关于半无爪图点泛圈性的两个结果

给出了半无爪图(quasi-claw-freegraph)点泛圈性方面的两个结果,作为推论,可得到D.Oberly,D.Sumner,L.Clark等人的相关结果.     

Meyniel's conjecture holds for random d‐regular graphs

In the game of cops and robber, the cops try to capture a robber moving on the vertices of the graph. The minimum number of cops required to win on a given graph G is called the cop number of G. The biggest open conjecture in this area is the one of Meyniel, which asserts that for some absolute constant C, the cop number of every connected graph G is at most . In a separate paper, we showed that Meyniel's conjecture holds asymptotically almost surely for the binomial random graph. The result was obtained by showing that the conjecture holds for a general class of graphs with some specific expansion‐type properties. In this paper, this deterministic result is used to show that the conjecture holds asymptotically almost surely for random d‐regular graphs when d = d(n) ≥ 3.     

一类4-正则平面图的邻点可区别关联色数

所谓图R_n是指具有如下结构的平面图:R_n=(V,E),其中顶点集合V={u_1,u_2,…,u_n}U{v_1,v_2,…,v_n},边集合E={u_iu_(i+1),v_iv_(i+1),u_iv_i,u_iv_(i+1)|i=1,2,…,n},其中u_(n+1)=u_1,v_(n+1)=v_1.通过研究R_n的邻点可区别关联着色,给出了当n=4,n是3或者5的正整数倍时,R_n的邻点可区别关联色数.     

新型BODIPY荧光染料的合成及光谱性质研究

传统的BODIPY荧光染料具有荧光量子效率高、摩尔消光系数大、紫外吸收和荧光发射峰窄等优点,然而这类荧光染料普遍存在荧光发射波长短和Stokes位移小的缺点,因而限制了它们在体内生物传感及成像方面的广泛应用。为了得到荧光发射波长较长和Stokes位移大的BODIPY荧光染料,以BODIPY母核为基本结构,通过在它的8位连接吸电子性质的酯基来增加分子内电荷转移程度,同时在其3,5位引入供电子的芳香取代基增加分子的π共轭结构,合成得到了一类8位酯基取代的新型BODIPY荧光染料。所得到的新型BODIPY荧光染料的化学结构经过1H NMR, 13C NMR和HR-MS得以确认。光谱测试结果表明,这类染料的紫外吸收光谱(λ_abs=536 nm)和荧光发射光谱(λ_em=592 nm)与普通的BODIPY相比都发生显著红移(80 nm),并且保持了较高的荧光量子效率(Ф=0.43)。此外,这类BODIPY荧光染料的紫外可见吸收光谱和荧光发射光谱几乎完全分开,Stokes位移长达60 nm,可以有效地避免自吸收和生物样品的背景干扰。密度泛函理论计算结果表明,这种相对较大的Stokes位移主要是由于染料分子在基态和激发态下不同的几何构型所造成的。该类化合物的光物理性能受溶剂的影响小,是一类性能优良的新型荧光染料。细胞成像结果表明,染料1具有良好的细胞渗透性和光稳定性,可以实现对细胞的荧光成像。     

The effect of boundary conditions on the mesoscopic lattice Boltzmann method: Case study of a reaction-diffusion based model for Min-protein oscillation

Min-protein oscillation in Escherichia coli has an essential role in controlling the accurate placement of the cell division septum at the middle-cell zone of the bacteria. This biochemical process has been successfully described by a set of reaction-diffusion equations at the macroscopic level. The lattice Boltzmann method (LBM) has been used to simulate Min-protein oscillation and proved to recover the correct macroscopic equations. In this present work, we studied the effects of LBM boundary conditions (BC) on Min-protein oscillation. The impact of diffusion and reaction dynamics on BCs was also investigated. It was found that the mirror-image BC is a suitable boundary treatment for this Min-protein model. The physical significance of the results is extensively discussed.     

Uniform Mixed Hypergraphs: The Possible Numbers of Colors

For a mixed hypergraph , where and are set systems over the vertex set X, a coloring is a partition of X into ‘color classes’ such that every meets some class in more than one vertex, and every has a nonempty intersection with at least two classes. The feasible set of , denoted , is the set of integers k such that admits a coloring with precisely k nonempty color classes. It was proved by Jiang et al. [Graphs and Combinatorics 18 (2002), 309–318] that a set S of natural numbers is the feasible set of some mixed hypergraph if and only if either or S is an ‘interval’ for some integer k ≥ 1. In this note we consider r-uniform mixed hypergraphs, i.e. those with |C| = |D| = r for all and all , r ≥ 3. We prove that S is the feasible set of some r-uniform mixed hypergraph with at least one edge if and only if either for some natural number k ≥ r − 1, or S is of the form where S′′ is any (possibly empty) subset of and S′ is either the empty set or {r − 1} or an ‘interval’ {k, k + 1, ..., r − 1} for some k, 2 ≤ k ≤ r − 2. We also prove that all these feasible sets can be obtained under the restriction , i.e. within the class of ‘bi-hypergraphs’. Research supported in part by the Hungarian Scientific Research Fund, OTKA grant T-049613.     

