A cascadic multigrid method for a kind of semilinear elliptic problem

In this paper, we analyze a cascadic multigrid method for semilinear elliptic problems in which the derivative of the semilinear term is Hölder continuous. We first investigate the standard finite element error estimates of this kind of problem. We then solve the corresponding discrete problems using the cascadic multigrid method. We prove that the algorithm has an optimal order of convergence in energy norm and quasi-optimal computational complexity. We also report some numerical results to support the theory.     

On optimizing edge connectivity of product graphs

This work studies the super edge connectivity and super restricted edge connectivity of direct product graphs, Cartesian product graphs, strong product graphs and lexicographic product graphs. As a result, sufficient conditions for optimizing the edge connectivity and restricted edge connectivity of these graphs are presented.     

A hybrid trust region algorithm for unconstrained optimization

This paper presents a hybrid trust region algorithm for unconstrained optimization problems. It can be regarded as a combination of ODE-based methods, line search and trust region techniques. A feature of the proposed method is that at each iteration, a system of linear equations is solved only once to obtain a trial step. Further, when the trial step is not accepted, the method performs an inexact line search along it instead of resolving a new linear system. Under reasonable assumptions, the algorithm is proven to be globally and superlinearly convergent. Numerical results are also reported that show the efficiency of this proposed method.     

Microfluidic chip electrophoresis for biochemical analysis

Microfluidic chip electrophoresis has been widely employed for separation of various biochemical species owing to its advantages of low sample consumption, low cost, fast analysis, high throughput, and integration capability. In this article, we reviewed the development of four different modes of microfluidics‐based electrophoresis technologies including capillary electrophoresis, gel electrophoresis, dielectrophoresis, and field (electric) flow fractionation. Coupling detection schemes on microfluidic electrophoresis platform were also reviewed such as optical, electrochemical, and mass spectrometry method. We further discussed the innovative applications of microfluidic electrophoresis for biomacromolecules (nucleic acids and proteins), biochemical small molecules (amino acids, metabolites, ions, etc.), and bioparticles (cells and pathogens) analysis. The future direction of microfluidic chip electrophoresis was predicted.     

Beam propagation factor of radial Gaussian-Schell model beam array in non-Kolmogorov turbulence

The analytical expression for the beam propagation factor (M²-factor) of a radial Gaussian-Schell model (GSM) beam array propagating in non-Kolmogorov turbulence is derived. The influences of beam number, ring radius and generalized exponent on the M²-factor are investigated. The results indicate that the M²-factor has great dependence on the generalized exponent and the beam number. Moreover, there is an optimum ring radius, which leads to a minimum M²-factor and increases with increase in beam number. Further, the M²-factor for the superposition of the intensity is larger than that for the superposition of the cross-spectral density function (CSDF). However, the M²-factor for the superposition of the intensity is less sensitive to the turbulence than that for the superposition of the CSDF.     

Calibration of a multiple axes 3-D laser scanning system consisting of robot, portable laser scanner and turntable

A multiple axes 3-D laser scanning system consisting of a portable 3-D laser scanner, a industrial robot and a turntable is demonstrated. By using a criterion sphere, a robot tool center point (TCP) calibration approach is proposed to calibrate the relation between the laser 3-D scanner and the robot end-effector. In this approach, two different translational motions of robot are first made to determine the rotation part, and then at least three different rotational motions are made to determine the translation part. Meanwhile, by using the criterion sphere, a turntable approach is proposed to calibrate the pose of the turntable relative to the robot. In this approach, several rotational angles of turntable and two different heights of the sphere are made to determine the rotational axis of turntable. Experiment is performed on a portable laser scanner mounted on an industrial robot ABB IRB4400 with a turntable. The experiment results show that the two proposed calibration algorithms are stable and flexible. The application of 3-D measurement is also given to demonstrate the effectiveness and stability of the multiple axes 3-D laser scanning system.     

拉盖尔-高斯光束在界面反射和折射的质心偏移特性研究

在圆柱坐标系中研究了傍轴线偏振拉盖尔-高斯光束在两种各向同性介质界面反射和折射后光强质心的偏移. 基于菲涅耳近似和泰勒级数展开,分别得到了部分反射和全反射两种情形下,质心的横向偏移和纵向偏移与光束拓扑荷的解析关系式. 研究表明,部分反射时,反射和折射光束的横向偏移的大小与光束的拓扑荷成正比,方向由拓扑荷的符号决定;而纵向偏移仅仅大小与光束的拓扑荷有关. 全反射时,反射光束质心偏移不受拓扑荷影响. 通过数值模拟验证了解析结果的正确性,并得到了解析公式的适用条件. 拉盖尔-高斯光束的质心偏移特性可应用于测量光 关键词： 拉盖尔-高斯光束 横向偏移 纵向偏移 拓扑荷     

LC–MS–MS Method to Simultaneously Determine Six Probe Drugs for CYP450 Isozymes in Human Liver Microsomes

Here, we report a rapid and specific method based on high-performance liquid chromatography coupled with tandem mass spectrometry (LC–MS–MS) capable of quantifying six CYP450-specific probe substrates in human liver microsomal incubation mixtures simultaneously. These analytes were prepared by single-step extraction and detected in one run by switching polarity of electrospray ionization mode three times. Following optimization of the chromatographic conditions, the peaks were well separated, and retention times ranged between 2.0 and 8.4 min. The total run time for a single injection was within 9 min. This method was fully validated over linear range of 18.8–3,000.0 ng mL^?1 for diclofenac, 0.8–3,000.0 ng mL^?1 for dapson, 1.5–3,000.0 ng mL^?1 for dextromethorphan, 2.0–4,000.0 ng mL^?1 for omeprazole, 75.0–3,000.0 ng mL^?1 for chlorzoxazone and 0.8–3,000.0 ng mL^?1 for phenacetin using diazepam as internal standard. Samples were prepared by protein precipitation and analyzed on the LC–MS–MS equipped with ESI interface. For each analyte, inter- and intra-day precision (RSD%) were <15 % and accuracy was within 85–115 %. The specificity, precision, accuracy, stabilities and matrix effect were evaluated.     

Incompressible limits of the Navier-Stokes equations for all time

We study the asymptotic behaviors of the regular solutions to the compressible Navier-Stokes equations for “well-prepared” initial data for all time as the Mach number tends to zero, by deriving a differential inequality with certain decay property. The estimates obtained in this paper are uniform both in time and Mach number.     

碘-淀粉光度法测定水中溶解氧含量

根据碘与淀粉反应生成蓝色络合物以及此络合物在574 nm波长处有吸收峰,提出了水样中溶解氧的光度测定法.为固定样品中的溶解氧,于碱性介质中加入硫酸锰与之形成三氧化二锰沉淀物.测定时加入硫酸使与沉淀物反应而释出所固定的氧,并立即与同时由溶液中已加入的碘化钾与硫酸反应而释出碘而使溶液中呈现蓝色.用光度法在574 nm波长处测得其吸光度.从由碘酸钾标准溶液作为溶解氧标准所制作的标准曲线上查得试样中溶解氧的含量,对显色的条件作了系统试验并选定了优化的反应条件,溶解氧的质量浓度在0.027～0.80 mg·L-1之间符合比耳定律.取3种不同来源的水样按此方法测定其溶解氧含量,所得结果与碘量法及溶解氧测定仪所测得的结果相符.