Corrections of proofs for Hansen and Mélot's two theorems

The Randi? index R(G) of a (chemical) graph G is also called connectivity index. Hansen and Mélot [Variable neighborhood search for extremal graphs 6: analyzing bounds for the connectivity index, J. Chem. Inf. Comput. Sci. 43 (2003) 1-14] in their paper, characterized the chemical trees of given order and number of pendent vertices which have the minimum and maximum Randi? index, respectively. In this note, we point out the mistakes in the proofs of their results Theorems 8 and 10, while we still believe that the two theorems are true, and then we give their corrected proofs.     

Carathéodory's method for a class of second order differential equations on the half-line

The method of equivalent variational methods, originally due to Carathéodory for free problems in the calculus of variations is extended to investigate boundary value problems for a class of second order differential equations on the half-line. Some applications are presented to illustrate the potential of this method.     

铸膜液溶剂体系的物理参数与BCA不对称膜的透气性

铸膜液的溶剂体系（溶剂和非溶剂）对不对称膜形态的形成有重要作用。为了探索溶剂和透气性间的关系，本文考虑到了制备ＢＣＡ梯度密度不对称膜的各种溶剂的一系列物理参数，得到了一些定性结果，并指出了更全面、明确、解释两者关系的研究方向。     

Linear Ramsey numbers of sparse graphs

The Ramsey number R(G₁,G₂) of two graphs G₁ and G₂ is the least integer p so that either a graph G of order p contains a copy of G₁ or its complement G^c contains a copy of G₂. In 1973, Burr and Erd?s offered a total of $25 for settling the conjecture that there is a constant c = c(d) so that R(G,G)≤ c|V(G)| for all d‐degenerate graphs G, i.e., the Ramsey numbers grow linearly for d‐degenerate graphs. We show in this paper that the Ramsey numbers grow linearly for degenerate graphs versus some sparser graphs, arrangeable graphs, and crowns for example. This implies that the Ramsey numbers grow linearly for degenerate graphs versus graphs with bounded maximum degree, planar graphs, or graphs without containing any topological minor of a fixed clique, etc. © 2005 Wiley Periodicals, Inc. J Graph Theory     

离子束引起的在Al／Cr双层薄膜界面处的原子混合

用600keV的Kr~ 离子轰击Al/Cr双层薄膜样品进行界面原子反应及相互混合的研究。实验样品是在单晶硅上蒸镀约500nm厚的铝膜,相继再蒸上所需厚度的铬膜而制成的。轰击剂量为2.0×10~(15)-2.5×10~(16)Kr~ /cm~2。用2.0MeVa粒子对轰击前后的样品进行了卢瑟福背散射(RBS)分析,发现界面处有明显的原子混合存在;当轰击剂量≥1.0×10~(16)Kr~ /cm~2时,RBS谱出现有明显的坪台,经拟合计算和x射线衍射(XRD)测量证实确有化合物Al_(13)Cr_2存在;还分别得到了原子混合量及混合效率与轰击剂量的关系;最后对界面处的原子混合机制进行了讨论。     

中能区光学势的温度效应

本文在Skyr}e相互作用、核物质近似和自洽半经典方法的基础上，将微观光学势的自洽研究推J“到中能区(60-r300MeV)，研究了”+907r在该能区光学势的径向形状和温度效应     

PERSISTENCE AND GLOBAL STABILITY FOR TWO-SPECIES NONAUTONOMOUS PREDATOR-PREY SYSTEM WITH DIFFUSION AND TIME DELAY

In this paper, a non-autonomous predator-prey model with diffusion andcontinuous time delay is studied, where the prey can diffuse between two pat-ches of a heterogeneous environment with barriers between patches, but for thepredator, the diffusion does not involve a barrier between patches, further itis assumed that all the parameters are time-dependent. It is shown that thesystem can be made persistent under some appropriate conditions. Moreover,sufficient conditions that guarantee the existence of a unique periodic solutionwhich is globally asymptotic stable are derived.     

One convenient synthesis route to boron nitride nanotube

We describe one convenient synthesis route to boron nitride (BN) nanotube by the reaction of boron powder, iron oxide, and ammonium chloride at 600 °C for 12 h. Characterized by XRD, FTIR, XPS, TEM and SAED, the composition and morphology of the products are confirmed. The possible reaction mechanism is also discussed.