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.     

喷雾干燥-固相煅烧法制备球形钛酸狸负极材料的研究

通过喷雾干燥-固相煅烧法制备了球形钛酸钾.不同于传统喷雾干燥工艺采用固态钛源进行制备,本文采用的前驱体是钾盐,分散剂和钛酸四丁酯制备出的硝酸氧钛的混合溶液.由于制备方法中前驱体为原子级均匀分布,化学计量比可精确控制,制备出的材料颗粒细小,粒径、成分分布均匀,电化学性能优异.同时研究了不同钾钛摩尔比以及煅烧温度对球形钛酸钾的形貌和成分的影响,并研究了其作为钾离子电池电极材料的电化学性能.结果表明,钾钛摩尔比为0.816,煅烧温度为 800 ℃时钛酸钾的电化学性能最好,首圈容量 185.1 mAh/g,30 圈后容量为173.9 mAh/g,循环100圈后还有169.7 mAh/g的容量.     

氧化石墨烯/多壁碳纳米管负载金铂核壳纳米粒子构建一种三维新型抗坏血酸电化学传感器

该文采用涂覆的方式构建了一种用于灵敏检测抗坏血酸(AA)的电化学传感器。先将多壁碳纳米管(MWCNTs)和氧化石墨烯(GO)混合悬浮液修饰在玻碳电极(GCE)表面,修饰的GO可有效防止MWCNTs聚集,再将具有良好电催化性能的金铂核壳纳米粒子(Au@Pt NPs)修饰在GO/MWCNTs电极上,层层组装构建形成GO/MWCNTs/Au@Pt NPs/GCE三维新型抗坏血酸电化学传感器。该修饰电极在磷酸缓冲溶液中对AA显示了较宽的线性范围和极低的检出限,氧化峰电流与AA浓度在0.005～0.5μmol/L和0.5～1 000μmol/L范围内呈良好的线性关系,相关系数均为0.999,检出限(S/N=3)为4×10~(-9) mol/L,稀释人体血清样品的加标浓度为0.01、0.1、10μmol/L,回收率为90.9%～108%,相对标准偏差(RSD,n=3)为1.2%～2.8%。该修饰电极对AA具有良好的选择性,可有效排除多巴胺、尿酸、葡萄糖等生物小分子的干扰。方法简单、高效、灵敏,可用于临床实际检测。     

Scattering of Tollmien-Schlichting waves by localized roughness in transonic boundary layers

The laminar-turbulent transition in boundary-layer flows is often affected by wall imperfections, because the latter may interact with either the freestream perturbations or the oncoming boundary-layer instability modes, leading to a modification of the accumulation of the normal modes. The present paper particularly focuses on the latter mechanism in a transonic boundary layer, namely, the effect of a two-dimensional(2 D) roughness element on the oncoming Tollmien-Schlichting(T-S) modes when they propagate through the region of the rapid mean-flow distortion induced by the roughness. The wave scattering is analyzed by adapting the local scattering theory developed for subsonic boundary layers(WU, X. S. and DONG, M. A local scattering theory for the effects of isolated roughness on boundary-layer instability and transition: transmission coefficient as an eigenvalue. Journal of Fluid Mechanics, 794, 68–108(2006)) to the transonic regime, and a transmission coefficient is introduced to characterize the effect of the roughness. In the sub-transonic regime, in which the Mach number is close to, but less than, 1, the scattering system reduces to an eigenvalue problem with the transmission coefficient being the eigenvalue; while in the super-transonic regime, in which the Mach number is slightly greater than 1, the scattering system becomes a high-dimensional group of linear equations with the transmission coefficient being solved afterward. In the largeReynolds-number asymptotic theory, the K′arm′an-Guderley parameter is introduced to quantify the effect of the Mach number. A systematical parametric study is carried out,and the dependence of the transmission coefficient on the roughness shape, the frequency of the oncoming mode, and the K′arm′an-Guderley parameter is provided.     

