Theoretical study of (e,2e) triple differential cross sections of pyrimidine and tetrahydrofurfuryl alcohol molecules using multi-center distorted-wave method

We report theoretical studies of electron impact triple differential cross sections of two bio-molecules,pyrimidine and tetrahydrofurfuryl alcohol,in the coplanar asymmetric kinematic conditions with the impact energy of 250 eV and ejected electron energy of 20 eV at three scattering angles of-5°,-10°,and-15°.Present multi-center distorted-wave method well describes the experimental data,which was obtained by performing(e,2e)experiment.The calculations show that the secondary electron produced by the primary impact electron is strongly influenced by the molecular ionic multi-center potential,which must be considered when the low energy electron interacts with DNA analogues.     

Generalized Jacobi spectral Galerkin method for fractional pantograph differential equation

This work is concerned with the extension of the Jacobi spectral Galerkin method to a class of nonlinear fractional pantograph differential equations. First, the fractional differential equation is converted to a nonlinear Volterra integral equation with weakly singular kernel. Second, we analyze the existence and uniqueness of solutions for the obtained integral equation. Then, the Galerkin method is used for solving the equivalent integral equation. The error estimates for the proposed method are also investigated. Finally, illustrative examples are presented to confirm our theoretical analysis.     

基于TOPSIS模型的机场网络节点重要度评估

在机场网络中单个机场节点的失效往往会对其他的节点产生影响,特别是关键节点的失效会波及整个网络.准确客观的识别重要节点机场关乎整个机场网络的安全运营.本文分析了机场网络拓扑特性中的度、集聚系数和接近度指标,考虑了机场旅客吞吐量和所在城市人口等交通经济特性指标,使用熵权法确定权重的基础上,应用TOPSIS法构建综合评价体系模型,最后以华东地区机场网络为例进行节点重要度排序.结果表明与单一指标的评估结果相比,该方法更加全面客观的确定不同属性指标的权重,避免了不同指标取值的差异性,使评价更加全面,更符合机场网络实际运营情况.     

阳离子交换皂石黏土在基质辅助激光解吸电离飞行时间质谱分析中的应用

将一种人工合成的无机聚合物——蒙脱石皂石黏土（smectite，Sm）应用于基质辅助激光解吸电离飞行时间质谱分析（matrix-assisted laser desorption/ionization time of flight mass spectrometry, MALDI-TOF-MS），以检测糖类化合物。 将传统的有机基质2，4，6-三羟基苯乙酮（trihydroxyacetophenone, THAP）与阳离子交换后的皂石黏土混合制备成新型复合基质，应用于糖类化合物的检测。通过比较不同的制样方法，测定不同分子直径的糖类化合物，发现由于受复合基质晶面间距的限制，只有小分子糖类化合物能进入晶面间隙充分接触有机基质并被离子化，从而实现对小分子糖类化合物的选择性检测。     

计算代数方程组孤立奇异解的符号数值方法

求解代数方程组是计算代数几何的最基本问题之一,孤立奇异解的计算则是其中最具挑战性的课题之一,在科学与工程计算中有着广泛的应用,如机器人、计算机视觉、机器学习、人工智能、运筹学、密码学和控制论等.本文结合作者的研究成果,综述了符号数值方法在计算代数系统孤立奇异解、特别是近似奇异解精化与验证方面的研究进展,并对未来的研究方向提出了展望.     

Local discontinuous Galerkin method for a nonlocal viscous conservation laws

The purpose of this article is to investigate high‐order numerical approximations of scalar conservation laws with nonlocal viscous term. The viscous term is given in the form of convolution in space variable. With the help of the characteristic of viscous term, we design a semidiscrete local discontinuous Galerkin (LDG) method to solve the nonlocal model. We prove stability and convergence of semidiscrete LDG method in L² norm. The theoretical analysis reveals that the present numerical scheme is stable with optimal convergence order for the linear case, and it is stable with sub‐optimal convergence order for nonlinear case. To demonstrate the validity and accuracy of our scheme, we test the Burgers equation with two typical nonlocal fractional viscous terms. The numerical results show the convergence order accuracy in space for both linear and nonlinear cases. Some numerical simulations are provided to show the robustness and effectiveness of the present numerical scheme.     

基于模糊综合评判的大学数学考核方式改革

独立高校数学课程的开设旨在让学生掌握数学知识的基础上,提高数学应用能力.然而现行的考核方式存在重考试结果,轻学习过程等问题.从传统考核方式入手,指出其不足之处,基于模糊综合评判法建立新型评价体系和数学模型,通过试点运行验证了新的考核方式的可行性、客观性、合理性和科学性.     

(Sm0.5Gd0.2Nd0.3)2(Hf0.3Ce0.7)2O7复合氧化物的热物理性能

为寻求新型热障涂层用陶瓷材料,本文采用高温固相烧结法制备了(Sm_0.5Gd_0.2Nd_0.3)₂(Hf_0.3Ce_0.7)₂O₇复合氧化物。利用XRD分析了其晶体结构,SEM分析其显微组织,膨胀仪测试其热膨胀性能,激光热导仪测试其热扩散系数。结果表明,成功制备了具有单一萤石晶体结构的(Sm_0.5Gd_0.2Nd_0.3)₂(Hf_0.3Ce_0.7)₂O₇复合氧化物。其显微组织结构致密,晶界清晰无其他相存在。由于复杂的元素组成和较大的原子量,其热导率明显低于7YSZ和Sm₂Ce₂O₇。其较低的热膨胀系数则归因于B位离子较小的离子半径,但其热膨胀系数依然满足热障涂层的要求。