Halin-图的点强全染色

图G(V,E)的一个k-正常全染色f叫做一个k-点强全染色当且仅当对任意v∈V(G), N[v]中的元素被染不同色,其中N[v]={u|uv∈V(G)}∪{v}．χTvs(G)=min{k|存在图G的k- 点强全染色}叫做图G的点强全色数．对3-连通平面图G(V,E),如果删去面fo边界上的所有点后的图为一个树图,则G(V,E)叫做一个Halin-图．本文确定了最大度不小于6的Halin- 图和一些特殊图的的点强全色数XTvs(G),并提出了如下猜想:设G(V,E)为每一连通分支的阶不小于6的图,则χTvs(G)≤△(G) 2,其中△(G)为图G(V,E)的最大度．     

黏惰化及酸敏感修饰对纳米粒子黏膜穿透的影响

使用纳米粒子进行疾病的诊断和治疗是当前研究的一个热点. 由于受到黏液层的阻碍, 纳米粒子对于黏膜上皮细胞的进入效果不佳, 从而限制了其对黏膜相关疾病的诊断和治疗. 本文设计合成了一种具有黏惰性的酸敏感纳米粒子(MSNs-pCBMA-DMMA), 可有效穿透黏液层进入黏膜上皮细胞. 首先采用溶胶-凝胶法合成了表面氨基化的介孔二氧化硅纳米粒子(MSNs-NH₂), 然后通过原子转移自由基聚合法(ATRP)使两性离子羧基甜菜碱甲基丙烯酸酯(CBMA)在MSNs-NH₂表面上聚合形成聚羧基甜菜碱甲基丙烯酸酯(pCBMA), 获得惰性化的粒子(MSNs-pCBMA), 最后将酸响应性分子2,3-二甲基马来酸酐(DMMA)修饰于MSNs-pCBMA表面, 制备了MSNs-pCBMA-DMMA. 场发射透射电子显微镜(TEM)、 傅里叶变换红外光谱(FTIR)、 氢核磁共振波谱(¹H NMR)和纳米粒度Zeta电位测定仪等分析结果表明, 本文合成了MSNs-pCBMA-DMMA, 且粒子表面电位随pH值降低显著增加, 在pH=7.4~5.7范围内具有酸敏感能力. Transwell^?小室实验表明, pCBMA的接枝提高了粒子在模拟黏液中的渗透速率, 而DMMA的修饰则进一步增强了粒子的扩散能力, 4 h内MSNs-pCBMA-DMMA的模拟黏液渗透率达到16.3%, 为MSNs-pCBMA的1.9倍, MSNs-NH₂的3倍, 而以MSNs-NH₂的表观渗透系数（P_app）为标准计算得到的MSNs-pCBMA-DMMA的相对表观渗透系数达到了2.96. 细胞毒性试验验证MSNs-pCBMA-DMMA粒子的生物安全性良好. 细胞摄取试验表明, 相比于其它粒子MSNs-pCBMA-DMMA能够更快的被黏膜上皮细胞摄取. 本文所构建的纳米粒子能够快速渗透黏液且易于被黏膜上皮细胞摄取, 为其应用于黏膜相关疾病的活体诊断和治疗提供了基础.     

一类优美图

设u、ν是两个固定顶点.用b条内部互不相交且长度皆为a的道路连接u、ν所得的图用P_a,b表示.KM.Kathiresan证实P_2,2m-1(r,m皆为任意正整数)是优美的,且猜想:除了(a,b)=(2r+1,4s+2)外,所有的P_a,b都是优美的.杨元生已证实P_2r+1,2m-1是优美的,并且证实了当r=1,2,3,4时的P_2r,2m也是优美的.本文证实r=5,6,7时P_{2r,2m相似文献}   

Characterization of Ti6Al4V implant surface treated by Nd:YAG laser and emery paper for orthopaedic applications

A more noble and biocompatible Ti alloy was achieved at fluence of 140 J cm⁻² where the implant indicated a higher degree of hardness (825HV), higher corrosion resistance (−0.21 V) and highest hydrophilicity (i.e. θ_c = 37°) compared with 70° of the control sample. These values corresponded to 58 and 39 mN m⁻¹ of surface tension respectively. The laser treated samples at 140 J cm⁻² showed higher wettability characteristics than mechanically roughened surface. Cell growth and their spreading condition in a specific area were analyzed by SEM and Image J Program software. Clearly, more cells were attached (1.2 × 10⁵) to and spread (488 μm²) over the surface at 140 J cm⁻² than in any other condition. Pathologically, the treated samples indicated no sign of infection.