Polynomial area bounds for MST embeddings of trees

In their seminal paper on geometric minimum spanning trees, Monma and Suri (1992) [31] showed how to embed any tree of maximum degree 5 as a minimum spanning tree in the Euclidean plane. The embeddings provided by their algorithm require area O(n²²)×O(n²²) and the authors conjectured that an improvement below cn×cn is not possible, for some constant c>0. In this paper, we show how to construct MST embeddings of arbitrary trees of maximum degree 3 and 4 within polynomial area.     

低分子量聚乙烯亚胺/金纳米棒纳米载体的制备及毒性研究

以表面修饰巯基十一烷酸的金纳米棒 (GNRs/MUA)为骨架, 将低分子量的聚乙烯亚胺(PEI)连接到GNRs/MUA表面, 构建GNRs/MUA/PEI纳米载体.首先采用MUA对GNRs进行表面修饰, 减少由于GNRs表面的十六烷基三甲基溴化铵(CTAB)所造成的生物毒性.然后采用低分子量 PEI 进一步修饰, 同时利用GNRs巨大的比表面积进一步放大 PEI 的携带基因能力, 这样既能够降低阳离子聚合物的毒性, 又能够提高整个体系的转染效率.利用透射电子显微镜(TEM)、紫外可见吸收光谱(UV-Vis)、Zeta电位等对纳米载体进行了表征.结果显示, MUA与PEI已成功修饰到GNRs表面, 并很好地保留了GNRs的光学性质, 其表面电位发生正负交替变化.采用噻唑蓝(MTT)比色法对纳米载体进行细胞毒性研究, 结果显示GNRs/MUA/PEI(1.8 kDa)非病毒纳米载体, 细胞存活率在控制聚合物浓度为300 μg/mL时仍然稳定在75%以上, 明显高于商品化的PEI(25 kDa).     

Universality for bounded degree spanning trees in randomly perturbed graphs

We solve a problem of Krivelevich, Kwan and Sudakov concerning the threshold for the containment of all bounded degree spanning trees in the model of randomly perturbed dense graphs. More precisely, we show that, if we start with a dense graph G_α on n vertices with δ(G_α) ≥ αn for α > 0 and we add to it the binomial random graph G(n,C/n), then with high probability the graph G_α∪G(n,C/n) contains copies of all spanning trees with maximum degree at most Δ simultaneously, where C depends only on α and Δ.     

Hydrophobically modified chitosan/gold nanoparticles for DNA delivery

Present study dealt an application of modified chitosan gold nanoparticles (Nac-6-Au) for the immobilization of necked plasmid DNA. Gold nanoparticles stabilized with N-acylated chitosan were prepared by graft-onto approach. The stabilized gold nanoparticles were characterized by different physico-chemical techniques such as UV-vis, TEM, ELS and DLS. MTT assay was used for in vitro cytotoxicity of the nanoparticles into three different cell lines (NIH 3T3, CT-26 and MCF-7). The formulation of plasmid DNA with the nanoparticles corresponds to the complex forming capacity and in-vitro/in-vivo transfection efficiency was studied via gel electrophoresis and transfection methods, respectively. Results showed the modified chitosan gold nanoparticles were well-dispersed and spherical in shape with average size around 10～12 nm in triple distilled water at pH 7.4, and showed relatively no cytotoxicity at low concentration. Addition of plasmid DNA on the aqueous solution of the nanoparticles markedly reduced surface potential (50.0～66.6%) as well as resulted in a 13.33% increase in hydrodynamic diameters of the formulated nanoparticles. Transfection efficiency of Nac-6-Au/DNA was dependent on cell type, and higher β-galactosidase activity was observed on MCF-7 breast cancer cell. Typically, this activity was 5 times higher in 4.5 mg/ml nanoparticles concentration than that achieved by the nanoparticles of other concentrations (and/or control). However, this activity was lower in in-vitro and dramatically higher in in-vivo than that of commercially available transfection kit (Lipofectin®) and DNA. From these results, it can be expected to develop alternative new vectors for gene delivery.     

A parallel algorithm for generating multiple ordering spanning trees in undirected weighted graphs

1.IntroductionLetG=(V,E,W)beaconnected,weightedandundirectedgraph,VeEE,w(e)(相似文献   

On the Minimum Spanning Tree Determined by n Points in the Unit Square

§１．　ＩｎｔｒｏｄｕｃｔｉｏｎＡｍｉｎｉｍｕｍｓｐａｎｎｉｎｇｔｒｅｅ（ＭＳＴ）ｉｓｗｉｄｅｌｙａｐｐｌｉｅｄｔｏｔｈｅｆｉｅｌｄｓｏｆｃｏｍｐｕｔｅｒ,ｃｏｍｍｕｎｉｃａｔｉｏｎ,ｎｅｒｗｏｒｋａｎｄｓｏｏｎ．Ｍａｎｙｒｅｓｕｌｔｓｈａｖｅｂｅｅｎｏｂｔａｉｎｅｓ,ｂｕｔｆｅｗｏｆｔｈｅｍｄｅａｌｗｉｔｈｔｈｅｗｏｒｓｔ－ｃａｓｅａｎａｌｙｓｉｓｆｏｒｔｈｅｇｉｖｅｎｆｉｎｉｔｅｒｅｇｉｏｎ．Ｉｎｆａｃｔ,ｉｔｉｓａｍａｘｉｍｉｎｐｒｏｂｌｅｍ（ｓｅｅ［１］——［３］）．Ｔｈｉｓｐａｐｅｒｉ…     

回传波矩阵法在杆系结构静力分析中的应用

回传波矩阵法最初是由Pao等人分析二维框架结构动力响应时提出的。对于三维杆系结构的静力分析,为了确定结构的位移和内力,先要建立传递分配矩阵和载荷源向量,这可通过列出所有节点的静力平衡方程和位移协调方程来实现。同时,通过分析每根杆近端位移和远端位移的关系,建立结构的回传波矩阵（重分配矩阵）。在此基础上求解线性方程组,就可以得到结构的位移和内力。本文推导了空间杆系结构的有关矩阵方程式,并给出了一固定梁的两端弯矩求解算例。     

Proof of a conjecture of Alan Hartman

A tree T is said to be bad, if it is the vertex‐disjoint union of two stars plus an edge joining the center of the first star to an end‐vertex of the second star. A tree T is good, if it is not bad. In this article, we prove a conjecture of Alan Hartman that, for any spanning tree T of K_2m, where m ≥ 4, there exists a (2m − 1)‐edge‐coloring of K_2m such that all the edges of T receive distinct colors if and only if T is good. © 1999 John Wiley & Sons, Inc. J Graph Theory 30: 7–17, 1999