Bernstein <Emphasis Type="Italic">n</Emphasis>-widths of Besov embeddings on Lipschitz domains

In this paper, using an equivalent characterization of the Besov space by its wavelet coefficients and the discretization technique due to Maiorov, we determine the asymptotic degree of the Bernstein n-widths of the compact embeddings Bq0s＋t（Lp0（Ω））→Bq1s（Lp1（Ω））, t〉max{d（1/p0-1/p1）, 0}, 1 ≤ p0, p1, q0, q1 ≤∞,where Bq0s＋t（Lp0（Ω）） is a Besov space defined on the bounded Lipschitz domain Ω ？ Rd. The results we obtained here are just dual to the known results of Kolmogorov widths on the related classes of functions.     

On the Linearized Darboux Equation Arising in Isometric Embedding of the Alexandrov Positive Annulus

In the present paper, the solvability condition of the linearized Gauss-Codazzi system and the solutions to the homogenous system are given. In the meantime, the solvability of a relevant linearized Darboux equation is given. The equations are arising in a geometric problem which is concerned with the realization of the Alexandrov’s positive annulus in ?³.     

PATHS AND CYCLES EMBEDDING ON FAULTY ENHANCED HYPERCUBE NETWORKS

Let Qn,k(n≥3,1≤k≤n-1) be an n-dimensional enhanced hypercube which is an attractive variant of the hypercube and can be obtained by adding some complementary edges,fv and fe be the numbers of faulty vertices and faulty edges,respectively.In this paper,we give three main results.First,a fault-free path P [u,v] of length at least 2n-2fv-1(respectively,2n-2fv-2) can be embedded on Qn,k with fv+fe≤n-1 when d Qn,k(u,v) is odd(respectively,d Qn,k(u,v) is even).Secondly,an Qn,k is(n-2) edgefault-free hyper Hamiltonian-laceable when n(≥3) and k have the same parity.Lastly,a fault-free cycle of length at least 2n-2fv can be embedded on Qn,k with fe≤n-1 and fv+fe≤2n-4.     

高压下钼的声子色散的改进分析型嵌入原子法研究北大核心CSCD

应用改进分析型嵌入原子法模型计算了不同高压下金属钼的原子力常数和动力学矩阵,重现了压强下金属钼沿[00ζ]、[0ζζ]和[ζζζ]3个高对称方向上声子色散的实验结果,预测了钼在压强分别为60、80和100 GPa时的声子色散曲线。结果表明:压强分别为0.1 MPa、17 GPa和37 GPa时金属钼的声子色散曲线的模拟结果和实验值符合较好,特别在低频附近二者几乎一致,而在布里渊区的边界点附近,两者在数值上略有差异;在压强分别为60、80和100 GPa时所预测的声子色散曲线和常压下声子色散曲线的形状都非常相似;高压下所有振动支的振动频率均高于常压下的振动频率,且振动频率随压强的增大而增大。     

与直径和围长有关的最大亏格的下界的一个注记

改正了文章"与直径和围长有关的最大亏格的下界(数学学报2004,47(6):1201-1204)"中的一个错误结论,并得到了如下结果:设G是直径为d(G)的简单图,若G的围长g(G)■d(G),则ξ(G)■2,从而γM(G)■(1/2)β(G)-1.     

Generalized Besov spaces and Triebel-Lizorkin spaces

In this paper the classical Besov spaces Bsp.q and Triebel-Lizorkin spaces Fsp.q for s ∈R are generalized in an isotropy way with the smoothness weights {|2j|aln}∞j=0. These generalized Besov spaces and Triebel-Lizorkin spaces, denoted by Bap.q and Fap.q for a ∈Irk and k ∈N, respectively, keep many interesting properties, such as embedding theorems (with scales property for all smoothness weights), lifting properties for all parameters a, and duality for index 0 < p < ∞. By constructing an example, it is shown that there are infinitely many generalized Besov spaces and generalized Triebel-Lizorkin spaces lying between Bs,p.q and ∪tsBt,p.q,and between Fsp.q and ∪ts Ftp.q, respectively. Between Bs,p,q and ∪tsBt,p.qq,and between Fsp,qand ∪tsFtp.q,respectively.     

Menger空间对拟距离空间族的嵌入定理及其应用

在本文中,我们引进了Menger空间中拟距离空间族的嵌入概念并研究了它的一些性质.证明了Menger空间中连续映象序列的一个公共不动点定理.这些映象是假设满足广义的压缩条件的.这里采用的证明方法对于Menger空间的映象而言是一种新的思想.     

LiNi0.3Co0.7O2的结构及其锂电池行为的研究

利用XRD、XPS、CV等方法研究了LiNi_0.3Co_0.7O₂的结构及其锂电池行为。结果表明:LiNi_0.3Co_0.7O₂具有六方晶系空间群结构,其晶胞参数a=0.2826nm,c=1.4130nm;其表面存在Li₂O;Li⁺在其中的化学扩散系数为1～7×10^-8cm²·s^-1;其锂电池在4.30～3.00V间放电容量可达120～140mA·h·g^-1,放电机理为Li⁺在其中进行两步嵌入反应。     

MoO3在Ga2O3上的分散研究

采用ＸＲＤ,ＬＲＳ,ＦＴ－ＩＲ,ＵＶ－ＤＲＳ和ＴＰＲ研究了ＭｏＯ３在体载体Ｇａ２Ｏ３上的分散情况。结果表明：ＭｏＯ３的分散状态受Ｇａ２Ｏ３表面结构的影响,ＭｏＯ３在Ｇａ２Ｏ３上的分散容量约为８．４μｍｏｌ／ｍ＾２;低于该分散容量时,Ｍｏ＾６＋主要以高分散态存在于Ｇａ２Ｏ３表面,而高于该分散容量时,除在分散态的Ｍｏ－Ｏ物种外,还有残余的ＭｏＯ３晶相出现。ＴＰＲ结果表明：ＭｏＯ３低于分散容量时,体系中     

锂在共轭双键高分子中的电化学嵌入反应3: 锂在聚萘中的电 化学嵌入反应

研究了锂在导电高聚物---聚萘中的嵌入反应。聚萘样品经650℃处理,作为锂电池的正极,组装成Li/(C~1~0H~6)~n电池。X射线衍射分析、ESR实验、X射线光电子能谱分析等一系列实验证实上述电池的正板反应是锂在聚萘中的电化学嵌入反应。通过XPS实验对嵌入聚萘的锂进行了价态分析,认为嵌进去的锂是以原子态及离子态两种状态存在,其结合能分别为55.7eV和57.4eV。采用电化学暂态测量技术研究了锂在导电高聚物---聚萘中的扩散,计算了锂在嵌合物中的离子电导率及淌度。用Hebb-Wagner直流极化法测量了嵌合物的电子电导。