给定零点的最近复系数多项式计算问题

Nearest polynomial with given properties has many applications in control theory and applied mathematics. Given a complex univariate polynomial f(z) and a zero α, in this paper we explore the problem of computing a complex polynomial f(z) such that f(α) = 0 and the distance ∥f-f ∥ is minimal. Considering most of the existing works focus on either certain polynomial basis or certain vector norm, we propose a common computation framework based on both general polynomial basis and general vector norm, and summarize the computing process into a four-step algorithm. Further, to find the explicit expression of f(z), we focus on two specific norms which generalize the familiar lp-norm and mixed norm studied in the existing works, and then compute f(z) explicitly based on the proposed algorithm. We finally give a numerical example to show the effectiveness of our method.     

Stress-induced polymer deformation in shear flows

By means of dynamic Monte Carlo simulation of bulk lattice polymers in Couette shear flow, it was demonstrated that in addition to velocity gradient the constant driving forces acting as the activation aspect of shear stresses can also raise polymer deformation. Moreover, enhancing driving forces in a flow without any velocity gradient can reproduce nonNewtonian fluid behaviors of long-chain polymers. The simulations of Poiseuille shear flow with a gradient of shear stresses show that, the velocity gradient dominates small deformation in the flow layers of low shear stresses, while the shear stress dominates large deformation in the flow layers of high shear stresses. This result implies that the stress-induced deformation could be mainly responsible for the occurrence of non-Newtonian fluid behaviors of real polymers at high shear rates.     

Extensional flow of bulk polymers studied by dynamic Monte Carlo simulations

Dynamic Monte Carlo simulations of bulk lattice polymers driven through planar geometries with sequentially converging,parallel and diverging spaces between two neutrally repulsive solid plates are reported.The spatial profiles of polymer velocity and deformation along the course of such a laminar extensional flow have been carefully analyzed.The results appear consistent with experimental observations in literature.In the entrance and exit regions,a linear dependence of chain extension upon the excess velocity has been observed.Moreover,an annexed shear flow and a molecular-dispersion effect are found.The results demonstrate a useful strategy of this approach to study polymer flows and bring new insights into the non-Newtonian-fluid behaviors of bulk polymers in capillary rheometers and micro-fluidic devices.     

火棘叶挥发油化学成分的GC-MS分析

采用水蒸气蒸馏法从火棘叶中提取挥发油,利用气相色谱-质谱(GC-MS)联用方法分析火棘叶挥发油化学成分,并以面积归一法测定各成分的相对含量。从火棘叶挥发油中共鉴定出69种化合物,占挥发油总量的80.52%,主要成分为(-)-b-杜松烯(22.62%)、植物醇(19.90%)、二环倍半水芹烯(5.95%)、β-桉叶醇(5.78%)、1,2,3,4,4a,7-六氢-1,6-二甲基-4-(1-甲基乙基)-萘(2.78%)、表圆线藻烯(2.34%)等。     

顶空-气相色谱法测定土壤和沉积物中丙烯酸酯类化合物

提出了顶空-气相色谱法测定土壤和沉积物中丙烯酸甲酯、丙烯酸乙酯、甲基丙烯酸甲酯、丙烯酸丙酯和丙烯酸丁酯等5种丙烯酸酯类化合物含量的方法。分别选择70℃及20 min作为样品在顶空瓶中的平衡温度和平衡时间。用HP-INNOWAX毛细管色谱柱（30 m×0.32 mm,0.32μm）分离,氢火焰离子化检测器测定。5种丙烯酸酯类化合物在9 min内能完全分离。5种丙烯酸酯类化合物的质量分数在20.0～2000μg·kg^-1范围内与其峰面积呈线性关系,检出限（3S/N）在2.0～10.0μg·kg^-1之间。方法用于土壤和沉积物样品分析,加标回收率在86.8%～104%之间,测定值的相对标准偏差（n=6）在3.5%～5.4%之间。     