一种基于特征分解的图像融合方法

一幅图像可以分解成几何特征不同的纹理部分和卡通部分,基于这两大特征提出了一种图像融合方法.利用卡通和纹理特征的差异,通过学习分别得到卡通字典和纹理字典.在融合过程中,分别利用特定的卡通和纹理字典对源图像的卡通和纹理部分进行融合,融合后的卡通和纹理部分经简单相加得到融合图像.实验结果表明,所提方法是有效的.     

球形WC增强铁基复合等离子堆焊层的组织与摩擦学性能

为提高304不锈钢的摩擦学性能,将质量分数为30%和60%的球形WC添加到铁基复合粉末,采用等离子堆焊技术在其表面制备了WC增强铁基复合涂层.分析其显微组织结构、物相和显微硬度,在恒定载荷(50 N)和滑动速度(20 mm/s)下进行干摩擦磨损试验,研究其干滑动摩擦学性能.结果表明:富含Cr的固溶强化奥氏体、高硬度的Cr7C3和WC增强相的存在,提高了WC增强铁基堆焊层的硬度,30%WC和60%WC涂层的显微硬度达到HV0.2665和HV0.2724,比铁基涂层提高了21.1%和31.9%,是304基体的3.7和4倍;30%WC和60%WC涂层的摩擦系数和磨损率分别为0.59和2.639×10~(–6) mm~3·N~(–1)·m~(–1),0.42和1.111×10~(–6) mm~3·N~(–1)·m~(–1).30%WC和60%WC涂层均表现出优异的耐磨性能,其磨损机理分别为黏着磨损和二体磨粒磨损的混合机制,和三体磨粒磨损.     

Measured and Predicted Solubility Phase Diagrams of Quaternary Systems LiBr-NaBr-MgBr2-H2O and LiBr-KBr-MgBr2-H2O at 298.15 K

The stable phase equilibria of quaternary systems LiBr-NaBr-MgBr₂-H₂O and LiBr-KBr-MgBr₂-H₂O at 298.15 K were studied by both experimental measurement(isothermal solution saturation method) and theoretical prediction(Pitzer model). The solubilities of the saturated solution have been determined experimentally and two stable phase diagrams and relevant water diagrams of the two quaternary systems were obtained. Results show that quaternary system LiBr-NaBr-MgBr₂-H₂O is hydrate II type as NaBr and NaBr·2H₂O coexistence. Its phase diagram consists of only one invariant point, four univariant curves, and five crystallization fields. The quaternary system LiBr-KBr-MgBr₂-H₂O is a complex type as the double salt KBr·MgBr₂·6H₂O formed. In addition to this double salt, the three single salts LiBr·2H₂O, KBr and MgBr₂·6H₂O also crystallize. In this paper, the solubilities of phase equilibria in above quaternary systems were also calculated by the Pitzer's electrolyte solution model. All the needed parameters can be obtained from the literature or be fitted by experimental data. On the Basis of the experimental and calculated results, the phase diagram of the quaternary system was plotted for comparison. It shows that the calculation results are consistent with the experimental ones.     

Stability analysis of switched fractional-order continuous-time systems

Nonlinear Dynamics - In this paper, a class of switched fractional-order continuous-time systems with order $$0<\alpha <1$$ is investigated. First, an interesting property of...     

消光式核壳二聚体传感器的设计与光谱特性分析

根据ITO/Au纳米核壳二聚体粒子在生物医学领域的应用合理性,设计了一种实时检测生物液体的核壳二聚体探针消光式传感器;由偶极子理论推导出输出波长与外界环境折射率关系;利用MATLAB设计ITO/Au纳米核壳二聚体粒子结构;采用软件DDSCAT7.3结合离散偶极近似法,利用二聚体有效半径模拟计算了300~950nm可见光到红外光波段不同核壳比、二聚体间距、以及不同介质折射率的消光光谱;根据传感芯片折射率与偶极共振、耦合八级共振的响应关系得出ITO/Au二聚体的折射率灵敏特性。与传统Ag/Au核壳纳米粒子相比,ITO/Au纳米核壳二聚体结构引入了可作为传感芯片灵敏性自参考参数的耦合八级共振峰,同时ITO/Au二聚体结构的折射率灵敏度可达到419nm/RIU。这些工作及其结果对制作消光式传感器具有重要的意义。