对称向量拟均衡问题有效解的存在性

利用标量化方法建立对称向量拟均衡问题有效解的存在性定理。作为标量化方法的应用，利用这一方法得到向量变分不等式和拟向量变分不等式有效解的存在性定理。     

基于NiCo2O4纳米片电极的非对称混合电容器

The looming global energy crisis and ever-increasing energy demands have catalyzed the development of renewable energy storage systems. In this regard, supercapacitors (SCs) have attracted widespread attention because of their advantageous attributes such as high power density, excellent cycle stability, and environmental friendliness. However, SCs exhibit low energy density and it is important to optimize electrode materials to improve the overall performance of these devices. Among the various electrode materials available, spinel nickel cobaltate (NiCo₂O₄) is particularly interesting because of its excellent theoretical capacitance. Based on the understanding that the performances of the electrode materials strongly depend on their morphologies and structures, in this study, we successfully synthesized NiCo₂O₄ nanosheets on Ni foam via a simple hydrothermal route followed by calcination. The structures and morphologies of the as-synthesized products were characterized by X-ray diffraction, scanning electron microscopy, and Brunauer-Emmett-Teller (BET) surface area analysis, and the results showed that they were uniformly distributed on the Ni foam support. The surface chemical states of the elements in the samples were identified by X-ray photoelectron spectroscopy. The as-synthesized NiCo₂O₄ products were then tested as cathode materials for supercapacitors in a traditional three-electrode system. The electrochemical performances of the NiCo₂O₄ electrode materials were studied and the area capacitance was found to be 1.26 C·cm^-2 at a current density of 1 mA·cm^-2. Furthermore, outstanding cycling stability with 97.6% retention of the initial discharge capacitance after 10000 cycles and excellent rate performance (67.5% capacitance retention with the current density from 1 to 14 mA·cm^-2) were achieved. It was found that the Ni foam supporting the NiCo₂O₄ nanosheets increased the conductivity of the electrode materials. However, it is worth noting that the contribution of nickel foam to the areal capacitance of the electrode materials was almost zero during the charge and discharge processes. To further investigate the practical application of the as-synthesized NiCo₂O₄ nanosheets-based electrode, a device was assembled with the as-prepared samples as the positive electrode and active carbon (AC) as the negative electrode. The assembled supercapacitor showed energy densities of 0.14 and 0.09 Wh·cm^-3 at 1.56 and 4.5 W·cm^-3, respectively. Furthermore, it was able to maintain 95% of its initial specific capacitance after 10000 cycles. The excellent electrochemical performance of the NiCo₂O₄ nanosheets could be ascribed to their unique spatial structure composed of interconnected ultrathin nanosheets, which facilitated electron transportation and ion penetration, suggesting their potential applications as electrode materials for high performance supercapacitors. The present synthetic route can be extended to other ternary transition metal oxides/sulfides for future energy storage devices and systems.     

求解矩阵方程AXB+CXD=F参数迭代法的最优参数分析

本文针对求矩阵方程AXB+CXD=F唯一解的参数迭代法，分析当矩阵A，B，C，D均是Hermite正（负）定矩阵时，迭代矩阵的特征值表达式，给出了最优参数的确定方法，并提出了相应的加速算法.     

恒定非均匀磁场调控下的强制对流传热数值研究

分别对雷诺数、磁场强度和磁纳米流体浓度进行了讨论，并将数字高程模型(DEM)应用到梯度磁场模型的建立，分析了磁场梯度大小和方向对传热效果的影响。结果表明：雷诺数、磁场强度和梯度与传热效果呈正相关，在磁场介入的情况下，磁纳米流体浓度对传热效果的影响存在一个最佳值；磁场梯度方向垂直于流动方向时对传热的强化效果最显著。以平均努塞尔数和压降为目标参数，利用正交试验设计的方法研究了各变量对传热效果影响的权重大小，得到各变量取值范围内的最佳组合。     

