Recognition of the Finite Simple Groups F 4(2m) by Spectrum

The spectrum of a finite group is the set of its element orders. A finite group G is said to be recognizable by spectrum, if every finite group with the same spectrum as G is isomorphic to G. The purpose of the paper is to prove that for every natural m the finite simple Chevalley group F ₄(2 ^m ) is recognizable by spectrum.     

Transmission of a Gaussian beam after incidenting nonnormally on a Fabry–Perot etalon: a nonresonant case

Under the nonresonant case where the carrier frequency of a Gaussian beam deviates from the resonant frequency of a Fabry–Perot etalon, the transmission of a Gaussian beam after incidenting nonnormally on a Fabry–Perot etalon has been investigated. The results show that under the nonresonant case, variations of the peak intensity, the position of the peak intensity and the spot size of the transmitted beam with the input angle behave differently and even with a reversed tendency compared with those obtained under the resonant case.     

平面交叉玻璃波导型微透镜阵列光学性能研究

介绍了平面交叉玻璃光波导型半球形微透镜阵列的制作方法.利用积分形式的光线方程式讨论了半球形微透镜的光学特性,得到了半球形微透镜的光线轨迹方程式和焦距表示式,理论结果与实验数据是一致的.     

Bifurcations of Invariant Tori and Subharmonic Solutions of Singularly Perturbed System

This paper deals with bifurcations of subharmonic solutions and invariant tori generated from limit cycles in the fast dynamics for a nonautonomous singularly perturbed system. Based on Poincare map, a series of blow-up transformations and the theory of integral manifold, the conditions for the existence of invariant tori are obtained, and the saddle-node bifurcations of subharmonic solutions are studied.     

Partially Strictly Monotone and Nonlinear Penalty Functions for Constrained Mathematical Programs

We introduce the concept of partially strictly monotone functions and apply it to construct a class of nonlinear penalty functions for a constrained optimization problem. This class of nonlinear penalty functions includes some (nonlinear) penalty functions currently used in the literature as special cases. Assuming that the perturbation function is lower semi-continuous, we prove that the sequence of optimal values of nonlinear penalty problems converges to that of the original constrained optimization problem. First-order and second-order necessary optimality conditions of nonlinear penalty problems are derived by converting the optimality of penalty problems into that of a smooth constrained vector optimization problem. This approach allows for a concise derivation of optimality conditions of nonlinear penalty problems. Finally, we prove that each limit point of the second-order stationary points of the nonlinear penalty problems is a second-order stationary point of the original constrained optimization problem.     

强预不变凸函数的充要条件

本文讨论了强预不变凸函数与预不变凸函数、严格预不变凸函数及半严格预不变凸函数之间的关系,得到它的三个充要条件：(i)在一定条件下,f是强预不变凸函数的充分必要条件是f是预不变凸函数且f满足中间点强预不变凸性；(ii)在一定条件下,f是强预不变凸函数的充分必要条件是f是严格预不变凸函数且f满足中间点强预不变凸性；(iii)在一定条件下,f是强预不变凸函数的充分必要条件是f是半严格预不变凸函数且f满足中间点强预不变凸性．     

A Highly Sensitive Spectrophotometric Assay of Bleomycins Based on the Fading Reaction of Some Halofluorescein Dyes

In weak acidic medium, anticancer antibiotics bleomycin A5 （BLMA5） and bleomycin A2 （BLMA2） can react with halofluorescein dyes such as erythrosin （Ery）, eosin Y （EY）, eosin B （EB） and rose bengal （RB） by virtue of electrostatic attraction and hydrophobic force to form the ion-association complexes, which can result in the fading reactions of four halofluorescein dyes. The maximum fading wavelengths of these four dyes were located at 527 nm for Ery, 515 nm for EY, 517 nm for EB and 546 nm for RB, respectively. The decrements of absorbance （AA） were directly proportional to the concentrations of bleomycin in a certain range. A new method for the determination of bleomycins anticancer drugs based on fading reactions of halofluorescein dyes has been developed. The method was not only highly sensitive but also simple and rapid. The molar absorptivities （ε） ranged from 1.5 × 10^5 to 7.5 × 10^5 L·mol^-1·cm^-1. It was applied to determination of the bleomycins in human serum, urine and rabbit serum samples. In this work, the spectral properties and the optimum reaction conditions were investigated. The structure of ion-association complexes and the reaction mechanism were discussed.     

放热型金属合金化对钒基贮氢材料性能影响的理论研究

利用电荷自洽离散变分Xα(SCC-DV-Xα)方法计算了放热型金属合金化对钒基贮氢材料性能的影响。研究结果表明:在钒氢化物V₆₃H₆₄中加入放热型金属后，钒原子的净电荷都减少，而氢原子的净电荷既有增加又有减少，加入Ti、Ca以后，H原子的净电荷减少，而加入Mg、Zr以后，H原子的净电荷增加。研究还表明放热型金属合金化以后，V4s轨道电子态密度峰发生分裂，与H1s和H2s轨道电子态密度重叠程度增大，V-H之间相互作用增强;差分电荷密度还表明M-H之间也有较强的相互作用。Mg合金化导致氢化物V₅₁M₁₂H₆₄的费米能增加，氢化物稳定性减弱;Ca、Ti、Zr合金化导致氢化物V₅₁M₁₂H₆₄的费米能减少，氢化物更稳定。     

Determination of medecamycin by adsorptive stripping voltammetry with an activated electrode

The adsorptive and electrochemical behaviors of medecamycin were investigated on a glassy carbon electrode (GCE) pretreated by anodic oxidation at +1.8 V for 5 min in 0.025 mol l^–1 NH₃-NH₄Cl (pH 8.6) solution. An adsorptive stripping voltammetric method for the determination of medecamycin at the pretreated glassy carbon electrode has been developed. Medecamycin was accumulated in NH₃-NH₄Cl buffer (pH 9.0) at a potential of –0.7 V (vs. saturated calomel electrode (SCE)) for a certain time, and then determined by second-order differential anodic stripping voltammetry. The second-order differential anodic stripping peak current at +0.72 V was proportional to the concentration of medecamycin in the range 2.0 g ml^–1 to 50.0 g ml^–1. The detection limit (three times the signal-to-noise) was 1.0 g ml^–1 and the relative standard deviation of the results was 3.28% for eight successive determinations of 10.0 g ml^–1 medecamycin. This method has been applied to the direct determination of medecamycin in commercial tablets and spiked urine samples with satisfactory results.     

Electrochemical characteristics of a platinum electrode modified with a matrix of polyvinyl butyral and colloidal Ag containing immobilized horseradish peroxidase

A new hydrogen peroxide biosensor was constructed, which consisted of a platinum electrode modified by a matrix of polyvinyl butyral (PVB) and nanometer-sized Ag colloid containing immobilized horseradish peroxidase (HRP), and using Co(bpy)₃³⁺ as mediator in the hydrogen peroxide solution. The electrochemical characteristics of the biosensor were studied by cyclic voltammetry and chronoamperometry. The modified process was characterized by electrochemical impedance spectroscopy and cyclic voltammetry. The HRP immobilized on colloidal Ag was stable and retained its biological activity. The sensor displays excellent electrocatalytic response to the reduction of H₂O₂. Analytical parameters such as pH and temperature were also studied. Linear calibration for H₂O₂ was obtained in the range of 1×10^–5 to 1×10^–2 M under optimized conditions. The sensor was highly sensitive to H₂O₂, with a detection limit of 2×10^–6 M, and the sensor achieved 95% of steady-state current within 10 s. The sensor exhibited high sensitivity, selectivity and stability.