一个R2上含双曲函数核的Hilbert型不等式

通过引入参数，构造了一个全平面上的、含双曲函数的非齐次核函数。利用正切函数的有理分式展开，建立了最佳常数因子与正切函数高阶导数相关联的Hilbert型积分不等式。 作为应用，通过赋予参数不同的值，建立了一些有意义的特殊结果。     

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.     

Macroscopic Polarization Change of Mononuclear Valence Tautomeric Cobalt Complexes Through the Use of Enantiopure Ligand

The crystallization of a complex having electron transfer properties in a polar space group can induce the polarization switching of a crystal in a specific direction, which is attractive for the development of sensors, memory devices, and capacitors. Unfortunately, the probability of crystallization in a polar space group is usually low. Noticing that enantiopure compounds crystallize in Sohncke space groups, this paper reports a strategy for the molecular design of non-ferroelectric polarization switching crystals based on the use of intramolecular electron transfer and chirality. In addition, this paper describes the synthesis of a mononuclear valence tautomeric (VT) cobalt complex bearing an enantiopure ligand. The introduction of enantiomer enables the crystallization of the complex in the polar space group (P2₁). The polarization of the crystals along the b-axis direction is not canceled out and the VT transition is accompanied by a change in the macroscopic polarization of the polar crystal. Polarization switching via electron transfer is realized at around room temperature.     

Ethanol‐Precipitable,Silica‐Passivated Perovskite Nanocrystals Incorporated into Polystyrene Microspheres for Long‐Term Storage and Reusage

Perovskite nanocrystals (PNCs) are emerging luminescent materials due to their fascinating physic‐optical properties. However, their sensitive surface chemistry with organic polar solvents, oxygen, and moisture greatly hinders their developments towards practical applications. Herein we promote silica‐passivated PNCs (SP‐PNCs) by in situ hydrolyzing the surface ligands of (3‐aminopropyl) triethoxysilane. The resultant SP‐PNCs possesses a high quantum yield (QY) of 80 % and are precipitable by polar solvents, such as ethanol and acetone, without destroying their surface chemistry or losing QY, which offers an eco‐friendly and efficient method for separation, purification, and phase transfer of PNCs. Moreover, we further promoted a swelling–deswelling encapsulation process to incorporate the as‐made SP‐PNCs into non‐crosslinked polystyrene microspheres (PMs), which can largely increase the stability of the SP‐PNCs against moisture for long‐term storage.     

New convolutions and their applicability to integral equations of Wiener-Hopf plus Hankel type

We propose four new convolutions exhibiting convenient factorization properties associated with two finite interval integral transformations of Fourier-type together with their norm inequalities. Moreover, we study the solvability of a class of integral equations of Wiener-Hopf plus Hankel type (on finite intervals) with the help of the factorization identities of such convolutions. Fourier-type series are used to produce the solution formula of such equations, and a Shannon-type sampling formula is also obtained.     

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。     

New findings for two new type sine hyperbolic potentials

We propose two new type sine hyperbolic potentials $V(x)=a^2{\sinh }^2?(x)?k{\tanh }^2?(x)$ and $V(x)=c^2{\sinh }^4?(x)?k{\tanh }^2?(x)$. They may become single- or double-well potentials depending on the potential parameters $a,c$ and k. We find that its exact solutions can be written as the confluent Heun functions $H_c(\alpha ,\beta ,\gamma ,\delta ,\eta ;z)$, in which the energy level E is involved inside the parameter η. The properties of the wave functions, which is strongly relevant for the potential parameters $a,c$ and k, are illustrated.     

一种提高极值点处收敛精度的三阶WENO-Z格式

为了提高三阶WENO-Z格式在极值点处的计算精度，通过理论推导给出三阶WENO格式满足收敛精度的充分条件。采用泰勒级数展开的方式，推导给出所构造格式非线性权重的计算公式，并综合权衡计算精度和计算稳定性确定所构造格式的参数。通过两个典型的精度测试，验证了改进格式在光滑流场极值点区域逼近三阶精度。进一步选用激波与熵波相互作用和Richtmyer-Meshkov不稳定性等经典算例，证实了本文提出的改进格式WENO-PZ3相较其他格式（WENO-JS3和WENO-Z3）不仅具有较高的精度，而且降低了格式的耗散，提高了对流场结构的分辨率。     

On the Lipschitz equivalence of self‐affine sets

Recently Lipschitz equivalence of self‐similar sets on has been studied extensively in the literature. However for self‐affine sets the problem is more awkward and there are very few results. In this paper, we introduce a w‐Lipschitz equivalence by repacing the Euclidean norm with a pseudo‐norm w. Under the open set condition, we prove that any two totally disconnected integral self‐affine sets with a common matrix are w‐Lipschitz equivalent if and only if their digit sets have equal cardinality. The main methods used are the technique of pseudo‐norm and Gromov hyperbolic graph theory on iterated function systems.