高居里温度铁电单晶PIN-PT的机电性能

弛豫铁电单晶Pb(In_1/2Nb_1/2)O₃-PbTiO₃(PIN-PT)相较于常用的Pb(Mg_1/3Nb_2/3)O₃-PbTiO₃(PMN-PT)具有更高的居里温度,在高稳定性、高性能的传感器、换能器方面具有应用前景。本工作采用谐振法研究了[001]方向极化的0.66PIN-0.34PT铁电单晶的全矩阵机电性能参数。0.66PIN-0.34PT 单晶的三方-四方相变温度(T_RT)约为160 ℃,居里温度(T_C)约为260 ℃,室温压电系数d₃₃、d₃₁、d₁₅分别为1 340 pC/N、-780 pC/N、321 pC/N,介电常数ε^T₃₃、ε^S₃₃、ε^T₁₁、ε^S₁₁分别为2 700、905、2 210、1 927,机电耦合系数 k₃₃、k₃₁、k₁₅、k_t分别为 87%、58%、38%、61%。其纵向压电常数(d₃₃)和纵向机电耦合系数(k₃₃)小于 PMN-PT 单晶,但是横向压电性能(d₃₁)和剪切压电性能(d₁₅)都略高于PMN-PT单晶。另外,研究了机电耦合性能随温度的变化趋势,发现0.66PIN-0.34PT单晶在150 ℃以下有较好的温度稳定性。     

基于分块压缩感知理论的太赫兹波宽光束成像技术

提出了一种基于分块压缩感知理论的太赫兹波宽光束成像技术。模拟结果显示,该技术可以实现高分辨率、高质量的快速成像。采用连续太赫兹波CO_2气体激光器光源,基于宽光束矩阵调制采样,对不同物体进行了分块压缩感知成像,并与基于单像素随机采样的分块压缩感知方法进行了对比。结果表明,所提技术具有更高的成像稳定性,且其采样过程对不同成像物体的普适性更好。     

基于手机信令大数据的城市居民出行OD预测

为得到具有客观性、动态性的居民出行起止点间交通出行量(OD trips),以中国移动手机信令大数据为基础,阐述了手机信令数据的来源与构成,针对城市居民出行目的,通过数据分析,设置10分钟为划分出行活动的阈值,提出基于手机信令数据获得的OD矩阵的原理与方法,应用数据挖掘技术,对贵阳市居民出行OD矩阵进行了预测.为进一步加强大数据与城市智能交通系统的融合,将得到的城市居民出行OD矩阵应用到真实的城市公交线网中.最后通过MicroCity平台,将数据结果实现可视化.分析结果表明:与传统OD调查方式相比,利用手机信令大数据获得的OD矩阵客观性、动态性较强,信息采集分析周期短,更容易与城市智能交通系统融合,应用可视化平台,可实时反映出城市公交运营状态,为城市智能规划和调度提供重要参考.     

基于正交试验设计的我国高科技企业技术创新获取途径选择对创新能力的影响研究

技术获取途径的选择对于高科技企业的创新驱动发展具有重要的影响,正确的获取途径选择,可以有效提高企业的竞争力。本文通过广义试验方法,以企业技术研发或改造项目的成功率、企业整体创新能力以及企业整体创新能力孕育潜力为试验指标,进行多指标试验,通过对试验结果进行部分正交多项式回归分析,讨论内部创新技术研发程度、购买新技术程度和合作开发新技术程度对试验指标的影响规律,得出了加强对企业内部技术研发投入以及扩大与科技院所合作来提高企业创新能力的相关建议。     

巧用构造法解线性代数题

本文总结了使用构造法解线性代数题目的技巧,通过举例阐述了该方法在线性代数课程不同章节中的使用.     

多元统计分析中一类矩阵迹函数最小化问题的有效算法

研究来源于多元统计分析中的一类矩阵迹函数最小化问题$\min c+ tr(AX)+\sum\limits_{j=1}^{m}tr(B_j X C_jX^{T}),\ \ {\rm s. t.} \ X^TX=I_p,$其中$c$为常数, $A\in R^{p\times n}\ (n\geq p)$, $B_j\in R^{n\times n}, C_j\in R^{p\times p}$为给定系数矩阵. 数值实验表明已有的Majorization算法虽可行, 但收敛速度缓慢且精度不高. 本文从黎曼流形的角度重新研究该问题, 基于Stiefel流形的几何性质, 构造一类黎曼非单调共轭梯度迭代求解算法, 并给出算法收敛性分析.数值实验和数值比较验证所提出的算法对于问题模型是高效可行的.