含磺基苯甲酸及联吡啶钌配合物的合成、结构和催化苯甲硫醚氧化研究

利用水热方法合成了一个三联吡啶钌磺基苯甲酸配合物, [Ru(2, 2′-bipy)₃](3-Hsb)(3-sb)·5H₂O (1)(2, 2′-bipy为2, 2′-联吡啶;3-sb^2-为3-磺基苯甲酸根离子), 对配合物进行了元素分析、红外、紫外、荧光和差热热重表征, 解析了配合物的晶体结构。晶体结构解析表明:配合物1是阴离子-阳离子型化合物, 阴离子与水分子形成三维有孔洞的氢键网络, 阳离子占据这些孔洞。电化学性质测试表明:氧化还原是一个单电子可逆的过程, 对应的可逆对为Ru(Ⅳ)/Ru(Ⅲ), E_1/2=1.350 V。室温苯甲硫醚氧化催化实验表明:钌配合物与酸结合具有较高的催化活性与亚砜选择性。     

微波辅助萃取/气相色谱-质谱法同时测定纸质食品接触材料中18种多环芳烃

建立了同时测定纸质食品接触材料中18种禁用多环芳烃的气相色谱-质谱/选择离子监测方法。以二氯甲烷-正己烷(1∶1)为提取溶剂,在90℃下微波辅助萃取纸质食品接触材料中的多环芳烃,提取液经二甲亚砜萃取、环己烷反萃取、硅胶固相萃取柱净化后,进行气相色谱-质谱/选择离子监测分析,外标法定量。各组分的检出限为0.1~1.0μg/kg,相关系数均大于0.997,加标回收率为56.3%~95.4%,相对标准偏差均小于7%。该方法简便快捷、灵敏度高、定性定量准确,适用于纸质食品接触材料中多环芳烃的同时测定。     

基于捷联式光纤陀螺的工程结构三维形变测量方法

提出了利用捷联式光纤陀螺进行水下管道三维形变的测量方法,对这一方法的测量原理进行了详细阐述,并利用坐标转换、姿态矩阵求解、形变的计算等方法给出了详细的数学模型及算法。另外,针对惯性传感器和测量系统给出了减小误差的措施,以提高测量精度。     

Surface rumples and band gap reductions of cubic BaZrO3 (001) surface studied by means of first-principles calculations

Electronic properties of the (001) surface of cubic BaZrO$_{3}$ with BaO and ZrO$_{2}$ terminations have been studied using first-principles calculations. Surface structure, partial density of states, band structure and surface energy have been obtained. We find that the largest relaxation appears in the first layer of atoms, and the relaxation of the BaO-terminated surface is larger than that of the ZrO$_{2}$-terminated surface. The surface rumpling of the BaO-terminated surface is also larger than that of the ZrO$_{2}$-terminated surface. Results of surface energy calculations reveal that the BaZrO$_{3}$ surface is likely to be more stable than the PbZrO$_{3}$ surface.     

餐厨垃圾与市政污泥共消化厌氧产氢研究

为探求高温(55℃)、高含固率(20％)条件下餐厨垃圾和市政污泥共消化厌氧产氢的性能, 将餐厨垃圾与市政污泥按挥发性固体(VS)质量比(1:1、2:1、3:1、4:1、5:1)混合进行共消化厌氧产氢实验, 观察不同比例混合物料厌氧产氢系统内的pH、挥发性脂肪酸(VFAs)和氨氮的变化, 以及单位VS产气量和氢气的体积分数. 结果表明, 餐厨垃圾与市政污泥混合共消化厌氧能取得较好的产氢效果. 当餐厨垃圾与市政污泥的物料比为3:1时, 厌氧系统单位VS产气量和氢气体积分数均达到最大值, 分别为118.2mL·g-1 VS和37.47％; 各比例混合物料在整个厌氧产氢过程中系统均运行良好, 未出现系统“酸中毒”或失败的现象.