A protocol for the measurement of all the parameters of the mass transfer kinetics in columns used in liquid chromatography

Band broadening in chromatography results from the combination of the dispersive effects that are associated with the different steps involved in the migration of compound bands along the column. These steps include longitudinal diffusion, trans-particle mass transfer, external film mass transfer, overall eddy diffusion, including trans-column, short-range inter-channel, trans-channel eddy diffusion, and the possible, additional mass transfer contributions arising from heat friction and the thermal heterogeneity of the column. We describe a series of experiments that provide the data needed to determine the coefficients of the contributions to band broadening of each one of these individual mass transfer steps. This specifically designed protocol can provide key information regarding the kinetic performance of columns used in liquid chromatography and explain why different columns behave so differently. The limitations, accuracy and precision of these methods are discussed. Further avenues of research that could improve the characterization of the mass transfer mechanisms in chromatographic columns, possibly contributing to the development of better columns, are suggested.     

Statistical models in assessing fold change of gene expression in real-time RT-PCR experiments

Real-time RT-PCR has been frequently used in quantitative research in molecular biology and bioinformatics. It provides remarkably useful technology to assess expression of genes. Although mathematical models for gene amplification process have been studied, statistical models and methods for data analysis in real-time RT-PCR have received little attention. In this paper, we briefly introduce current mathematical models, and study statistical models for real-time RT-PCR data. We propose a generalized estimation equations (GEE) model that properly reflects the structure of repeated data in RT-PCR experiments for both cross-sectional and longitudinal data. The GEE model takes the correlation between observations within the same subjects into consideration, and prevents from producing false positives or false negatives. We further demonstrate with a set of actual real-time RT-PCR data that different statistical models yield different estimations of fold change and confidence interval. The SAS program for data analysis using the GEE model is provided to facilitate easy computation for non-statistical professionals.     

Longitudinal diffusion behavior of hemicyanine dyes across phospholipid vesicle membranes as studied by second-harmonic generation and fluorescence spectroscopies

The adsorption and longitudinal diffusion behaviors of a series of hemicyanine dyes to phospholipid vesicle membranes were studied by second-harmonic generation (SHG) and fluorescence spectroscopies. It was observed that the longitudinal diffusion of cationic hemicyanine dyes takes place immediately after the initial adsorption of these dyes to the outer surface of the vesicle membrane. In contrast, hardly any amount of a zwitterionic hemicyanine dye with a sulfonate group diffused across the vesicle membrane within the measurement time (<2000 s). Based on the difference in the time-course responses of SHG and fluorescence spectroscopies for all of the hemicyanine dyes tested, we propose that hydration of the sulfonate group is mainly responsible for the low diffusivity of the zwitterionic hemicyanine dye.     

The critical properties of magnetic films

Within the framework of the transverse Ising model and by using the effective field theory with a probability distribution technique that accounts for the self spin correlations, we have studied the critical properties of an L-layer film of simple cubic symmetry in which the exchanges strength are assumed to be different from the bulk values in N_S surface layers. We derive and illustrate the expressions for the phase diagrams, order parameter profiles and susceptibility. In such films, the critical temperature can shift to either lower or higher temperature compared with the corresponding bulk value. We calculate also some magnetic properties of the film, such as the layer magnetizations, their averages and their profiles and the longitudinal susceptibility of the film. The film longitudinal susceptibility still diverges at the film critical temperature as does the bulk longitudinal susceptibility.     

