Minimax Theorems with Bregman Distance in Banach Spaces

Since Bregman distance is a generalized distance function which does not satisfy the triangle inequality nor symmetry, it is important to study minimax theorems in reflexive Banach spaces. Our minimax theorems differ from those in previous literature.     

Applications of the growth characteristics induced by the spectral distance

Let A be a complex unital Banach algebra. Using a connection between the spectral distance and the growth characteristics of a certain entire map into A, we derive a generalization of Gelfand’s famous power boundedness theorem. Elaborating on these ideas, with the help of a Phragm´en-Lindel¨of device for subharmonic functions, it is then shown, as the main result, that two normal elements of a C^?-algebra are equal if and only if they are quasinilpotent equivalent.     

Using synchrotron radiation inline phase‐contrast imaging computed tomography to visualize three‐dimensional printed hybrid constructs for cartilage tissue engineering

Synchrotron radiation inline phase‐contrast imaging combined with computed tomography (SR‐inline‐PCI‐CT) offers great potential for non‐invasive characterization and three‐dimensional visualization of fine features in weakly absorbing materials and tissues. For cartilage tissue engineering, the biomaterials and any associated cartilage extracellular matrix (ECM) that is secreted over time are difficult to image using conventional absorption‐based imaging techniques. For example, three‐dimensional printed polycaprolactone (PCL)/alginate/cell hybrid constructs have low, but different, refractive indices and thicknesses. This paper presents a study on the optimization and utilization of inline‐PCI‐CT for visualizing the components of three‐dimensional printed PCL/alginate/cell hybrid constructs for cartilage tissue engineering. First, histological analysis using Alcian blue staining and immunofluorescent staining assessed the secretion of sulfated glycosaminoglycan (GAGs) and collagen type II (Col2) in the cell‐laden hybrid constructs over time. Second, optimization of inline PCI‐CT was performed by investigating three sample‐to‐detector distances (SDD): 0.25, 1 and 3 m. Then, the optimal SDD was utilized to visualize structural changes in the constructs over a 42‐day culture period. The results showed that there was progressive secretion of cartilage‐specific ECM by ATDC5 cells in the hybrid constructs over time. An SDD of 3 m provided edge‐enhancement fringes that enabled simultaneous visualization of all components of hybrid constructs in aqueous solution. Structural changes that might reflect formation of ECM also were evident in SR‐inline‐PCI‐CT images. Summarily, SR‐inline‐PCI‐CT images captured at the optimized SDD enables visualization of the different components in hybrid cartilage constructs over a 42‐day culture period.     

光学频率梳啁啾干涉实现绝对距离测量

本文提出一种基于光学频率梳的啁啾脉冲干涉绝对距离测量的方法.通过一对衍射光栅啁啾参考脉冲,分析参考脉冲和测量脉冲的干涉光谱,得到脉冲的中心频率偏移量,从而解算出被测距离.文中详细分析了脉冲啁啾原理和啁啾脉冲干涉测距原理,以及影响测距范围的因素并给出仿真.搭建了改进的Michelson干涉结构,实验得出测距范围受啁啾参数的影响,并与理论分析吻合;在地下长导轨上,进行大范围测距实验.实验结果表明当,在65 m范围内,测量结果与参考测距仪相比,测距精度为33μm,相对精度达到5.1×10~(-7).此外,根据理论分析,通过实验优化了实验装置的测量不确定度.     

基于光谱连接空间的彩色相机光谱重构研究

针对彩色相机三通道响应值重构光谱反射率精度低的问题,提出了基于光谱连接空间的彩色相机光谱反射率重构方法。首先通过光谱反射率已知的训练样本集和多项式拟合方法建立相机响应值到光谱连接空间的转换矩阵,然后利用该矩阵将待重构样本的相机响应值映射到光谱连接空间,最后选用合适的光谱重构算法在光谱连接空间内实现光谱反射率重构,并利用色度误差和光谱误差两个指标对重构结果进行评价。在上述过程中,鉴于转换矩阵的重要性,采用了基于反距离加权的最小二乘法计算转换矩阵以提高相机响应值到光谱连接空间的转换精度。实验结果表明:本文方法切实可行且精度可靠,与基于彩色相机三通道响应值的光谱重构方法相比,色度重构精度和光谱重构精度均显著提高,平均色差和谱差分别为1.145 2和0.010 3,可在较大程度上满足数字典藏、高保真颜色复制等的需要。     

Comparison theorems for hyperbolic type metrics

The connection between several hyperbolic type metrics is studied in subdomains of the Euclidean space. In particular, a new metric is introduced and compared to the distance ratio metric.     

Boundary behaviour of invariant functions on planar domains

Precise behaviour of the Carathéodory, Kobayashi and Bergman metrics and distances near smooth boundary points of planar domains is found under various assumptions of regularity.     

一类二元容错码的扩展和算法

d-析取矩阵是非适应性群测(NGT)算法和二元叠加码最有效的数学模型,研究了d-析取矩阵M_q(n,k,d)的扩展码M_q~*(n,k,d)的析取性和容错性.     

基于岭估计的岭马田系统在复共线性数据中的应用

在多变量模式识别领域,变量间经常会存在复共线性,复共线性不仅会影响参数估计的效果,也会使变量的敏感性出现显著异常.马田系统是以马氏距离作为测量尺度的多变量模式识别方法,复共线性会通过马氏距离影响马田系统变量筛选的效果和判别的准确率.基于岭估计提出了一种新的测量尺度—岭马氏距离,利用岭迹法确定岭参数,将其引入马田系统使得马田系统对病态数据具有更好的耐受性.通过案例验证了岭马氏距离可以很好的克服复共线性,并提高马田系统的判别准确率.