搜索区传递2-（q，4，1）设计

对于区传递但非旗传递的可解2-（q，4，1）设计，Camina指出，当q=13，37，61，109，157，181时有具体的例子，但是否有更多的q产生具体例子有待研究。主要结果：设q是素数幂且q=13（mod24），则对于每个q〈2000，总存在区传递但非旗传递的2-（q，4，1）设计。     

Tuning the electrocatalytic activity of Pt nanoparticles on carbon nanotubes via surface functionalization

Polyelectrolytes with various characteristic functional groups as interlinkers to anchor Pt nanoparticles were used to functionalize carbon nanotubes (CNTs) as Pt electrocatalyst support. It was found that polyanions (poly(styrenesulfonic acid) (PSS), and poly(acrylic acid sodium) (PAA)) have a beneficial effect on methanol electrooxidation on Pt nanoparticles supported on carbon nanotubes via modifying their electronic structure through charge transfer from polyanions to Pt sites and supply of oxygen-containing species. The increased electron density around Pt sites by the charge transfer from polyanions would cause partial filling of Pt 5d-bands, resulting in the downshift of d-band center and weaker chemisorption with oxygen-containing species (e.g. CO_ad). The weakened chemisorption of CO on Pt nanoparticles would promote the methanol electrooxidation. On the contrary, polycations would have an opposite effect on the electronic structure and chemisorption properties of Pt nanoparticles.     

Positive solutions of the system for nth-order singular nonlocal boundary value problems

The paper deals with the existence and multiplicity of positive solutions to systems of nth-order singular nonlocal boundary value problems. The main tool used in the proof is fixed point index theory in cone. Some limit type conditions for ensuring the existence of positive solutions are given.     

Associative Cones and Integrable Systems

Abstract We identify ℝ⁷ as the pure imaginary part of octonions. Then the multiplication in octonions gives a natural almost complex structure for the unit sphere S⁶. It is known that a cone over a surface M in S⁶ is an associative submanifold of ℝ⁷ if and only if M is almost complex in S⁶. In this paper, we show that the Gauss-Codazzi equation for almost complex curves in S⁶ are the equation for primitive maps associated to the 6-symmetric space G₂=T², and use this to explain some of the known results. Moreover, the equation for S¹-symmetric almost complex curves in S⁶ is the periodic Toda lattice, and a discussion of periodic solutions is given. (Dedicated to the memory of Shiing-Shen Chern) * Partially supported by NSF grant DMS-0529756.     

Effect of a “Zn Bridge” on the Consecutively Tunable Retention Characteristics of Volatile Random Access Memory Materials

Polyimide memory materials with a donor–acceptor structure based on a charge-transfer mechanism exhibit great potential for next-generation information storage technology due to their outstanding high-temperature resistance and good dimensional and chemical stability. Precisely controlling memory performance by limited chemical decoration is one of core challenges in this field. Most reported work mainly focuses on designing novel and elaborate electron donors or acceptors for the expected memory behavior of polyimides; this takes a lot of time and is not always efficacious. Herein, we report a series of porphyrinated copolyimides coPI−Znx (x=5, 10, 20, 50, 80), where x represents the mole percentage of Zn ion in the central core of the porphyrin. Experimental and theoretical analysis indicate that the Zn ion could play a vital bridge role in promoting the formation and stabilization of a charge-transfer complex by enhancing the hybridization of local and charge transfer (HLCT) excitations of porphyrinated polyimides, endowing coPI−Znx with volatile random access memory performance and continuously tunable retention time. This work could provide one simple strategy to precisely regulate memory performance merely by altering the metal content in porphyrinated polyimides.     

双轴晶体主平面上倍频的相位匹配参量

根据折射率椭球方程及双光轴晶体中光波的传播与偏振特性，分析双轴晶体在主平面内激光倍频相位匹配的特性与方法，导出光波在主平面上传播时倍频的相位失配关系；给出双轴晶体中容许相位匹配倍频的相位匹配角及混频的有效非线性系数deff的表达式。利用可相位匹配的类型、相位匹配角公式和有效非线性系数deff表达式的表，容易对任意一具体晶体在一给定波长求出实际能实现相位匹配的类型或偏振组合，算出相位匹配角，比较不同的相位匹配类型或偏振组合的有效非线性系数，选择最佳的相位匹配类型与方向。从相位失配关系可以计算晶体主平面内倍频的接收角、接收光谱宽度等特性参量。     

感应同步器鉴幅测角系统静态误差分析及关键电路设计

本文系统论述了采用感应同步器进行角位置测量的连续绕组激磁，分段绕组输出的鉴幅方案，对这个方案的工作原理进行介绍，并对此方案产生的静态误差进行分析，给出减小误差的方法，最后得出相关结论。     

饱和地基上含刚核弹性圆板的竖向振动分析

基于作者提出的饱和土弹性波动方程，研究了饱和地基上含刚核弹性圆板在竖向集中谐和力作用下的振动特性。首先应用Hankel积分变换求解该饱和土波动方程，然后按混合边值条件建立起一组描述含刚核弹性圆板振动的对偶积分方程，并将其化为第二类Fredholm积分方程进行数值求解。文末给出了含刚核弹性圆板在饱和地基上振动的阻抗函数随无量纲频率a0的变化曲线，并考察了土的渗透系数，弹性板含刚域的大小以及板的柔度等参数对阻抗函数的影响，得出了一些有意义的结论。     

定态火焰在可燃预混气中产生的压力波

火焰在可燃预混气中传播时，在火焰面前方产生一道压力波。忽略点火及火焰的初期加速，仅考虑火焰达到稳定传播速度的情况。用Ｏｐｅｎｈｅｉｍ自相似解分析流场，得到相应的控制方程及定解条体；用自适应步长的四阶Ｒｕｎｇｅ－Ｋｕｔｔａ法对方程积分，讨论了流场压力波结构及弱激波近似声波解；认为火焰为间断面，能量释放在火焰面后瞬时完成。利用火焰面两侧的能量关系，得到了火焰位置、燃速及对应Ｃ－Ｊ条件的火焰位置、Ｃ－Ｊ燃速。