High-frequency lengthwise diffraction by the curve separating soft and hard part of the surface

The paper examines the model problem of high-frequency diffraction by a convex surface consisting of two parts. One is soft, the other is hard. The incident wave falls at a small angle to the line which separates soft and hard parts of the surface. The change in the boundary condition provokes the field in the Fock zone to have a rapid transverse variation. This causes a special boundary-layer to be formed. The boundary value problem for the three dimensional parabolic equation is reduced to the Riemann problem solved by the factorization in the form of infinite products containing the zeros of the Airy function and zeros of its derivative. the results of this factorization appear under the sign of double Fourier integral in the representation of the field. Both numerical and asymptotic analysis of this representation is carried out and illustrates the effects of high-frequency diffraction caused by the line of the boundary condition discontinuity.     

Bi/Bi_2O_3 nanoparticles supported on N-doped reduced graphene oxide for highly efficient CO_2 electroreduction to formate

Electrocatalytic CO_2 reduction(CO_2 ER) into formate is a desirable route to achieve efficient transformation of CO_2 to value-added chemicals,however,it still suffers from limited catalytic activity and poor selectivity.Herein,we develop a hybrid electrocatalyst composed of bismuth and bismuth oxide nanoparticles(NPs) supported on nitrogen-doped reduced graphene oxide(Bi/Bi_2 O_3/NrGO) nanosheets prepared by a combined hydrothermal with calcination treatment.Thanks to the combination of undercoordinated sites and strong synergistic effect between Bi and Bi_2 O_3,Bi/Bi_2 O_3/NrGO-700 hybrid displays a promoted CO2 ER catalytic performance and selectivity for formate production,as featured by a small onset potential of-0.5 V,a high current density of-18 mA/cm~2,the maximum Faradaic efficiency of85% at-0.9 V,and a low Tafel slope of 166 mV/dec.Experimental results reveal that the higher CO_2 ER performance of Bi/Bi_2 O_3/NrGO-700 than that of Bi NPs supported on NrGO(Bi/NrGO) can be due to the partial reduction of Bi_2 O_3 NPs into Bi,which significantly increases undercoordinated active sites on Bi NPs surface,thus boosting its CO_2 ER performance.Furthermore,a two-electrode device with Ir/C anode and Bi/Bi_2 O_3/NrGO-700 cathode could be integrated with two alkaline batteries or a planar solar cell to achieve highly active water splitting and CO_2 ER.     

改进的PNC方法及其在非线性偏微分方程多解问题中的应用

2017年，李昭祥等提出了一种偏牛顿-校正法（Partial Newton-Correction Method，简记为PNC方法），并利用它成功地计算出了三类非线性偏微分方程的多重不稳定解.本文在PNC方法的基础上，提出并发展了一种改进的PNC方法.首先，利用Nehari流形$\mathcal{N}$与零平凡解的可分离性，建立并证明了$\mathcal{N}$的某特殊子流形$\mathcal{M}$上的全局分离定理及其推广（即局部分离定理）.全局分离定理只跟非线性偏微分算子或相应的非线性泛函本身有关，而与具体的计算方法无关.对一些典型的非线性偏微分方程多解问题（比如，Henon方程问题），该全局分离定理的分离条件，经验证是成立的.另一个方面，通过修改或补充原辅助变换的定义，去掉了原辅助变换的奇异性；接着建立并证明了某些非线性偏微分方程问题的新未知解与该非线性偏微分算子零核空间的密切关系；在证明中，去掉了在原奇异变换下所需的标准收敛（standard convergence）假设.最后，计算实例与数值结果验证了改进的PNC方法的可行性和有效性；同时表明子流形$\mathcal{M}$与已知解的可分离性是PNC方法和本文新方法能成功找到多解的关键.     

具有恒定冲击载荷的梯度泡沫金属材料设计

多胞材料可通过大变形大量地吸收冲击能量，引入密度梯度可进一步提高其耐撞性。梯度多胞材料的宏观力学响应对材料密度分布极为敏感，不同类型的细观构型的影响也极为不同。已有的研究工作主要局限在对给定的密度梯度分析其动态响应，较少对耐撞性设计方法进行研究。本文针对梯度闭孔泡沫金属材料，基于非线性塑性冲击波模型发展了耐撞性反向设计方法，以维持冲击物受载恒定为目标，运用级数法获得了简化模型和渐近解。利用变胞元尺寸法构建了连续梯度变化的三维Voronoi细观有限元模型，并利用ABAQUS/Explicit有限元软件对理论设计进行数值验证。结果表明，反向设计理论简化模型的渐近解对于梯度闭孔泡沫金属材料的耐撞性设计是有效的，所提出的耐撞性设计方法在控制冲击吸能过程和冲击物受载方面具有指导意义。     

Energy-preserving algorithm for gyrocenter dynamics of charged particles

Numerical Algorithms - Gyrocenter dynamics of charged particles plays a fundamental and important role in plasma physics, which requires accuracy and conservation in a long-time simulation....     

Generation and Reactivity of a One-Electron-Oxidized Manganese(V) Imido Complex with a Tetraamido Macrocyclic Ligand

The synthesis and X-ray structure of a new manganese(V) mesitylimido complex with a tetraamido macrocyclic ligand (TAML), [Mn^V(TAML)(N-Mes)]⁻ ( 1 ), are reported. Compound 1 is oxidized by [(p-BrC₆H₄)₃N ]^+.[SbCl₆]⁻ and the resulting Mn^VI species readily undergoes H-atom transfer and nitrene transfer reactions.     

Local Least Product Relative Error Estimation for Varying Coefficient Multiplicative Regression Model

Acta Mathematicae Applicatae Sinica, English Series - In this article, we consider the varying coefficient multiplicative regression model, which is very useful to model the positive response. The...     

单色仪波长定标中狭缝设置的影响分析

单色仪作为一种分光仪器，在传感器的辐射定标等方面具有重要应用。在实际应用过程中，其波长和带宽的设置对传感器的精确定标具有重要影响。使用低压汞灯作为波长标准光源，通过对其特征谱线扫描的方法，研究了传感器定标过程中，设置单色仪不同的狭缝宽度，对传感器精确定标具有重要影响。结果显示，当出射入射狭缝相同，同时改变其宽度的情况下，与典型校准状态(出射入射狭缝宽度设置为0.5 mm)相比，波长偏差量达到0.17 nm；当入射狭缝与出射狭缝不一致时，与典型校准状态相比，波长偏差量达到0.18 nm；当光源未充满入射狭缝与充满入射狭缝相比，最大误差达到0.02 nm，该影响几乎可以忽略。在相关的传感器光谱辐射定标实验研究中，单色仪的定标精度和准确性评估等方面具有重要应用。