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.     

优化端点条件的平面二次均匀B样条插值曲线

在利用反求法构造B样条插值曲线时，往往需要选取端点条件。 因此，可对端点条件进行优化选取，使得构造的B样条插值曲线满足特定要求。提出了一种利用曲线内能极小选取平面二次均匀B样条插值曲线端点条件的算法。首先给出了二次均匀B样条插值曲线分控制顶点与首个控制顶点（即端点条件）的递推关系式；然后给出了利用曲线内能极小优化选取首个控制顶点的算法，证明了利用该算法构造的C¹连续二次均匀B样条插值曲线为保形插值，并通过数值算例证明了算法的有效性；最后，为便于实际应用，基于MATLAB平台设计了算法所对应的图形用户界面，用户通过简单的操作即可获得光顺的C¹连续二次均匀B样条保形插值曲线。     

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.     

双曲冷却塔塔筒水平地震响应分析

为明确冷却塔在水平地震下的内力环向分布特征及内在原因,同时探究不同地震波时程与规范反应谱所得内力差异的原因,以某大型双曲冷却塔为例,在动力特性分析的基础上,通过反应谱方法和时程方法的水平地震响应计算及对比分析,对上述两个问题进行了研究。研究表明:由于仅侧弯振型对水平地震有贡献,而塔筒的侧弯振型和实际响应均表现为整体侧倾并伴随微弱的截面“流动”变形,这也使塔筒各内力的环向分布分别呈现正弦、余弦分布特征;其整体侧倾可类比于悬臂杆结构,塔筒子午向轴力FY、子午向弯矩MY、剪力FXY和扭矩MXY的环向分布可借助悬臂杆侧倾时截面正应力和剪应力分布来解释;而截面“流动”变形则决定了环向轴力FX和环向弯矩MX的环向分布;整体侧移显著而截面变形极小也使FY和FXY的幅值在塔筒中下部明显大于FX;由于冷却塔第1阶侧弯振型在水平地震响应中往往起绝对主导作用,因此可先对所选地震波计算得到其反应谱,对比第1阶侧弯振型周期对应的水平地震影响系数α值,即可初步推断不同时程及规范反应谱方法所得结果的大小关系。     

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.     

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.     

Internal plasticization of poly(vinyl) chloride using glutamic acid as a branched linker to incorporate four plasticizers per anchor point

Internal plasticization of polyvinyl chloride (PVC) using thermal azide‐alkyne Huisgen dipolar cycloaddition between azidized PVC and electron‐poor acetylenediamides incorporating a branched glutamic acid linker resulted in incorporation of four plasticizing moieties per attachment point on the polymer chain. A systematic study incorporating either alkyl or polyethylene glycol esters provided materials with varying degrees of plasticization, with depressed T_g values ranging from ?1 °C to 62 °C. Three interesting trends were observed. First, T_g values of PVC bearing various internal plasticizers were shown to decrease with increasing chain length of the plasticizing ester. Second, branched internal plasticizers bearing triethylene glycol chains had lower T_g values compared to those with similar length long‐chain alkyl groups. Finally, thermogravimetric analysis of these internally plasticized PVC samples revealed that these branched internal plasticizers bearing alkyl chains are more thermally stable than similarity branched plasticizers bearing triethylene glycol units. These internal tetra‐plasticizers were synthesized and attached to PVC‐azide in three simple synthetic steps. © 2019 Wiley Periodicals, Inc. J. Polym. Sci., Part A: Polym. Chem. 2019 , 57, 1821–1835