声学超表面的非对称声分束特性研究

非对称声分束超表面是由人工微单元结构按照特定序列构建的二维平面结构,可将垂直入射的声波分成两束传播方向和分束比自由调控的透射波,在声功能器件设计及声通信领域具有广泛的应用前景。本文系统研究了一种实现非对称声分束的设计理论和实现方法,基于局域声功率守恒条件研究了声分束器的设计理论、阻抗矩阵分布、法向声强分布、声压场分布等。利用遗传算法对四串联共振腔结构进行参数优化实现了声分束器所需的阻抗矩阵分布,声压场分布表明声波入射到声分束器后在入射侧激发出两列传播方向相反且幅值和衰减系数均相同的表面波,实现了入射侧与透射侧的局域声功率相互匹配。声波经过声分束器后被分为两束透射波,两束透射波的折射角和透射系数与理论值十分吻合,证明了设计理论及实现方法的正确性和可行性。本文的研究工作可以为新型非对称声分束结构设计提供理论参考、设计方法和技术支持,并促进其在工程领域的实际应用。     

Catalytic Asymmetric Syntheses of Alkylidenecyclopropanes from Allenoates with Donor-Acceptor and Diacceptor Diazo Reagents

The first diastereo- and enantioselective cyclopropanation reactions of electron-deficient allenes with donor-acceptor and diacceptor diazo reagents are described. The desired enantioenriched alkylidenecyclopropanes (ACPs) were obtained in high yields with high diastereo- and enantioselectivities in the presence of Rh₂((S)-TCPTAD)₄ or Rh₂((R)-BTPCP)₄ catalysts (up to 95 % yield, >95 : 5 d.r. and 99 : 1 e.r.). This methodology gave a direct access to ACPs bearing multiple electron-deficient substituents and allows to further expand the availability of ACPs chemistry. Interestingly, during the examination of the scope of this reaction, the asymmetric intramolecular C−H insertion reaction into tert-butyl group was observed as a side reaction with up to 94 : 6 e.r.     

Dinuclear Zinc Catalyzed Enantioselective Dearomatization [3+2] Annulation of 2-Nitrobenzofurans and 2-Nitrobenzothiophenes

The application of dinuclear zinc catalysts in a dearomatization reaction has been developed. Catalytic asymmetric dearomatization [3+2] annulations of 2-nitrobenzofurans or 2-nitrobenzothiophenes with CF₃-containing N-unprotected isatin-derived azomethine ylides catalyzed by dinuclear zinc catalysts are realized with excellent diastereomer ratios (dr) of >20 : 1 and enantiomeric excess (ee) of up to 99 %. This protocol provides a practical, straightforward access to structurally diverse pyrrolidinyl spirooxindoles containing a 2,3-fused-dihydrobenzofuran (or dihydrobenzothiphene) moiety, and four contiguous stereocenters. Reactions can be performed on a gram scale. The absolute configuration of products is confirmed by X-ray single crystal structure analysis, and a possible mechanism is proposed.     

Subset representations and eigenvalues of the universal intertwining matrix

We solve a combinatorial question concerning eigenvalues of the universal intertwining endomorphism of a subset representation.     

Enantioselective C−H Activation with Earth‐Abundant 3d Transition Metals

Molecular syntheses largely rely on time‐ and labour‐intensive prefunctionalization strategies. In contrast, C?H activation represents an increasingly powerful approach that avoids lengthy syntheses of prefunctionalized substrates, with great potential for drug discovery, the pharmaceutical industry, material sciences, and crop protection, among others. The enantioselective functionalization of omnipresent C?H bonds has emerged as a transformative tool for the step‐ and atom‐economical generation of chiral molecular complexity. However, this rapidly growing research area remains dominated by noble transition metals, prominently featuring toxic palladium, iridium and rhodium catalysts. Indeed, despite significant achievements, the use of inexpensive and sustainable 3d metals in asymmetric C?H activations is still clearly in its infancy. Herein, we discuss the remarkable recent progress in enantioselective transformations via organometallic C?H activation by 3d base metals up to April 2019.     

An analysis of overlapping Schwarz method for a weakly coupled system of singularly perturbed convection-diffusion equations

In this article, we have developed an overlapping Schwarz method for a weakly coupled system of convection-diffusion equations. The method splits the original domain into two overlapping subdomains. A hybrid difference scheme is proposed in which on the boundary layer region, we use the central finite difference scheme on a uniform mesh, whereas on the nonlayer region, we use the mid-point difference scheme on a uniform mesh. It is shown that the numerical approximations converge in the maximum norm to the exact solution. We have proved that, when appropriate subdomains are used, the method produces almost second-order convergence. Furthermore, it is shown that two iterations are sufficient to achieve the expected accuracy. Numerical examples are presented to support the theoretical results. The main advantage of this method used with the proposed scheme is that it reduces iteration counts very much and easily identifies in which iteration the Schwarz iterate terminates.     

A Structurally Robust Chiral Borate Ion: Molecular Design,Synthesis, and Asymmetric Catalysis

Catalysis by chiral weakly‐coordinating anions (WCAs) remains underdeveloped due to the lack of a molecular design strategy for exploiting their characteristics, such as the non‐nucleophilic nature. Here, we report the development of a chiral borate ion comprising an O,N,N,O‐tetradentate backbone, which ensures hitherto unattainable structural robustness. Upon pairing with a proton, the hydrogen borate acts as an effective catalyst for the asymmetric Prins‐type cyclization of vinyl ethers, providing access to structurally and stereochemically defined dihydropyrans. The key to selectivity control is the distinct ability of the borate ion to discriminate the prochiral faces of the acyclic oxonium ion intermediate and dictate the regiochemical outcome. We anticipate that this study paves the way for exploring the untapped potential of WCA catalysis for selective chemical synthesis.