不同聚合机理的“平均聚合度”公式的分析讨论

平均聚合度和聚合度分布是决定聚合物产品质量的一个重要指标。平均聚合度直接表征聚合产品的分子量的大小,它的大小又决定高分子材料的性能,因此,研究平均聚合度具有重要的理论意义和实际意义。聚合反应按机理分类,可分为链型聚合和逐步聚合,链型聚合又分为自由基聚合、离子聚合、配位聚合,逐步聚合又分为缩聚和加聚反应。本文以自由基聚合、离子聚合、配位聚合以及缩聚的聚合机理为主线,对不同聚合机理对应的平均聚合度的公式进行推导和讨论,并加深理解,掌握其内涵。旨在提高学生对平均聚合度的认识和把握。     

Cheminformatics in MS-based environmental exposomics: Current achievements and future directions

Compound annotation using MS/MS data is the major bottleneck in interpretation of mass spectrometry data during non-targeted screening and suspect screening exposomics studies. Apart from compound identification using available databases or mass spectral libraries, the true challenge comes when completely new compounds have to be identified. Along with recent advances in MS instrumentation that set grounds to a new revolutionary age in environmental exposomics, a multitude of cheminformatics annotation approaches has been developed. Herein, we review the basic principles of the cutting-edge cheminformatics MS-based approaches employed in eco-exposome annotation.We give a solid background discussing the eco-exposome concept in relation to the advances in MS instrumentation, and define the three crucial cheminformatics tasks used in the eco-exposome annotation: molecular formula assignment, compound prioritization and compound annotation. The basic principles of compound annotation are discussed, which are based on three approaches of utilizing structural information inherent to MS data. These involve direct, indirect and joint annotation approaches. We assess their performance through the ability to annotate eco-exposome constituents. We discuss future perspectives and give directions to new annotation strategies and performance evaluation protocols aiming to solve current issues hampering the incorporation of cheminformatics annotation approaches in regular eco-exposome annotation workflows.     

分析化学教材中关于离子活度系数计算公式的讨论

在处理电解质溶液的化学平衡理论中,有关离子的活度和活度系数的计算或估算都有比较严谨的理论公式或经验公式,而国内分析化学教材中关于经验公式的表述略显随意。以0.050 mol·L^-1AlCl₃水溶液中Cl^-和Al³⁺的活度计算为例,结合国内外分析化学教材中关于活度系数计算的经验公式进行讨论。由计算结果可知,关于活度系数计算的经验公式需给出明确的使用条件。     

积分中值定理的推广及其应用

给出了积分中值定理的一个推广,讨论了推广的积分中值定理中间值的渐近性.     

On the Relative Twist Formula of l-adic Sheaves

We propose a conjecture on the relative twist formula of l-adic sheaves, which can be viewed as a generalization of Kato—Saito's conjecture. We verify this conjecture under some transversal assumptions. We also define a relative cohomological characteristic class and prove that its formation is compatible with proper push-forward. A conjectural relation is also given between the relative twist formula and the relative cohomological characteristic class.     

关于Euler-Maclaurin公式的一个注记

利用梯形公式的余项,将被积函数的二阶导数做幂级数展开,证明了余项是关于求积区间长度的奇数次幂级数.推导出了复合梯形公式的一类渐近展开式,从另一方面印证了Euler-Maclaurin公式.     

一个二进小波变换像空间的再生核函数

1 引言 小波分析是结合泛函分析、应用数学、逼近论、调和分析、广义函数论等数学知识的结晶,具有深刻的理论意义和广泛的应用范围,被称为”数学显微镜”.基于其多分辨分析的特点以及在时、频两域都具有表征信号局部特征的功能,应用它可以解决许多Fourier变换不能解决的难题,为工程应用提供了一种新的、更有效的分析工具[1],由...     

变角度纤维复合材料层合斜板的颤振分析

假设纤维方向角沿层合板的长度方向线性变化,研究了变角度纤维复合材料层合斜板的颤振．通过坐标变换将斜板变换为正方形板,采用层合板表面连续变化的速度环量来模拟空气对其的作用,速度环量分布利用Cauchy积分公式计算．建立了系统的Lagrange方程并采用Ritz法得到了层合板的自振频率和颤振/不稳定性分离临界速度．通过数值算例验证了本文模型和方法的正确性和收敛性,分析了各个铺层内纤维方向角的变化对自振频率和颤振/不稳定性分离临界速度的影响．研究结果表明,通过纤维的变角度铺设,可有效地提高层合板的基频和颤振/不稳定性分离临界速度．经合理设计的变角度复合材料层合板具有抑制颤振的作用．     

Vertex correction and conductivity in 2D Dirac-like systems with non-conserving spin disorder

We determine the classical diffusion of two dimensional Dirac-like quasiparticles, in the presence of conserving spin disorder (scattering off electric impurities) and non-conserving spin disorder (scattering off magnetic impurities). We use the Kubo formula for the conductivity tensor and employ diagrammatic perturbation theory to calculate the vertex correction and the renormalisation of the current operator for both electric and magnetic scattering. Scattering off electric impurities is isotropic and the current operator renormalised to two times the bare current operator irrespective of the direction of the dynamics, as usual for Dirac-like fermions. For magnetic scattering the renormalisation of the current operator depends on the direction of the dynamics and on the polarisation of the magnetic impurities, making the system anisotropic. We calculate the anisotropic magnetoresistance (AMR) and analyse it as a function of the ratio of the strength of the electric to the magnetic scattering potentials, for short range Gaussian correlation.     

Comparative study of optical analysis methods for thin films

Three popular optical analysis methods (the transfer-matrix method, the Tinkham formula, and Beer's law) have been used for analyzing the optical spectra of thin films. While the transfer-matrix method is an accurate method, the Tinkham formula and Beer's law are approximate methods. Here we investigated the three methods using measured transmittance spectra of insulating transition-metal dichalcogenide (TMD) thin films on a quartz substrate. Three different semiconducting 2H-TMD systems (MoS₂, MoSe₂, and MoTe₂) were measured and analyzed. The optical conductivities obtained from the measured transmittance spectra using the transfer-matrix method and Tinkham formula and the absorption coefficients obtained using the transfer-matrix method and Beer's law were compared. The comparisons show some discrepancies. The reasons for the discrepancies between the results obtained via the two different methods were examined and the application limitations of the Tinkham formula and Beer's law were discussed.