基于颜色主波长与补色波长的比色法定量检测

利用sRGB(Standard RGB)颜色空间与国际照明委员会(CIE)色度系统的转化关系以及CIE 1931色品图的性质,编写MATLAB程序实现了颜色的RGB信息到颜色主波长或补色波长的转化,并将此程序用于分析面光源下采集到的显色产物的图片。利用颜色的主波长实现了对pH值的定量检测,利用颜色的补色波长完成了对亚硝酸根离子的定量检测。当pH值分别在4.0~7.0和7.5~10.0范围内,pH值均与其显色产物颜色的主波长呈线性变化;亚硝酸根离子浓度在10~40 mg/L范围内与其显色产物颜色的补色波长有良好的线性关系,通过结合图片的G值分析,扩大了传统吸收光谱法的检测范围。     

Remarks on the wonderful compactification of semisimple algebraic groups

We prove that ifG is a semisimple algebraic group of adjoint type over the field of complex numbers,H is the subgroup of all fixed points of an involution σ ofG that is induced by an involution σ of the simply connected coveringĜ ofG, then the wonderful compactification of the homogeneous spaceG/H is isomorphic to the G.I.T quotientG ^ss (L)//H of the wonderful compactificationG ofG for a suitable choice of a line bundleL onG. We also prove a functorial property of the wonderful compactifications of semisimple algebraic groups of adjoint type.     

扩展数字图像相关方法中裂尖位移函数的表征研究

探寻适用于扩展数字图像相关方法(X-DIC)的裂纹尖端位移函数,对于提高该方法在裂尖测试精度方面具有重要意义。本文基于断裂力学裂纹尖端位移场函数,进行主导项影响分析,并探究裂尖位移函数中各项及其组合项对位移场表征的贡献程度及对测试精度的影响。通过对I型、II型及混合型裂纹进行测试,发现各项及其组合项在不同裂纹类型测试中的影响有着较大区别,从而得出在X-DIC测试计算中影响裂尖位移场表征的主导项。最后,应用上述研究成果对某航空超硬铝合金的单边裂纹进行拉伸测试。     

基于科学思维学习进阶的高一元素化合物单元整体教学设计

以学习进阶理论为指导,以高一化学教材中金属铝在3个学习阶段的教学设计为例,在构建知识层级和认识层级的基础上,对元素化合物知识中的科学思维方法进行显性构建和整体安排,提出在化学学习中,尤其要注重科学思维的进阶学习,以更好地实现学习进阶的实质内涵,更好地培养学生的科学素养。     

Computing the nearest diagonally dominant matrix

We solve the problem of minimizing the distance from a given matrix to the set of symmetric and diagonally dominant matrices. First, we characterize the projection onto the cone of diagonally dominant matrices with positive diagonal, and then we apply Dykstra's alternating projection algorithm on this cone and on the subspace of symmetric matrices to obtain the solution. We discuss implementation details and present encouraging preliminary numerical results. Copyright © 1999 John Wiley & Sons, Ltd.     

Short Communication: Two Properties of Diagonally Dominant Matrices

A property of strictly diagonally dominant matrices and a generalization of a Varga's bound for ∥ A⁻¹∥∞ to the case ∥ A⁻¹B∥∞ are given and the two-sided bounds for the determinants of strictly diagonally dominant matrices are derived     

On sums of squares of k-nomials

In 2005, Boman et al. introduced the concept of factor width for a real symmetric positive semidefinite matrix. This is the smallest positive integer k for which the matrix A can be written as $A=V{V}^T$ with each column of V containing at most k non-zeros. The cones of matrices of bounded factor width give a hierarchy of inner approximations to the PSD cone. In the polynomial optimization context, a Gram matrix of a polynomial having factor width k corresponds to the polynomial being a sum of squares of polynomials of support at most k. Recently, Ahmadi and Majumdar [1], explored this connection for case $k=2$ and proposed to relax the reliance on polynomials that are sums of squares in semidefinite programming to polynomials that are sums of binomial squares In this paper, we prove some results on the geometry of the cones of matrices with bounded factor widths and their duals, and use them to derive new results on the limitations of certificates of nonnegativity of quadratic forms by sums of k-nomial squares using standard multipliers. In particular we show that they never help for symmetric quadratics, for any quadratic if $k=2$, and any quaternary quadratic if $k=3$. Furthermore we give some evidence that those are a complete list of such cases.     

Extended rough set model based on known same probability dominant valued tolerance relation

Classical rough set theory is based on the conventional indiscernibility relation. It is not suitable for analyzing incomplete information. Some successful extended rough set models based on different non-equivalence relations have been proposed. The data-driven valued tolerance relation is such a non-equivalence relation. However, the calculation method of tolerance degree has some limitations. In this paper, known same probability dominant valued tolerance relation is proposed to solve this problem. On this basis, an extended rough set model based on known same probability dominant valued tolerance relation is presented. Some properties of the new model are analyzed. In order to compare the classification performance of different generalized indiscernibility relations, based on the category utility function in cluster analysis, an incomplete category utility function is proposed, which can measure the classification performance of different generalized indiscernibility relations effectively. Experimental results show that the known same probability dominant valued tolerance relation can get better classification results than other generalized indiscernibility relations.