商高确实证明了勾股定理——兼论这里的“矩”不宜理解为长方形

严格遵守"矩"是古代中国的测量仪器,"矩"在古文字中的含义为"矩线",或为"磬折形",将"矩"理解为长方形(包含正方形)是不可取的.商高确实证明了一般勾股定理.古证应该是最原始、最简单的.     

Charge ordering modulations in a Bi_0.4Ca_0.6MnO₃ film with a thickness of 110 nm

The low temperature sample stage in a transmission electron microscope is used to investigate the charge ordering behaviours in a Bi 0.4 Ca 0.6 MnO 3 film with a thickness of 110 nm at 103 K.Six different types of superlattice structures are observed using the selected-area electron diffraction(SAED) technique,while three of them match well with the modulation stripes in high-resolution transmission electron microscopy(HRTEM) images.It is found that the modulation periodicity and direction are completely different in the region close to the Bi 0.4 Ca 0.6 MnO 3 /SrTiO 3 interface from those in the region a little further from the Bi 0.4 Ca 0.6 MnO 3 /SrTiO 3 interface,and the possible reasons for this are discussed.Based on the experimental results,structural models are proposed for these localized modulated structures.     

染料敏化TiO2/WO3薄膜电池的光电变色

用光电化学方法研究了染料Ru(П) (4, 4′di COOEt 2, 2′bpy)2 (2, 2′bpy 4, 4′di CONH L tyrosineethylester) (PF6)2 (简写为Ru4)敏化TiO2 纳米结构电极的光电转换过程,同时,在导电玻璃上电沉积得到WO3 薄膜.结果表明,染料敏化的TiO2 多孔膜具有光电转换性能, WO3 薄膜具有良好的电致变色效应,将前者与电沉积得到的WO3 薄膜组成电池,在白光照射下可产生显著的颜色变化,有望用于自供电源的电色灵巧窗(Self poweredsmartwindow).     

广义鞍点问题的改进的类SOR算法

针对广义鞍点问题,本文提出了一个改进的类逐次超松弛迭代算法,在较弱的条件下,分析了算法的收敛性及线性收敛率.新算法的每步计算量与已有的算法类似,都是需要（近似）求解线性方程组,但新算法有更好的灵活度通过合适地选取参数矩阵,每一步子问题可以容易地求解,甚至可以有闭式解（closed-form solution）.数值实验结果显示了新算法的有效性.     

膨胀腔类超材料的传递损失研究*

声学超材料及结构已被广泛研究,其超结构通常利用3D打印技术实现,当结构刚度较小或者面积较大时,由声固耦合所导致的声学效果与设计不符的情况广泛存在。本文针对含有膨胀腔类的超材料,研究了声固耦合对其声学性能的影响,采用有限元计算结合阻抗管实验的方法,得到其传递损失,分析了声固耦合现象对传递损失的影响。结果表明：薄壁膨胀腔结构的作用频率范围与只考虑声学理论计算的设计不符,声固耦合现象对传递损失产生显著影响;采用增加膨胀腔壁厚、减少膨胀腔内径或选择金属材料的方式,都可以使得声固耦合现象对传递损失的影响减小;仿真结果与实验结果基本吻合。该研究结果说明：对于膨胀腔类超材料,当刚度较小或者面积较大时,对其进行声固耦合分析是完全必要的。     

无衍射特殊光束的产生与三维表征

无衍射光束(如贝塞尔光束、艾里光束)因具有无衍射、自愈合的特性, 在很多领域都有广泛的应用. 本文提出使用纯相位型空间光调制器对光场的复振幅进行调控, 从而可以产生多种复杂模式的无衍射光束, 如强度可独立调控的多个零阶贝塞尔光束, 两个高阶贝塞尔光束干涉生成的花瓣状无衍射光束, 具有多个主瓣的加速光束等特殊的无衍射光束. 通过在待测焦场附近放置一个平面反射镜, 使其沿光轴快速扫描光场, 并由数字相机同步拍摄反射回来的一系列二维光场强度分布信息, 可实现对无衍射光束三维光场强度分布的快速测量和表征. 本实验方法和技术可以快速产生各种复杂的特殊光场并获得其精确的三维可视化重建效果, 在光学显微、光学俘获、光学微加工等领域有潜在的应用价值.     

一类平面五次系统的定性分析

本文研究平面五次系统（１．１），应用［４，５］的最新结果，给出了奇点Ｏ（０，０）为中心的充要条件和焦点量公式，以及（１．１）至多有一个，二个极限环的充分条件．     

关于不同分布两两NQD列的Jamison型加权乘积和的强稳定性

本文讨论了不同分布两两ＮＱＤ列的Ｊａｍｉｓｏｎ型加权乘积和的强稳定性及乘积和的Ｍａｒｃｉｎｋｉｅｗｉｃｚ型强大数律,推广并改进了Ｅｔｅｍａｄｉ［１］关于不同分布两两独立列部分和的工作及Ｍａｔｕｌａ［２］,王岳宝等［３］关于同分布两两ＮＱＤ列部分和的工作．     

On generalized hamiltonian systems

1. PreliminaryIt is well known that{1] a 8ymPlectic form is invariant along the trajectory of a Hamilto-nian system. Based on this fundamental property, certain techniques have been developed.The purpose of this paper is to extend such an approach to a wider class of dynamic systeIns,namely, genera1ized Hamiltonian systems. Our purpose is to investigate a class of dynaInicsystems, which possess a certain "geometric structure".Deflnition 1.1[1'2]. Let M be a tIlallifo1d. w E fl'(M) is call…     

Edge assisted epitaxy of CsPbBr3 nanoplates on Bi2O2Se nanosheets for enhanced photoresponse

Bi$_{2}$O$_{2}$Se has been proved to be a promising candidate for electronic and optoelectronic devices due to their unique physical properties. However, it is still a great challenge to construct the heterostructures with direct epitaxy of hetero semiconductor materials on Bi$_{2}$O$_{2}$Se nanosheets. Here, a two-step chemical vapor deposition (CVD) route was used to directly grow the CsPbBr$_{3}$ nanoplate-Bi$_{2}$O$_{2}$Se nanosheet heterostructures. The CsPbBr$_{3}$ nanoplates were selectively grown on the Bi$_{2}$O$_{2}$Se nanosheet along the edges, where the dangling bonds provide the nucleation sites. The epitaxial relationships between CsPbBr$_{3}$ and Bi$_{2}$O$_{2}$Se were determined as ${[200]}_{\rm Bi_{2}O_{2}Se}||{[110]}_{\rm CsPbBr_{3}}$ and ${[110]}_{\rm Bi_{2}O_{2}Se}||{[200]}_{\rm CsPbBr_{3}}$ by transmission electron microscopy characterization. The photoluminescence (PL) results reveal that the formation of heterostructures results in the remarkable PL quenching due to the type-I band arrangement at CsPbBr$_{3}$/Bi$_{2}$O$_{2}$Se interface, which was confirmed by ultraviolet photoelectron spectroscopy (UPS) and Kelvin probe measurements, and makes the photogenerated carriers transfer from CsPbBr$_{3}$ to Bi$_{2}$O$_{2}$Se. Importantly, the photodetectors based on the heterostructures exhibit a 4-time increase in the responsivity compared to those based on the pristine Bi$_{2}$O$_{2}$Se sheets, and the fast rise and decay time in microsecond. These results indicate that the direct epitaxy of the CsPbBr$_{3}$ plates on the Bi$_{2}$O$_{2}$Se sheet may improve the optoelectronic performance of Bi$_{2}$O$_{2}$Se based devices.