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     

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.     

New Synthetic Method for Industrial Manufacture of Glutaric Dialdehyde

A new synthetic method for the manufacture of glutaric dialdehyde is investigated. Glutaric dialdehyde was prepared by the addition-hydrolysis reaction of benzimidazolium salt with saturated dihalide as the di-Grignard reagent. The yield of glutaric dialdehyde by this method can reach 73%. Both infrared spectra and melting point of the compound were consistent with those reported earlier. Translated from Journal of Northwest University (Natural Science Edition), 2005, 35(2) (in Chinese)     

布尔“复合函数”的Walsh循环谱和自相关函数

本文利用布尔随机变量联合分布的分解式给出了布尔“复合函数”和某布尔函数符合率的分解算式,由此求得了布尔“复合函数”的 Walsh循环谱和自相关函数的计算公式,公式清楚地表明了“复合”所得布尔函数的 Walsh循环谱与起“复合”作用的函数和被“复合”的各函数所有线性组合的 Walsh循环谱之间的关系、“复合”所得布尔函数的自相关函数与起“复合”作用的函数谱和被“复合”的各函数的谱及相关函数之间的关系,这两个公式在布尔函数的密码学性质研究中会有广泛的应用.