An alternating direction algorithm for matrix completion with nonnegative factors

This paper introduces an algorithm for the nonnegative matrix factorization-and-completion problem, which aims to find nonnegative low-rank matrices X and Y so that the product XY approximates a nonnegative data matrix M whose elements are partially known (to a certain accuracy). This problem aggregates two existing problems: (i) nonnegative matrix factorization where all entries of M are given, and (ii) low-rank matrix completion where nonnegativity is not required. By taking the advantages of both nonnegativity and low-rankness, one can generally obtain superior results than those of just using one of the two properties. We propose to solve the non-convex constrained least-squares problem using an algorithm based on the classical alternating direction augmented Lagrangian method. Preliminary convergence properties of the algorithm and numerical simulation results are presented. Compared to a recent algorithm for nonnegative matrix factorization, the proposed algorithm produces factorizations of similar quality using only about half of the matrix entries. On tasks of recovering incomplete grayscale and hyperspectral images, the proposed algorithm yields overall better qualities than those produced by two recent matrix-completion algorithms that do not exploit nonnegativity.     

Synthesis and molecular characterization of the coordination polymer [Pb(2,2′-Bipy)(NO3)2(H2O)] n

A new coordination polymer [Pb(2,2′-Bipy)(NO₃)₂(H₂O)] _n has been successfully synthesized and characterized (where 2,2′-Bipy = 2,2′-bipyridine). The crystal structure of the polymer was determined by single-crystal X-ray diffraction, crystallizing in the monoclinic crystal system, space group P2₁/n with unit cell parameters: a = 7.1673(5), b = 9.8706(6), c = 19.1825(12) Å; β = 90.0780(10)°; V = 1357.08(15) ų, and Z = 16. The Pb atom was six-coordinated with N(1) and N(2) from 2,2′-Bipy, O(2), O(3), and O(6) in nitrate; O(1) from coordinated water, forming a slightly distorted octahedral geometry. The structure units aggregate together to give birth to the infinite 1D chains via bridged nitrate, and 2D networks and three-dimensional frameworks were obtained through hydrogen bonding and π-π-stacking interaction among aromatic rings, respectively.     

Photophysics of Hypericin and Hypocrellin A in Complex with Subcellular Components: Interactions with Human Serum Albumin

Time-resolved fluorescence and absorption measurements are performed on hypericin complexed with human serum albumin, HSA (1:4, 1:1 and approximately 5:1 hypericin: HSA complexes). Detailed comparisons with hypocrellin A/HSA complexes (1:4 and 1:1) are made. Our results are consistent with the conclusions of previous studies indicating that hypericin binds to HSA by means of a specific hydrogen-bonded interaction between its carbonyl oxygen and the N1-H of the tryptophan residue in the IIA subdomain of HSA. (They also indicate that some hypericin binds nonspecifically to the surface of the protein.) A single-exponential rotational diffusion time of 31 ns is measured for hypericin bound to HSA, indicating that it is very rigidly held. Energy transfer from the tryptophan residue of HSA to hypericin is very efficient and is characterized by a critical distance of 94 A, from which we estimate a time constant for energy transfer of approximately 3 x 10(-15) s. Although it is tightly bound to HSA, hypericin is still capable of executing excited-state intramolecular proton (or hydrogen atom) transfer in the approximately 5:1 complex, albeit to a lesser extent than when it is free in solution. It appears that the proton transfer process is completely impeded in the 1:1 complex. The implications of these results for hypericin (and hypocrellin A) are discussed in terms of the mechanism of intramolecular excited-state proton transfer, the mode of binding to HSA and the light-induced antiviral and antitumor activity.     

Electron dynamics in modulation p-doped InGaAs/GaAs quantum dots

We investigate the electron dynamics of p-type modulation doped and undoped InGaAs/GaAs quantum dots using up-conversion photoluminescence at low temperature and room temperature. The rise time of the p-doped sample is significantly shorter than that of the undoped at low temperature. With increasing to room temperature the undoped sample exhibits a decreased rise time whilst that of the doped sample does not change. A relaxation mechanism of electron-hole scattering is proposed in which the doped quantum dots exhibit an enhanced and temperature independent relaxation due to excess built-in holes in the valence band of the quantum dots. In contrast, the rise time of the undoped quantum dots decreases significantly at room temperature due to the large availability of holes in the ground state of the valence band. Furthermore, modulation p-doping results in a shorter lifetime due to the presence of excess defects.     

高效液相色谱溶剂系统四面体优化法

改进了Ｇｌａｊｃｈ的三角形法,建立了适合于高效液相色谱（ＨＰＬＣ）的四面体优化法。将７个溶剂系统的实验结果输入计算机,由计算机模拟２３１个溶剂系统的色谱行为,优选出最佳溶剂系统。将此法用于１２种磺胺药物的分离,得到了满意的结果。     

某些噻唑偶氮苯酚类试剂结构与性能关系的理论研究

噻唑偶氮试剂广泛应用于分析化学,近十来年发展较快,迄今已有170余种,但其结构和性能关系的理论研究报导较少。本文选取2-(2-噻唑偶氮)苯酚(简称TAP)及其九种甲基取代衍生物(见表1),用CNDO/2方法研究其结构与碱性关系,讨论这些试剂与金属离子螯合的可能位置,其结果和实验基本一致。计算分子构型所用TAP骨架取由文献,甲基用标准构型。原子编号见图1,计算在IBM PC/AT微机上完成。     

Several new types of bounded wave solutions for the generalized two-component Camassa–Holm equation

Li and Qiao studied the bifurcations and exact traveling wave solutions for the generalized two-component Camassa–Holm equation $$\begin{aligned} \left\{ \begin{array}{l} m_{t}+\sigma um_{x}-Au_{x}+2m \sigma u_{x}+3(1-\sigma )uu_{x}\\ \quad +\rho \rho _{x}=0, \\ \rho _{t} +(\rho u)_{x}=0, \end{array} \right. \end{aligned}$$ \(m=u-u_{xx}, A>0\) . They showed that there exist solitary wave solutions, cusp wave solutions, and periodic wave solutions for the equation, and their analysis focused on the bifurcations when \(\sigma >0\) . In this paper, we first complement the bifurcations when \(\sigma <0\) by following the same procedure as that of Li, and then show the existence and implicit expressions of several new types of bounded wave solutions, including solitary waves, periodic waves, compacton-like waves, and kink-like waves. In addition, the numerical simulations of the bounded wave solutions are given to show the correctness of our results.