Optimal control and numerical methods for hybrid stochastic SIS models

This work focuses on optimal controls of a class of stochastic SIS epidemic models under regime switching. By assuming that a decision maker can influence the infectivity period, our aim is to minimize the expected discounted cost due to illness, medical treatment, and the adverse effect on the society. In addition, a model with the incorporation of vaccination is proposed. Numerical schemes are developed by approximating the continuous-time dynamics using Markov chain approximation methods. It is demonstrated that the approximation schemes converge to the optimal strategy as the mesh size goes to zero. Numerical examples are provided to illustrate our results.     

Analysis of a new multispecies tumor growth model coupling 3D phase-fields with a 1D vascular network

In this work, we present and analyze a mathematical model for tumor growth incorporating ECM erosion, interstitial flow, and the effect of vascular flow and nutrient transport. The model is of phase-field or diffused-interface type in which multiple phases of cell species and other constituents are separated by smooth evolving interfaces. The model involves a mesoscale version of Darcy’s law to capture the flow mechanism in the tissue matrix. Modeling flow and transport processes in the vasculature supplying the healthy and cancerous tissue, one-dimensional (1D) equations are considered. Since the models governing the transport and flow processes are defined together with cell species models on a three-dimensional (3D) domain, we obtain a 3D–1D coupled model.     

Pure annihilation decay of strange beauty meson into two charm heavy mesons

In this study, the heavy to heavy decay of \begin{document}$ B^0_s\rightarrow D^{*+}D^- $\end{document} is evaluated through the factorization approach by using the final state interaction as an effective correction. Under the factorization approach, this decay mode occurs only through the annihilation process, so a small amount is produced. Feynman's rules state that six meson pairs can be assumed for the intermediate states before the final meson pairs are produced. By taking into account the effects of twelve final state interaction diagrams in the calculations, a significant correction is obtained. These effects correct the value of the branching ratio obtained by the pure factorization approach from \begin{document}$ (2.41\pm1.37)\times10^{-5} $\end{document} to \begin{document}$ (8.27\pm2.23)\times10^{-5} $\end{document}. The value obtained for the branching ratio of the \begin{document}$ B^0_s\rightarrow D^{*+}D^- $\end{document} decay is consistent with the experimental results.     

TFSI钝化晶体硅表面性质的第一性原理研究

晶体硅表面钝化是高效率晶体硅太阳能电池的核心技术,直接影响晶体硅器件的性能。本文采用第一性原理方法研究了一种超强酸-双三氟甲基磺酰亚胺(TFSI)钝化晶体硅(001)表面。研究发现,TFSI的四氧原子结构能够与Si(001)表面Si原子有效成键,吸附能达到-5.124 eV。电子局域函数研究表明,TFSI的O原子与晶体硅表面的Si的成键类型为金属键。由态密度和电荷差分密度分析可知,Si表面原子的电子向TFSI转移,从而有效降低了Si表面的电子复合中心,有利于提高晶体硅的少子寿命。Bader电荷显示,伴随着TFSI钝化晶体硅表面的Si原子,表面Si原子电荷电量减少,而TFSI中的O原子和S原子电荷电量相应增加,进一步证明了TFSI钝化Si表面后的电子转移。该工作为第一性原理方法预测有机强酸钝化晶体硅表面的钝化效果提供了数据支撑。     

广西经济增长、金融发展与城乡收入差距的实证研究

探讨了经济增长及金融发展与城乡收入差距之间互动影响,刻画了三者间的逻辑关系,并基于广西1990-2017年的统计数据,运用状态空间模型及卡尔曼滤波算法对三者间动态关系进行了实证分析.结果显示:经济增长对城乡收入差距呈现倒U型曲线形态,而金融发展则显示出具有不断缩小城乡收入差距的趋势.     

The Coordination Chemistry of f-Block Elements in Molten Salts

The coordination chemistry of f-block elements (lanthanide and actinide) in molten salts has become a resounding topic in view of its great importance to the research and development (R&D) of molten salt reactors and pyroprocessing. In this Review article, a general overview of the coordination chemistry of f-block elements in molten salts is provided including past achievements and recent advances. Particular emphases are placed on the oxidation state, speciation, and solution structure of f-block metal ions in molten salts, as well as their relationships with the salt composition. Furthermore, this review briefly discusses the spectroscopic and theoretical methods that complement each other in revealing the coordination properties.