The hierarchical product of graphs

A new operation on graphs is introduced and some of its properties are studied. We call it hierarchical product, because of the strong (connectedness) hierarchy of the vertices in the resulting graphs. In fact, the obtained graphs turn out to be subgraphs of the cartesian product of the corresponding factors. Some well-known properties of the cartesian product, such as reduced mean distance and diameter, simple routing algorithms and some optimal communication protocols are inherited by the hierarchical product. We also address the study of some algebraic properties of the hierarchical product of two or more graphs. In particular, the spectrum of the binary hypertree T_m (which is the hierarchical product of several copies of the complete graph on two vertices) is fully characterized; turning out to be an interesting example of graph with all its eigenvalues distinct. Finally, some natural generalizations of the hierarchic product are proposed.     

On the Reverse Wiener Indices of Unicyclic Graphs

We determine the maximum values of the reverse Wiener indices of the unicyclic graphs with given cycle length, number of pendent vertices and maximum degree, respectively, and characterize the extremal graphs. We also determine the unicyclic graphs of given cycle length and diameter with minimum Wiener index.      

链状正则图的平均距离

本文构造了一类链状正则图G_k∶δ,求出了它们的平均距离D(G_k.δ),并得到关系式上式等号成立当且仅当δ=4f且k=0.这个估计式指出了施容华猜想[1]D(G)≤n/(δ 1)不成立. 文中进一步证明了这一类链状正则图有最大的直径,所以可以作出猜想: 若G是n阶连通图,则D(G)<(n 1)/(δ 1),其中δ是图G的最小度。     

Preparation of biodegradable microspheres by anionic dispersion polymerization with PLA copolymeric dispersion stabilizer

We prepared poly(d,l-lactide) (PLA) microspheres by anionic dispersion polymerization of d,l-lactide. The polymerization was carried out in xylene/heptane (1:2 in v/v) mixture solution at 368 K for 9 h, with poly(dodecyl methacrylate)-co-poly[α-methacryloxyethoxy-poly(l-lactide)] (PDMA-co-P(MA-PLLA)) synthesized in this study, as a dispersion stabilizer. The number-averaged diameter and diameter distribution (coefficient of variation) of obtained PLA microspheres ranged from 180 to 800 nm and 14–40%, respectively, depending on the preparation condition. Furthermore, the time courses of monomer conversion, particle diameter, and particle number were investigated to clarify the formation mechanism of microspheres with PDMA-co-P(MA-PLLA) as a dispersion stabilizer. From this experiment, we found that the aggregation of primary particles occurred in anionic dispersion polymerization, and the particle diameter of obtained PLA microspheres decreased with increasing PDMA-co-P(MA-PLLA) concentration. In conclusion, we clarified that PDMA-co-P(MA-PLLA) effectively contributed to the stability of primary particles.     

心房纤颤转律的评价：附60例临床和超声心动图分析

本文对60例 Af 自然转律或主动转律者进行对比分析。结果显示:左房内径正常者多为阵发性 Af,而左房增大者以持续性 Af 者多见;阵发性 Af 者大多数心功能正常。在病因方面,冠心病与风心病比较,前者以阵发性 Af 更多见,易于转复,后者易发展为永久性 Af。左房内径正常的17例全部转律,而左房内径增大的则有8例发展为永久性 Af,但左房增大的程度与转律似无明显关系。     

藏山羊肌肉组织学特性研究

对藏山羊肌肉组织学特性作了研究。结果表明,藏山羊肌纤维细,背最长肌肌纤维直径27.407±3.120μ,股二头股29.733±2.151μ;肌纤维密度大,背最长肌1195.06±274.03根/mm~2,股二头肌997.16±107.53根/mm~2;肌内肌纤维比例大,背最长肌为81.428±2.920%,股二头肌为84.406±0.721%。在一定程度上反映了藏山羊肌肉肉质细嫩。提示在开发和综合利用藏山羊时,除重视其产绒性能外,同时,也应重视其产肉性能。     

On the connectivity index of trees

The connectivity index χ₁(G) of a graph G is the sum of the weights d(u)d(v) of all edges uv of G, where d(u) denotes the degree of the vertex u. Let T(n, r) be the set of trees on n vertices with diameter r. In this paper, we determine all trees in T(n, r) with the largest and the second largest connectivity index. Also, the trees in T(n, r) with the largest and the second largest connectivity index are characterized. Mei Lu is partially supported by NNSFC (No. 10571105).     

ON k-DIAMETER OF k-CONNECTED GRAPHS

Abstract. Let G be a k-connected simple graph with order n. The k-diameter, combining con-nectivity with diameter, of G is the minimum integer     

双锥型光纤布喇格光栅光谱特性

利用传输矩阵法和有限元法分析了光栅周期、调制深度、锥腰直径和不同设计区段长度比等光栅制作参量和结构设计参量对双锥型光纤布喇格光栅光谱特性的影响.软件仿真结果表明:限定相关参量后,光栅周期增大,双锥型光纤布喇格光栅整体反射谱右移,与均匀分布光纤布喇格光栅光谱变化规律一致;调制深度增强,两主反射峰基本不变,而两主反射峰中间的次级峰个数增多,光强增大;锥腰直径减小,激发更多包层模,干涉峰个数增多,强度提升;整根光栅长度保持1cm不变,锥腰区,标准光栅区和渐变光栅区长度比直接影响次级峰的数量和幅值,随着渐变光栅区长度占比的增大,次级峰的幅值增大,同时个数减少.双锥型光纤布喇格光栅可在多参量传感器、多通道滤波器、多通道半导体激光器、色散补偿和光上下载分插复用等方面广泛应用.     

Study on Diameter Controlled Growth of Carbon Nanotubes by LaAl1-xFexO3 Catalysts

A series of LaAl1-xFexO3 catalysts prepared with lanthanum nitrate, aluminium nitrate and iron nitrate was investigated in catalytical syntheses of carbon nanotubes with high yields and purity. The properties of carbon nanotubes prepared by the method of CVD(chemical vapor deposition) with n-hexane as the carbon resource were studied and it was shown that the diameter of carbon nanotubes can be controlled by the molar ratio of iron to aluminum in the catalysts and that the diameter of carbon nanotubes changes a little with the decrease of the iron content in the catalysts. From the TEM pictures of carbon nanotubes, it can be found that the LaAl1-xFexO3 catalysts have a significant influence on the wall thickness of the carbon nanotubes, whereas they have little influence on the inner diameter of the carbon nanotubes.