、4,4′-联吡啶配合物的合成、结构和电化学性质(英文)

The complex [Cu(bipy)(pc)(H2O)(ClO4)]·H2O(1)(bipy:4,4'-bipyridine;Hpc:α-pyridine carboxylic acid) has been synthesized and characterized by single crystal X-ray diffraction method and elemental analysis.It crysrallizes in the Monoclinic space group P21/n.The crystal structure reveals that Cu(Ⅱ) centre adopts a pseudo octahedral geometry.Ligand 4,4'-bipyridine as a bridge coordinates to two different Cu(Ⅱ) center to form a onedimensional zigzag chain.One dimensional chains are linked by C-H…O hydrogen bonding interactions to form two-dimensional layer.Layers are connected by O…H-O hydrogen bond to generate three-dimensional structure.The cyclic voltametric behavior of complex 1 is also investigated.     

Maximize the Q-index of graphs with fixed order and size

In this paper, we consider two kinds of spectral extremal questions. The first asks which graph attains the maximum Q-index over all graphs of order n and size $m=n+k$? The second asks which graph attains the maximum Q-index over all $(p,q)$-bipartite graphs with $m=p+q+k$ edges? We solve the first question for $4\le k\le n?3$, and the second question for $?p?q\le k\le p?q$. The maximum Q-index on connected $(p,q)$-bipartite graphs is also determined for $?1\le k\le p?2$.     

3，4-吡啶二甲酸根钙配合物的合成、结构和性质

配体3,4-吡啶二酸(H2pdc)和CaCO3反应合成了配合物[Ca2(pdc)2(H2O)7](1),用单晶X-射线、FTIR和元素分析对生成的晶体进行了表征。Ca(Ⅱ)采取八配位扭曲四方反棱柱几何构型,整个pdc2-作为三齿桥联配体连结3个不同的Ca(Ⅱ)原子形成一维链结构,一维链由π-π相互作用和O-H…N氢键连结形成二维层,二维层再进一步由O-H…O氢键连结形成三维结构。还研究了配合物1的荧光和热重性质。CCDC:806131。     

围长为r的n阶本原有向图的点指数

研究本原有向图的顶点指数,运用图论与数论方法,得到了n阶围长为r的本原有向图的点指数expD（k）的上界：若rn,且r为素数,D∈Dn,r={D｜D为n阶本原有向图且围长为r},则expD（n,k）=rn-2r＋k（1≤k≤n）;若r｜n,且r为素数或素数的幂,D∈Dn,r,则expD（n,1）=rn-3r＋2.     

关于高等代数中根子空间分解定理的教学

通过改进定理的证明、对定理进行推广、增加例题和习题等方法,改进高等代数中线性空间的根子空间分解定理的教学.