The (Δ+2,2)-incidence coloring of outerplanar graphs

An incidence coloring of graph G is a coloring of its incidences in which neighborly incidences are assigned different colors. In this paper, the incidence coloring of outerplanar graphs is discussed using the techniques of exchanging colors and the double inductions from the aspect of configuration property. Results show that there exists a (Δ+2,2)-incidence coloring in every outerplanar graph, where Δis the maximum degree of outerplanar graph.     

The(△+2,2)-incidence coloring of outerplanar graphs

An incidence coloring of graph G is a coloring of its incidences in which neighbody incidences are assigned different colors.In this paper,the incidence coloring of outerplanar graphs is discussed using the techniques of exchanging colors and the double inductions from the aspect of configuration property.Results show that there exists a(△ 2,2)-incidence coloring in every outerplanar graph,where △ is the maximum degree of outerplanar graph.     

The （△ ＋ 2,2）-incidence coloring of outerplanar graphs

An incidence coloring of graph G is a coloring of its incidences in which neighborly incidences are assigned different colors. In this paper, the incidence coloring of outerplanar graphs is discussed using the techniques of exchanging colors and the double inductions from the aspect of configuration property. Results show that there exists a （△ ＋ 2,2）-incidence coloring in every outerplanar graph, where A is the maximum degree of outerplanar graph.     

Gracefulness of disconnected graphs W(k)m∪G

文章证明了对任意自然数n≥1,P≥1,K≥1,当m1=2p+3或2p+4时,图W(k)m1U Kn,p为优美图,其中W(k)m1为由k个轮Wmi(i=1,2,…,k)的中心顶点合并后构成的连通图;当m1≥3,n≥[m1/2]时,非连通图W(k)m1∪St(n)为优美图;对任意自然数P≥1,图W(k)2p2+i∪Gpi为优美图,其中,Gpi表示p条边的i-优美图(i=1,2);对任意自然数n≥1,当m1=2n+5时,图W(k)m1∪(C3VKn)为优美图.     

The Functional Expansion of the “Demonstrative Pronoun(指) + Measure (量) + X + A (啊)” Sentence

基于前人的研究和对人民网语料的分析,可以讨论“指+量+X+啊”句式中“指+量”(主要是“那个”)的定性、X的功能分类问题.同时,从该句式的语体色彩、应用范围、在语段中的位置以及与同类句式的比较等几个方面出发,也可以对“指+量+X+啊”句式作全方位的研究.该句式的发展呈现出一种功能拓展的趋势.     

平面图是(Δ+2)-2-距离着色的充分条件

主要得到了围长至少6,最大度至少12的平面图是(Δ+2)-2-距离着色的1个充分条件.     

方程u_(tt)-Δu_(tt)-Δu=f(u)的初边值问题

用Galerkin方法研究了一类多维非线性色散波动方程utt-Δutt-Δu=f(u)的初边值问题,得到了其整体强解的存在性及唯一性,并在一定条件下证明了整体解的不存在性,给出了其解爆破的时间上界。     

Δ≥9且不含相邻4-圈的平面图是(Δ+1)-全可选和Δ-边可选的

设χ'l(G),χ″l(G)和Δ(G)分别表示平面图G的列表色数,列表全色数和最大度,目前已经证明:若G是Δ≥12的平面图,则χ'l(G)=Δ,χ″l(G)=Δ+1。本文将证明:若G是Δ≥9且不含相邻4-圈的平面图,则χ″l(G)=Δ+1,χ'l(G)=Δ。     

关于C2(H)上的初等算子Δ(X)=AXB+MXN

设H为复Hilbert空间, B(H)为H上所有有界线性算子构成的空间, C2(H)表示H上所有Hilbert-Schmidt类算子,按(X,Y)=tr(Y*X)构成Hilbert空间.在C2(H)中,定义算子Δ:X →AXB+MXN.文中给出了算子Δ为θ类算子的充分必要条件.     

Solid phase based DNA solution of the coloring problem

DNA computing has the potential to tackle computationally difficult problems that have real-world implications.The parallel search capabilities of DNA make it a valuable tool for approaching intractable computational problems,for which conventional computers have limited potentials.Up to now,many accomplishments have been achieved to improve its performance and increase its reliability.In this paper,the coloring problem has been solved by means of molecular biology techniques.The coloring problem is a well-known NP-complete problem.This work represents further evidence for the ability of DNA computing to solve NP-complete problems.     

方程utt-Δutt-Δu=f(u)的初边值问题

用 Galerkin方法研究了一类多维非线性色散波动方程 utt-Δutt-Δu =f(u)的初边值问题 ,得到了其整体强解的存在性及唯一性 ,并在一定条件下证明了整体解的不存在性 ,给出了其解爆破的时间上界。     

多项式恒等式dGΔkk(AX)=dGΔkk(X)成立的条件

讨论多项式恒等式d△kk^G(AX)=d△kk^G(X)（d△kk^G（X）（d△kk^G常简记为d△kk^G）↓AX∈Mm(C）成立的充要条件,这里G是m次对称群Sm的子群;d△kk^G(A）是群表示△的主元素△kk诱导的矩阵函数。     

关于u(2,2)的矩阵(个数)的几个问题

本文利用类合类的分类方法解决了(0,1)一矩阵行和列和等于2的类u(2,2)的矩阵个数问题,得到如下结果:     

Improvements of dielectric properties of Cu doped LaTiO_(3+δ)

The ceramic composites of Cu-doped La_(1-x )Cu_x TiO_(3+δ)(x=0.05, 0.15, 0.3, 0.5) were synthesized by conventional solid-state reaction. The complex dielectric properties of the composites were investigated as a function of temperature(77 K ≤T≤ 320 K) and frequency(100 Hz ≤ f ≤1 MHz) separately. In all composites, the dielectric constants increase monotonously and the dielectric loss undulates with temperature. And it is clearly observed that extraordinarily high low-frequency dielectric constant(～10~4)appear at room temperature in La_0.5Cu_0.5TiO_(3+δ), which is 100 times larger than that of La_0.95Cu_0.05 TiO_(3+δ). Interestingly, the dielectric constants increase remarkably with the doped Cu contents, meanwhile the dielectric loss for all samples is ideal lower than 1 at room temperature in the measured frequency range. By means of complex impedance analysis, the improvements of dielectric properties are attributed to both bulk contribution and grain boundary effect, in which the bulk polaronic relaxation and the Maxwell–Wagner relaxation due to grain boundary response are heightened remarkably with the high doped Cu contents.     

算子Δ(X)=AXB+MX为θ类算子的充要条件

文章给出了C2(H)空间上初等算子Δ(X)=AXB MX为θ类算子的充要条件,其中A正规,｛B,M｝为双交换有界线性算子。这一结论推广了文献[1]中相应的结果     

(2,2,…,2)型数域

■型数域K,即是由n个二次域合成的Q的2~n次扩城.本文对一般的n,较系统地研究了这类域的各代数结构.§2给出了域K的分类和标准生成,证明了奇素数p(以及2)在K 恰有4(以及6)种可能素分解情形.§3明显构作出K 的诸素理想.§4给出K 的整基、判别式和导子.§5证明了K 仅可能含2、4、6、8、12、24次单位根;从§2的结果导出K 的类数公式.上述诸结果与二次域的相应结果极为相似,是后者的自然拓广.