On condition numbers for Moore–Penrose inverse and linear least squares problem involving Kronecker products

In this paper, we investigate the normwise, mixed, and componentwise condition numbers and their upper bounds for the Moore–Penrose inverse of the Kronecker product and more general matrix function compositions involving Kronecker products. We also present the condition numbers and their upper bounds for the associated Kronecker product linear least squares solution with full column rank. In practice, the derived upper bounds for the mixed and componentwise condition numbers for Kronecker product linear least squares solution can be efficiently estimated using the Hager–Higham Algorithm. Copyright © 2012 John Wiley & Sons, Ltd.     

Fluorescence energy transfer-based multiplexed hybridization assay using gold nanoparticles and quantum dot conjugates on photonic crystal beads

A multiplexed assay strategy was developed for the detection of nucleic acid hybridization. It is based on fluorescence resonance energy transfer (FRET) between gold nanoparticles (AuNPs) and multi-sized quantum dots (QDs) deposited on the surface of silica photonic crystal beads (SPCBs). The SPCBs were first coated with a three-layer primer film formed by the alternating adsorption of poly(allylamine hydrochloride) and poly(sodium 4-styrensulfonate). Probe DNA sequences were then covalently attached to the carboxy groups at the surface of the QD-coated SPCBs. On addition of DNA-AuNPs and hybridization, the fluorescence of the donor QDs is quenched because of the close proximity of the AuNPs. However, the addition of target DNA causes a recovery of the fluorescence of the QD-coated SPCBs, thus enabling the quantitative assay of hybridized DNA. Compared to fluorescent dyes acting as acceptors, the use of AuNPs results in much higher quenching efficiency. The multiplexed assay displays a wide linear range, high sensitivity, and very little cross-reactivity. This work, where such SPCBs are used for the first time in a FRET assay, is deemed to present a new and viable approach towards high-throughput multiplexed gene assays.

基于全息液晶/聚合物光栅的分布反馈式激光器的波长调谐特性研究

首先制备了不同周期的染料掺杂全息液晶/聚合物光栅并进行激光抽运实验, 得到了激光器的调谐曲线,确定了激光器在574 nm到685 nm的谱带里均可以实现激光输出, 即激光器具有110 nm左右的可调谐范围. 之后, 通过温控仪控制样品的温度, 对周期为610 nm的染料掺杂全息液晶/聚合物光栅进行激光抽运, 探测不同温度下的输出激光光谱, 观察到随着温度由20℃升高到65℃, 激光器的中心波长由627.9 nm减小到623 nm, 产生了4.9 nm的波长蓝移.     

A general transformation class of semiparametric cure rate frailty models

We consider a class of cure rate frailty models for multivariate failure time data with a survival fraction. This class is formulated through a transformation on the unknown population survival function. It incorporates random effects to account for the underlying correlation, and includes the mixture cure model and the proportional hazards cure model as two special cases. We develop efficient likelihood-based estimation and inference procedures. We show that the nonparametric maximum likelihood estimators for the parameters of these models are consistent and asymptotically normal, and that the limiting variances achieve the semiparametric efficiency bounds. Simulation studies demonstrate that the proposed methods perform well in finite samples. We provide an application of the proposed methods to the data of the age at onset of alcohol dependence, from the Collaborative Study on the Genetics of Alcoholism.     

Equivalence of the Wei potential model and Tietz potential model for diatomic molecules

By employing the dissociation energy and the equilibrium bond length for a diatomic molecule as explicit parameters, we generate improved expressions for the well-known Rosen-Morse, Manning-Rosen, Tietz, and Frost-Musulin potential energy functions. It is found that the well-known Tietz potential function that is conventionally defined in terms of five parameters [T. Tietz, J. Chem. Phys. 38, 3036 (1963)] actually only has four independent parameters. It is shown exactly that the Wei [Phys. Rev. A 42, 2524 (1990)] and the well-known Tietz potential functions are the same solvable empirical function. When the parameter h in the Tietz potential function has the values 0, +1, and -1, the Tietz potential becomes the standard Morse, Rosen-Morse, and Manning-Rosen potentials, respectively.     

