Analysis of a viral disease model with saturated contact rate

A viral disease model with saturated contact rate is introduced and investigated. The model consists a host species, which is divided into two classes the susceptible and infected, and a virus, which causes a viral disease in the host and as the host induces, the infected releases more virus into the environment. Taking the virus replication rate as the bifurcating parameter, we prove that there exists a threshold value beyond which the endemic equilibrium bifurcates from the free disease one. Further increasing the value, the endemic equilibrium loses its stability, Hopf bifurcation occurs and a periodic solution arises from it. The orbital stability of the periodic orbits is analyzed by applying Poore’s condition. In the last, numerical simulation of the model is employed to explain the mathematical results of this paper.     

Solution dependence on initial conditions in differential variational inequalities

In the first part of this paper, we establish several sensitivity results of the solution x(t, ξ) to the ordinary differential equation (ODE) initial-value problem (IVP) dx/dt = f(x), x(0) =  ξ as a function of the initial value ξ for a nondifferentiable f(x). Specifically, we show that for $\Xi_T \equiv \{\,x(t,\xi^0): 0 \leq t \leq T\,\}$ , (a) if f is “B-differentiable” on $\Xi_T$ , then so is the solution operator x(t;·) at ξ⁰; (b) if f is “semismooth” on $\Xi_T$ , then so is x(t;·) at ξ⁰; (c) if f has a “linear Newton approximation” on $\Xi_T$ , then so does x(t;·) at ξ⁰; moreover, the linear Newton approximation of the solution operator can be obtained from the solution of a “linear” differential inclusion. In the second part of the paper, we apply these ODE sensitivity results to a differential variational inequality (DVI) and discuss (a) the existence, uniqueness, and Lipschitz dependence of solutions to subclasses of the DVI subject to boundary conditions, via an implicit function theorem for semismooth equations, and (b) the convergence of a “nonsmooth shooting method” for numerically computing such boundary-value solutions.     

Approximations of Nash equilibria

Inspired by previous works on approximations of optimization problems and recent papers on the approximation of Walrasian and Nash equilibria and on stochastic variational inequalities, the present paper investigates the approximation of Nash equilibria and clarifies the conditions required for the convergence of the approximate equilibria via a direct approach, a variational approach, and an optimization approach. Besides directly addressing the issue of convergence of Nash equilibria via approximation, our investigation leads to a deeper understanding of various notions of functional convergence and their interconnections; more importantly, the investigation yields improved conditions for convergence of the approximate Nash equilibria via the variational approach. An illustrative application of our results to the approximation of a Nash equilibrium in a competitive capacity expansion model under uncertainty is presented.     

Trace determination of dichlorodiphenyltrichloroethane and its main metabolites in environmental water samples with dispersive liquid–liquid microextraction in combination with high performance liquid chromatography and ultraviolet detector

Dichlorodiphenyltrichloroethane,1,1,1-trichloro-2,2-bis(p-chlorophenyl)ethane (DDT) and its main metabolites have been paid much more attention, and present paper describes a new process for the rapid determination of such pollutants in environmental water samples based on dispersive liquid–liquid microextraction (DLLME) and high performance liquid chromatography with ultraviolet detector, which has merits such as high enrichment factor and sensitivity, low cost and easy to operate. Significant parameters such as extraction solvent and dispersive solvent type and volume, pH, extraction time and centrifuging time, which would have important impact on the enrichment of target pollutants, have been investigated in detail. The results exhibited that excellent performance could be achieved with carbon tetrachloride and acetonitrile as the extraction solvent and dispersive solvent, respectively. Under the optimal conditions, excellent linear relationship was gained in the range of 1.0–50 μg L⁻¹, and detection limits were in the range of 0.32–0.51 μg L⁻¹. The precisions of the proposed method were in the range of 2.80–7.50% (RSD). The proposed method was validated with real water samples, and the results indicated the spiked recoveries were in the range of 85.58–119.6% and the established method was very good and competitive in the determination of DDT and its metabolites.     

