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.     

数学建模对高中生构建数学底层思维的作用及其教学实施建议

数学底层思维即用数学的眼光观察世界、用数学的思维分析世界以及用数学的语言表达世界,是人们面对自然和社会中纷繁多样的现象和问题时,所展现的自发的、不依赖监督的、融汇数学学科核心素养的思维方式.作为国家高中新课程标准中数学六大核心素养之一的数学建模,是培养学生数学底层思维的良好载体,对人才培养和社会发展均起到良好的促进作用.本文主要阐述了数学建模对高中生构建数学底层思维的作用,并结合教学实例给出教学实施建议.     

Homogeneous variable exponent Besov and Triebel–Lizorkin spaces

We introduce homogeneous Besov and Triebel–Lizorkin spaces with variable indexes. We show that their study reduces to the study of inhomogeneous variable exponent spaces and homogeneous constant exponent spaces. Corollaries include trace space characterizations and Sobolev embeddings.     

Establishment and validation of an SIL-IS LC–MS/MS method for the determination of ibuprofen in human plasma and its pharmacokinetic study

In this work, we developed and validated a highly sensitive, rapid and stable LC–MS/MS method for the determination of ibuprofen in human plasma with ibuprofen-d3 as a stable isotopically labeled internal standard (SIL-IS). Human plasma samples were prepared by one-step protein precipitation. The chromatographic separation was achieved on a Poroshell 120 EC-C₁₈ (2.1 × 50 mm, 2.7 μm). Aqueous solution (containing 0.05% acetic acid and 5 mm NH₄Ac) and methanol were selected as the mobile phase with gradient elution. An electrospray ionization source was applied and operated in negative ion mode. Multiple reaction monitoring mode was used for quantification using target fragment ions m/z 205.0 → 161.1 for ibuprofen and m/z 208.0 → 164.0 for SIL-IS, respectively. This method exhibited a linear range of 0.05–36 μg/ml for ibuprofen with correlation coefficient >0.99. Mean recoveries of ibuprofen in human plasma ranged from 78.4 to 80.9%. The RSD of intra- and inter-day precision were both < 5%. The accuracy was between 88.2 and 103.67%. The matrix effect was negligible in human plasma, including lipidemia and hemolytic plasma. A simple, efficient and accurate LC–MS/MS method was successfully established and applied to a pharmacokinetic study in healthy Chinese volunteers after a single oral administration of ibuprofen granules.     

三层流体中斜入射波作用下半无限板的水弹性响应

解析地研究了在三层流体中斜入射波浪与半无限弹性板的相互作用引起的波散射和板的水弹性响应. 三层流体在界面处的密度发生阶跃, 各层为一常数. 假设流体不可压缩、无黏、流体运动无旋. 在线性势流理论框架下, 使用本征函数展开法和内积式给出波板相互作用的半解析解. 根据色散关系分析, 得到了表面波模态和界面波模态入射时的临界入射角. 随着物理参数的变化, 临界角将随之发生变化. 临界角决定了当由开阔水域向板覆盖水域传播的表面波或界面波的存在性: (1)板覆盖水域入射界面上, 透射波能否存在; (2)入射界面之上界面中, 板覆盖水域中的透射波以及开阔水域中的反射波能否存在. 当下界面波入射时并且入射角足够大时, 开阔水域中的下界面波模态是整个流体域中唯一存在的模态.      

A safe minimum standard,the elasticity of substitution,and the cleanup of the Ganges in Varanasi

Despite repeated calls for a thorough cleanup of water pollution in the Ganges river, there are only two papers in the social sciences by Batabyal and Beladi (2017, 2019) that have shed theoretical light on this cleanup problem and its connection to the sustainability of tourism in Varanasi. Hence, we extend the above‐mentioned analyses and focus on two specific questions. First, we introduce the notion of a safe minimum standard (SMS) into the study and show how to analyze a probabilistic model of the Ganges cleanup problem when the SMS is accounted for. Second, for a representative citizen of Varanasi, we study how the magnitude of the elasticity of substitution between a composite consumption good and water quality in the Ganges—modeled by the SMS—affects the tradeoff between consumption and water quality maintenance.