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.     

Bloch Oscillations of Two-Component Bose-Einstein Condensates in Optical Lattices

We study the Bloch oscillations of two-component Bose-Einstein condensates trapped in spin-dependent optical lattices. The influence of the intercomponent atom interaction on the system is discussed in detail Accelerated breakdown of the Bloch oscillations and revival phenomena are found respectively for the repulsive and attractive case. For both the cases, the system will finally be set in a quantum self-trapping state due to dynamical instability.     

High temperature superconducting thin films for microwave filters

YBa₂Cu₃O_7-δ and Tl₂Ba₂CaCu₂O₈ thin films for microwave filters were synthesized by pulsed laser deposition and the two-step thalliation process. Substrate quality requirements and the relation of thin film morphology, microstructure with microwave surface resistance were discussed.     

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     

木质装饰板材贫氧条件下燃烧和热解特性研究

本文利用热重差热分析仪,在各种不同的氧气浓度下对落叶松、红木和红松样品进行实验。通过对TG、DTG和DTA曲线的分析,样品干燥基要经历两个失重过程,第一个失重过程主要是纤维素和半纤维素的热解,第二个失重过程主要是木质素的炭化分解和燃烧。在各氧气浓度条件下,热解失重的第一个阶段TG和DTG曲线差异很小;在各样品失重的第二个阶段,随着氧气浓度的增加,TG和DTG曲线左移,反应结束的温度明显降低。氧气能使木质素的炭化物氧化并进而可能使其着火燃烧,从而使反应进程加快。当氧气浓度大于6.32%时,各样品DTA曲线上均有两个明显放热峰,并且随着氧气浓度的增加,DTA曲线放热峰越尖锐,放热峰面积越大,说明氧气浓度越大,在两阶段失重过程中更多的挥发分物质和固体炭化物参与燃烧。