Two Alkali Metal Germanophosphates Na3[Ge(OH)(PO4)2]·2H2O and Li2Na[GeO(HPO4)(PO4)]:Crystal Structures and Thermal Stability

Two new alkali metal germanophosphates,namely,Na₃[Ge(OH)(PO₄)₂]·2 H2 O and Li₂Na[GeO(HPO₄)(PO₄)],have been prepared by solvothermal method,and their crystal structures were determined by single-crystal X-ray diffraction.The title two compounds crystalize in the same orthorhombic space group Pbcm(No.57)and feature similar chain-like structure which is built from zig-zag GeO₆ octahedral thread loop branched by PO₄ tetrahedra.For Na₃[Ge(OH)(PO₄)₂]·2 H₂O,a=10.1650(9),b=13.1975(12),c=6.9751(7)?,V=935.73(15)?³,Z=4,R=0.0356 and wR=0.1109;and for Li₂Na[GeO(HPO₄)(PO₄)],a=6.9855(5),b=14.5809(18),c=6.6620(5)?,V=678.56(11)?³,Z=4,R=0.0286,and w R=0.0762.The partial substitution of Na ions by Li ions not only significantly influences the total structural features and the water molecule contents,but also impacts on their thermal stabilities.Li₂Na[GeO(HPO₄)(PO₄)]is thermally stable up to 400℃,whereas only 150℃ for Na₃[Ge(OH)(PO₄)₂]·2 H2 O.     

辫子Hopf代数的积分(英)

本文引进了无限维辫子Hopf代数$H$的忠实拟对偶$H^d$和严格拟对偶$H^{d'}$.证明了每个严格拟对偶$H^{d'}$是一个$H$-Hopf 模. 发现了$H^{d}$的极大有理$H^{d}$-子模$H^{d {\rm rat} }$ 与积分的关系, 即: $H^{d {\rm rat}}\cong \int ^l_{H^d} \otimes H$.给出了在Yetter-Drinfeld范畴$(^B_B{\cal YD},C)$中的辫子Hopf代数的积分的存在性和唯一性.     

开展深度学习 提高学习效率

若要提高高三复习效率，就要改变传统“题海”所带来的“高耗能”的学习方式，引导学生进行深度学习.在开展深度学习时，应重视“四基”的培养，引导学生从问题的本质出发，关注学生的思维发展过程，从而在完善认知体系的基础上，促进学习效率提升.     

基于硅锗异质结的二维量子点阵列的制备与表征

硅基半导体量子点中的自旋量子比特近几年来发展迅速,其单比特门与两比特门操作保真度已经突破了容错量子计算的阈值.在此基础上,如何构建硅基量子点二维阵列变得广受学界关注,然而二维阵列复杂的结构在器件制备和测量上均带来挑战.本文设计并成功制备了一种Si/SiGe异质结上的2×4结构八量子点二维阵列器件.借助输运测量方法测量了八量子点器件的全部电荷稳定性相图,并进一步地使用电荷感应调制测量方法得到了器件内的少电子区电荷稳定性相图,说明了对量子点电荷态的高灵敏度探测能力.此外,通过调控势垒电极展示了对量子点间隧穿耦合的调控作用并测量了多量子点耦合的电荷稳定性相图.本文的研究结果展示了使用Si/SiGe异质结构建自旋量子比特二维阵列的潜力,为未来硅量子点二维阵列的进一步扩展提供经验与参考.