Signature of relations in mapping class groups and non-holomorphic Lefschetz fibrations

We introduce the notion of signature for relations in mapping class groups and show that the signature of a Lefschetz fibration over the 2-sphere is the sum of the signatures for basic relations contained in its monodromy. Combining explicit calculations of the signature cocycle with a technique of substituting positive relations, we give some new examples of non-holomorphic Lefschetz fibrations of genus and which violate slope bounds for non-hyperelliptic fibrations on algebraic surfaces of general type.

     

Shear Thickening Fluids Based on Additives with Different Concentrations and Molecular Chain Lengths

将二氧化硅颗粒和不同分子链长添加剂颗粒分散到聚乙二醇分散介质中制得剪切增稠液样品,研究了添加剂的不同含量和不同分子链长对剪切增稠液流变性能的影响. 对其流变特性的研究表明,随着添加剂含量的增加和分子链长的增长,样品的剪切增稠效应增强明显,并用大粒子簇的形成对增强机理给出了合理的解释.     

高效液相色谱-串联质谱法测定动物血浆中罗匹尼罗的浓度

建立高效液相色谱-串联质谱(LC-MS/MS)测定动物血浆中罗匹尼罗浓度的方法。血浆经乙酸乙酯萃取后,以HPLC分离,电喷雾离子化(ESI~+)串联质谱检测。以甲醇-乙腈-0.1‰冰醋酸(36:9:55)为流动相,流速为0.2mL·min~(-1),采用Ultimate XB-C 18柱(150mm×2.1mm,3μm)分离,在三级四极杆串联质谱中经电喷雾电离源(ESI)离子化,以多反应监测(MRM)方式进行检测。盐酸罗匹尼罗、盐酸苯海拉明(内标)的扫描离子对m/Z分别为261→114和m/Z 256→167。LC-MS/MS测定血浆中罗匹尼罗线性范围为0.02—400ng·mL~(-1),范围内线性关系良好(r=0.9998);以3个浓度水平的质量控制样品求得各浓度水平日内、日间精密度(RSD)均小于15.2%。在非临床药代动力学研究中,应用此法测定了受试兔子血浆中罗匹尼罗的浓度。该法灵敏、快速、准确,操作简便,样品处理方便,线性范围宽,该方法检测快速、专一、灵敏,可满足罗匹尼罗临床前药代动力学研究和临床药动学研究的要求。     

基于自适应斜坡补偿的双环电流模DC/DC混沌控制

提出了一种自适应斜坡补偿方法,将该方法引入到双环电流模buck DC/DC的混沌控制中,并给出实现该方法的电路结构.建立了双环电流模DC/DC系统稳定性分析的离散模型,理论分析了自适应斜坡补偿在双环控制下系统的稳定性条件,推导出了自适应因子k与系统工作的最大占空比的关系式.仿真结果表明该方法可有效控制系统的分岔和混沌现象,提高系统的工作范围和动态响应速度.     

Design considerations of depressed clad W-shaped single mode dispersion compensating fibers

Dispersion compensating fibers (DCFs) are being widely used as dispersion compensation techniques because of its superior characteristics. This work reports the theoretical modelling of a single mode DCF having W-shaped shallow as well as deeply depressed clad profile. The DCFs have been designed and optimized by suitable adjusting different fiber parameters such as, central relative index difference (Δ⁺), inner core radius (a), depression depth parameter (ρ), normalized end position of the depressed clad (p), etc. at a given spot size . The figure of merit (FOM) characteristics including the bend loss as well as other losses associated with fiber manufacturing technique have been thoroughly investigated. Performances of these DCFs for recent wavelength division multiplexing (WDM) transmission system have also been discussed. By adjusting different fiber parameters, the effective core area (A_eff) of the above DCFs can be controlled to minimize the effect of non-linearities on them.     

Concentration for Poisson U-statistics: Subgraph counts in random geometric graphs

Concentration bounds for the probabilities $\mathbb{P}(N\ge M+r)$ and $\mathbb{P}(N\le M?r)$ are proved, where $M$ is a median or the expectation of a subgraph count $N$ associated with a random geometric graph built over a Poisson process. The lower tail bounds have a Gaussian decay and the upper tail inequalities satisfy an optimality condition. A remarkable feature is that the underlying Poisson process can have a.s. infinitely many points.The estimates for subgraph counts follow from tail inequalities for more general local Poisson U-statistics. These bounds are proved using recent general concentration results for Poisson U-statistics and techniques involving the convex distance for Poisson processes.     

Conceptualizations of slope in Mexican intended curriculum

Slope is a fundamental mathematics concept in middle and high school that transcends to the university level. An understanding of slope is needed at the university level since slope plays an important role in understanding problems involving variation and change. In this study Mexican curricula documents were examined to determine which conceptualizations of slope are addressed in the intended mathematics curriculum. To explain the results, we use conceptualizations of slope identified in previous research. Our findings reveal that, to a certain extent, the conceptualizations proposed in the Mexican intended mathematics curriculum differ slightly in terms of the emphasis and timing of instruction from what others have identified in the U.S., with slope as a geometric ratio receiving less emphasis in the Mexican curriculum. There was also noted discontinuity within the Mexican curriculum in introducing slope in grade 9 and subsequently introducing of linear functions in grade 10 without explicit mention of slope. Suggestions are made for future studies, both to consider the conceptualizations of slope promoted in the Mexican textbooks and the impact they have in classroom instruction and student learning of slope.     

Effective reaction rates of a thin catalyst layer

The catalyst layer in a fuel cell can be described with a system of reaction diffusion eq uations for the oxygen concentration and the protonic overpotential. The Tafel law gives an exponential expression for the reaction rate, and the Tafel slope is a coefficient in this law. We present a rigorous thin layer analysis for two reaction regimes. In the case of thin catalyst layers and bounded potentials, the original Tafel law enters as an effective boundary condition. Instead, in the case of large protonic overpotentials, we derive an exponential law that contains the doubled Tafel slope. Copyright © 2009 John Wiley & Sons, Ltd.     

矿区土壤中含水率及重金属迁移转化的数值模拟

本文基于由连续性方程和达西定律所推出的土壤中水分运动基本方程,以一维垂向水分方程为研究对象,构造稳定收敛的有限差分格式,运用MATLAB数学工具,对地面饱水情况下土壤水分运动的一维垂向方程进行了数值模拟,得到了土壤中水分的迁移规律;同时,综合考虑对流扩散作用以及土壤对重金属的吸附解吸作用,利用非饱和土壤中重金属离子迁移转化模型,对锌离子在矿区土壤中的迁移转化进行了数值模拟,展示了锌离子在矿区土壤中的浓度分布规律．