Pt adsorption on the PbTiO3(110) polar surface: a density functional theory study

The monolayer (ML) and submonolayer Pt on both terminations of PbTiO₃(110) polar surface have been studied by using density functional theory (DFT) with projector‐augmented wave(PAW) potential and a supercell approach. The most favored ML Pt arrangements on PbTiO and O₂ terminations are the hollow site and the short‐bridge site, respectively. By examining the geometries of different ML arrangements, we know that the dominant impetus for stability of the favored adsorption site for PbTiO termination is the Pt–Ti interaction (mainly from covalent bonding), while that for O₂ termination is the Pt–O interaction (mainly from ionic bonding). In addition, the appearance of the gap electronic states in the outermost layers of each termination indicates that a channel for charge transfer between adsorbed layer and substrate is formed. Moreover, the interface hybridization between Pt 5d and O 2p orbitals is also observed, especially for ML Pt on O₂ termination. The stability sequences for various arrangements of 1/2 ML Pt adsorption conform well with those of ML Pt adsorption, and the most stable arrangement is energetically more favorable than the corresponding ML coverage in the view of adsorption energy maximization. The behavior, i.e. the increase in adsorption energy with decrease in coverage, indicates that Pt? Pt interactions weaken those between Pt and the substrate. Copyright © 2009 John Wiley & Sons, Ltd.     

Determination of molecular weight of polyethylene glycol using size-exclusion chromatography with multi-angle laser light scattering and acid–base titration

Size-exclusion chromatography with multi-angle laser light scattering (SEC-MALLS) and acid–base titration were used to determine the molecular weight of a polyethylene glycol with low molecular weight. All potential uncertainty factors for each measurement were evaluated using cause-effect diagrams. Weight analysis was applied to harmonize the two different measurement results. It was found that the main uncertainty sources of SEC-MALLS measurement arose from the dn/dc value, the calibration constant of the differential refractive index (DRI) detector, and the intermediate precision of the instrument, while the sample mass, the titration volume and the concentration of titrant contributed to the uncertainty of titration measurement. The weighted mean value of the two measurement results was taken as the molecular weight of the polyethylene glycol.     

羟基磷灰石/离子液体混合膜修饰电极的制备及其应用于水中痕量镉离子的高选择性测定

利用溴代十六烷基三甲基铵(CTAB)为模板, 合成制备了棒状羟基磷灰石颗粒, 并以SEM, XRD, IR等手段进行了表征. 用制备的羟基磷灰石与自制的离子液体([BMIM]PF6)充分混合涂覆在玻碳电极表面制备了羟基磷灰石/离子液体修饰电极, 研究了镉离子在该修饰电极上的富集和电化学行为. 结果发现, 羟基磷灰石对镉离子有较好的富集作用, 而离子液体则可以在开路条件下使镉离子还原为金属镉, 氧化扫描时可以得到镉的灵敏氧化溶出峰, 以此为基础建立了一种高选择性地测定痕量镉离子的新方法, 该方法可以较好地避免铅、汞、银等重金属离子的干扰, 对镉离子检出限可达2.0×10－8 mol•L－1, 在4.0×10－8～2.2×10－7 mol•L－1的浓度范围内, 氧化溶出峰电流与Cd(II)的浓度呈良好的线性关系. 该研究有望在环境检测和环境治理方面发挥重要作用.     

Construction of a universal model for non-invasive identification of cephalosporins for injection using near-infrared diffuse reflectance spectroscopy

A universal classification model has been developed for identification of 26 different products of cephalosporins for injection using near-infrared (NIR) spectroscopy. A total of 324 batches of the 26 products, from 166 manufacturers in China, were used in the study. The classification model was a principle component analysis (PCA)-based method consisting of a primary identification library with four sub-libraries. The accuracy and specificity of the model were tested and were both found to be approximately 95%. The transfer of the classification model between different instruments of the same brand and the same instrument model has been investigated in this study. This study has shown that it is feasible to build a universal classification model to quickly screen for counterfeit drugs in the open market and distribution channels.