A DFT Study on the Selective Extraction of Metallic Ions by 12-Crown-4

In order to predict the extraction ability of 12-crown-4 for different metallic ions, the complexes [M(12-crown-4)] and [M(H₂O)₄] (where M=Li⁺, Na⁺, K⁺, Be²⁺, Mg²⁺, Ca²⁺, Cu²⁺ and Zn²⁺) were investigated by the density functional theory without restrictions for their geometry. The metal binding capability was evaluated using the binding energy, and the effect of nature of the metal on the binding properties was also studied. The results of the calculations showed that the coordination ability of a donor molecule towards different metal ions increased in proportion to their ionization potential. In addition, based on the extraction distribution coefficient, we found that 12-crown-4 can selectively extract Cu²⁺ and Be²⁺ ions from aqueous solutions of mixed cations. Obviously, the stability of complexes and the extraction power of extractants depend greatly on the nature of the metal ions. Calculation results from our study could be used to predict the extraction power of this crown ether and could play a guiding role in planning experiments.     

Electrochemical noise analysis of the effects of a magnetic field on cathodic hydrogen evolution

The effect of a static magnetic field on the evolution of hydrogen gas from a small platinum electrode in an aqueous electrolyte has been studied by recording the noise spectrum of overpotential voltage fluctuations at a constant current density of ?50 mA mm^?2. A 1/f² variation of the power spectrum characteristic of droplet coalescence is found for frequencies >10 Hz. The overpotential for hydrogen evolution decreases with applied field. When the production of gas bubbles is quasiperiodic, there is a threshold field of 0.5 T beyond which the size of the bubbles released is approximately doubled. This is explained by enhanced coalescence of small bubbles swept across the electrode surface by forced convection due to the Lorentz force.     

A novel threefold‐interpenetrating primitive cubic network based on a dinuclear Zn2 node

In the mixed‐ligand metal–organic polymeric compound poly[[μ₂‐1,4‐bis(imidazol‐1‐yl)benzene](μ₂‐terephthalato)dizinc(II)], [Zn₂(C₈H₄O₄)₂(C₁₂H₁₀N₄)]_n or [Zn₂(bdc)₂(bib)]_n [H₂bdc is terephthalic acid and bib is 1,4‐bis(imidazol‐1‐yl)benzene], the asymmetric unit contains one Zn^II ion, with two half bdc anions and one half bib molecule lying around inversion centers. The Zn^II ion is in a slightly distorted tetrahedral environment, coordinated by three carboxylate O atoms from three different bdc anions and by one bib N atom. The crystal structure is constructed from the secondary building unit (SBU) [Zn₂(CO₂)₂N₂O₂], in which the two metal centers are held together by two bdc linkers with bis(syn,syn‐bridging bidentate) bonding modes. The SBU is connected by bdc bridges to form a two‐dimensional grid‐like (4,4)‐layer, which is further pillared by the bib ligand. Topologically, the dinuclear SBU can be considered to be a six‐connected node, and the extended structure exhibits an elongated primitive approximately cubic framework. The three‐dimensional framework possesses a large cavity with dimensions of approximately 10 × 13 × 17 Å in cross‐section. The potential porosity is filled with mutual interpenetration of two identical equivalent frameworks, generating a novel threefold interpenetrating network with an α‐polonium topology [Abrahams, Hoskins, Robson & Slizys (2002). CrystEngComm, 4 , 478–482].     

氧原子在Pt低指数面上的吸附和振动

应用原子和表面簇合物相互作用的5参数Morse势方法（简称5-MP）对O-Pt低指数表面体系进行了研究,并获得了全部临界点特性.计算结果表明,氧原子在Pt(100)面上只存在四重吸附态.在缺行重构的(110)面上,氧原子仍吸附于三重位,随着覆盖度的增加还会嵌切吸附于长桥位;通过分析三重态振动指纹性质的遗传和遗变,确认实验观察到的59.49和40.90 meV损失谱分别为氧原子在三重位和长桥位吸附态的表面垂直振动.     

Lanthanide-ion-tuned magnetic properties in a series of three-dimensional cyano-bridged Ln(III)W(V) assemblies

The reaction of [W(CN)(8)](3-) with Ln(3+) and pyrazine in acetonitrile yielded a series of isostructural compounds formulated as Ln(H(2)O)(4)(pyrazine)(0.5)W(CN)(8) (Ln = La(1), Ce(2), Pr(3), Nd(4), Sm(5), Eu(6), Gd(7)). The Ln(iii) and W(v) centers in the structure are linked through cyanide groups to form two-dimensional (2D) layers, which are further pillared by pyrazine, generating 3D frameworks. The magnetic behavior for compounds 1-7 were driven by the lanthanide ions involved. The Ln(iii) and W(v) ions in compounds 2 and 5 are ferromagnetically coupled with magnetic ordering occurring at 2.8 K, comparable with magnetic ordering with the critical temperature of 1.9 K for compound 4. In addition, the antiferromagnetic interactions were observed in compounds 3 and 7, while no significant magnetic couplings were found in compounds 1 and 6.