Pulsatile flow of Herschel–Bulkley fluid through catheterized arteries – A mathematical model

The pulsatile flow of blood through catheterized artery has been studied in this paper by modeling blood as Herschel–Bulkley fluid and the catheter and artery as rigid coaxial circular cylinders. The Herschel–Bulkley fluid has two parameters, the yield stress θ and the power index n. Perturbation method is used to solve the resulting quasi-steady nonlinear coupled implicit system of differential equations. The effects of catheterization and non-Newtonian nature of blood on yield plane locations, velocity, flow rate, wall shear stress and longitudinal impedance of the artery are discussed. The existence of two yield plane locations is investigated and their dependence on yield stress θ, amplitude A, and time t are analyzed. The width of the plug core region increases with increasing value of yield stress at any time. The velocity and flow rate decrease, whereas wall shear stress and longitudinal impedance increase for increasing value of yield stress with other parameters held fixed. On the other hand, the velocity, flow rate and wall shear stress decrease but resistance to flow increases as the catheter radius ratio (ratio of catheter radius to vessel radius) increases with other parameters fixed. The results for power law fluid, Newtonian fluid and Bingham fluid are obtained as special cases from this model.     

Theoretical and experimental study of a laser-diode-pumped actively Q-switched Nd:YVO4 laser with acoustic–optic modulator

By considering the Gaussian spatial distribution of the intracavity photon density and initial population-inversion density as well as the longitudinal distribution of the photon density along the cavity axis and turnoff time of the acoustic–optic Q-switch, the coupled equations of an LD-pumped actively Q-switched Nd:YVO₄ laser with acoustic–optic modulator are given. These coupled rate equations are solved numerically on a computer, and the dependences of pulse width, single-pulse energy and peak power on incident pump power are obtained. In the experiment, a laser-diode-pumped actively Q-switched Nd:YVO₄ laser with acoustic–optic modulator is realized, and the experimental results are in fair agreement with the numerical solutions.     

A dependent frequency–severity approach to modeling longitudinal insurance claims

In nonlife insurance, frequency and severity are two essential building blocks in the actuarial modeling of insurance claims. In this paper, we propose a dependent modeling framework to jointly examine the two components in a longitudinal context where the quantity of interest is the predictive distribution. The proposed model accommodates the temporal correlation in both the frequency and the severity, as well as the association between the frequency and severity using a novel copula regression. The resulting predictive claims distribution allows to incorporate the claim history on both the frequency and severity into ratemaking and other prediction applications. In this application, we examine the insurance claim frequencies and severities for specific peril types from a government property insurance portfolio, namely lightning and vehicle claims, which tend to be frequent in terms of their count. We discover that the frequencies and severities of these frequent peril types tend to have a high serial correlation over time. Using dependence modeling in a longitudinal setting, we demonstrate how the prediction of these frequent claims can be improved.     

How students structure their investigations and learn mathematics: insights from a long-term study

This paper reports on the mathematical thinking of participants of a long-term study, now in its 17th year, who did mathematics together through their public school and early university years. In particular, it describes how fundamental ideas and images of a cohort group of students are elaborated and presented in symbolic expressions of generalized mathematical ideas while exploring problems in grades 10 and 11. From high school and university interview data, we learn from participants how they viewed their mathematical activity in structuring their investigations and justifying their solutions.     

宽带宽波束纵向水声换能器研究

本文通过设计纵向水声换能器辐射头的形状及利用其弯曲振动模,实现宽带宽波束辐射特性,采用后质量块的嵌套结构有效缩小了换能器的长度。利用ANSYS有限元软件模拟了小型宽带宽波束纵向水声换能器的电声特性。研制了换能器样品,实现了与有限元模拟计算结果相一致的电声参数:谐振频率14kHz,最大发射电压响应141．9dB,-3dB带宽为11．3～18．7kHz,-3dB带通Q值为1．9,在14kHz频率下波束宽度为132°,比通常纵向换能器波束宽度宽23％。     

包含辐射阻尼效应的束流纵向微波不稳定性研究

 包含束团辐射阻尼效应的Fokker-Planck方程是比较完备地描述粒子运动状态的束团分布方程。在Fokker-Planck方程的基础上采用微扰展开方法对纵向微波不稳定性的发生机制及过程进行了分析，并且根据计算结果，研究了辐射阻尼效应对纵向微波不稳定性的影响。在计算中包含了静态的势阱畸变效应。计算结果表明，包含辐射阻尼效应的纵向微波不稳定性阈值高于没有辐射阻尼效应的不稳定性阈值。