Existence of two periodic solutions for a non-autonomous SIR epidemic model

A non-autonomous SIR model with periodic transmission rate and a constant removal rate is formulated. By using the continuation theorem of coincidence degree theory, sufficient conditions for the existence of at least two positive periodic solutions are obtained. The stability of the periodic solution for small seasonality is investigated. Numerical simulations are done to show our theoretical results.     

Hysteresis effects under CIR interest rates

Most decision making research in real options focuses on revenue uncertainty assuming discount rates remain constant. However, for many decisions revenue or cost streams are relatively static and investment is driven by interest rate uncertainty, for example the decision to invest in durable machinery and equipment. Using interest rate models from Cox et al. (1985b), we generalize the work of Ingersoll and Ross (1992) in two ways. Firstly, we include real options on perpetuities (in addition to zero coupon cash flows). Secondly, we incorporate abandonment or disinvestment as well as investment options, and thus model interest rate hysteresis (parallel to revenue uncertainty in Dixit (1989a)). Under stochastic interest rates, economic hysteresis is found to be significant, even for small sunk costs.     

An inventory model with generalized type demand,deterioration and backorder rates

This study is motivated by the paper of Skouri et al. [Skouri, Konstantaras, Papachristos, Ganas, European Journal of Operational Research 192 (1) (2009) 79–92]. We extend their inventory model from ramp type demand rate and Weibull deterioration rate to arbitrary demand rate and arbitrary deterioration rate in the consideration of partial backorder. We demonstrate that the optimal solution is actually independent of demand. That is, for a finite time horizon, any attempt at tackling targeted inventory models under ramp type or any other types of the demand becomes redundant. Our analytical approach dramatically simplifies the solution procedure.     

奇异Hamilton-Jacobi-Bellman方程粘性解的存在唯一性

研究系数在边界点有奇性的一类Hamilt on- Jacobi- Bellman (HJB)方程的粘性解的存在唯一性问题及解的渐近估计,这类问题包括波动系数振荡或爆破的情况.奇异HJB方程在随机最优控制和金融数学等许多领域都有重要的应用,包括金融数学中的随机利率模型.应用粘性上下解理论建立了一类奇异HJB方程的比较原理,给出了粘性解存在唯一性的条件.     

城市社区共享资源维护的个体异质性效应研究

城市社区共享资源经历日晒雨淋或人为频繁使用而逐渐耗损,为了"保值增值",必然出现对其维护捐赠的可持续性问题.在多人跨期均衡模型和数学赋值的随机模拟基础上,对个体偏好异质性等参数影响捐赠投入的机理进行了探讨,认为:差异程度与城市社区共享资源维护的捐赠投入正相关;且初始存量较大或耗损速率较慢时,异质性的作用更加显著.     

Isocratic Separation of Dansylated Biogenic Amines on a C8‐Bonded Silica Column under the LC Elution of Methanol‐Based Mobile Phase

Under the elution of methanol‐based mobile phase, the isocratic resolution of 12 biogenic amines, including 1 aromatic, 2 heterocyclic and 9 aliphatic amines, as the dansylated derivatives has been accomplished in less than 25 minutes on a 15 cm C₈‐bonded column. The resolution can not be reproduced on other examined alkyl‐bonded phases (e.g., C₄ and C₁₈) under the same chromatographic conditions, or in the reversed‐phase mode. The retention, mainly as a result of hydrophobic interaction between analyte and stationary phase, can be adjusted by varying the percentage of methanol in the mobile phase. Also, incorporating acetic acid as additive to the mobile phase to protonate the analyte and silanol groups that are little shielding on the surface of silica gel reduces the dipole‐dipole interaction, and thus the retention scale, which in turn deteriorates the resolution. Furthermore, the elution reversal is plausible for some of analytes as a greater percent of acetic acid is used in the elution. Values of correlation coefficients (R²) range between 0.9995 and 0.9996, indicating good linearity.     

Micellar nucleation differential microemulsion polymerization

Polymer nanoparticles within the range of 2–5 nm with a solid content of more than 13 wt.% and a narrow molecular weight polydispersity (Mw/Mn ∼ 1.1) were for the first time prepared using a micellar nucleation differential microemulsion polymerization system emulsified by sodium dodecyl sulfate (SDS), with SDS/monomer (methyl methacrylate) and SDS/H₂O weight ratios of up to 1:16 and 1:100, respectively. It was found that for benzoyl peroxide (BPO), micellar nucleation is more favorable for the synthesis of smaller polymer nanoparticles than ammonium persulfate (APS) which gives rise to homogeneous nucleation and 2,2′-azobisisobutyronitrile (AIBN) which involves partially heterogeneous nucleation. In the polymerization process, there exists a critical stability concentration (CSC) of SDS, above which the size of the nanoparticles is to be minimized and stabilized. With an increase in the monomer addition rate, the polymerization system changes from a microemulsion system to an emulsion system. A mechanism was proposed to describe the micellar nucleation process of differential microemulsion polymerization. This study may contribute to the development of fine polymer nanoparticles for drug delivery systems.     

Liquid phase microextraction applications in food analysis

Over the last years, liquid-phase microextraction (LPME) in its different application modes (single drop microextraction, dispersive liquid-liquid microextraction and hollow fiber-LPME) has been increasingly applied for the extraction of both inorganic and organic analytes from different matrices. Its advantages over conventional extraction procedures (simplicity, effectiveness, rapidity and low consumption of organic solvents) has also attracted its application in the complex food analysis field, in which it has clearly provided good and challenging results. A comprehensive review dealing with those articles published since its introduction till the end of March 2011 is presented, offering also a critical vision of the analytical potential of LPME for the analysis of foods.     

Characterization and modeling of nonlinear hydrophobic interaction chromatographic systems

A general rate model was employed in concert with a preferential interaction quadratic adsorption isotherm for the characterization of HIC resins and the prediction of solute behavior in these separation systems. The results indicate that both pore and surface diffusion play an important role in protein transport in HIC resins. The simulated and experimental solute profiles were compared for two model proteins, lysozyme and lectin, for both displacement and gradient modes of chromatography. Our results indicate that a modeling approach using the generate rate model and preferential interaction isotherm can accurately predict the shock layer response in both gradient and displacement chromatography in HIC systems. While pore and surface diffusion played a major role and were limiting steps for proteins, surface diffusion was seen to play less of a role for the displacer. The results demonstrate that this modeling approach can be employed to describe the behavior of these non-linear HIC systems, which may have implications for the development of more efficient preparative HIC separations.     

Description of the response of a fiber optic velocity sensor applied to capillary gas chromatography

This paper explores the response of a novel fiber optics sensor allowing real-time determination of the migration rate of vapor zones in capillary gas chromatography. The sensitivity is related to the gradient of the vapor zone distribution in the capillary and it is highest when vapor zones show steep variations in concentration. The expected linearity between the height of the velocity peaks and the response of a thermal conductivity detector is demonstrated experimentally. The sensor can be used to infer an approximate value of the analyte diffusion coefficient from the time response. Finally, the time evolution of the envelope of the optical signal is explained with experimental evidences.