On the Cayley-Bacharach Property

The Cayley-Bacharach Property (CBP), which has been classically stated as a property of a finite set of points in an affine or projective space, is extended to arbitrary 0-dimensional affine algebras over arbitrary base fields. We present characterizations and explicit algorithms for checking the CBP directly, via the canonical module, and in combination with the property of being a locally Gorenstein ring. Moreover, we characterize strict Gorenstein rings by the CBP and the symmetry of their affine Hilbert function, as well as by the strict CBP and the last difference of their affine Hilbert function.     

The Ihara zeta function of the complement of a semiregular bipartite graph

We study the Ihara zeta function of the complement of a semiregular bipartite graph. A factorization formula for the Ihara zeta function is derived via which the number of spanning trees is computed. For a class of complements of semiregular bipartite graphs, it is shown that they have the same Ihara zeta function if and only if they are cospectral.     

Grothendieck rings of a class of Hopf algebras of Kac-Paljutkin type

We construct the Grothendieck rings of a class of 2n²dimensional semisimple Hopf Algebras H_2n²,which can be viewed as a generalization of the 8 dimensional Kac-Paljutkin Hopf algebra H8.All irreducible H_2n²-modules are classified.Furthermore,we describe the Grothendieck rings r(H_2n²)by generators and relations explicitly.     

双路大电流源模块水中放电实验研究

高压电脉冲压裂技术是基于液电效应,通过水中脉冲放电产生强大的冲击波使岩石产生裂缝,近年来成为了岩石压裂领域的热点研究对象。搭建了两路电流源模块应用于水中放电,采用铜材料的针针电极,电极间距1 mm;研究了在不同放电电压下,单路和两路电流源模块电极间的电压、电流波形。实验结果表明,空载时在同一放电电压下,双路模块产生更大的放电电流,从而在放电时获得更高的瞬时功率;而在水中针针放电时,单路和双路模块水间隙的预击穿时间与放电电压之间具有很大的随机性。单路模块预击穿时间的标准差最小为0.285 ms,最大为1.481 ms;而双路模块最小为0.369 ms,最大为0.703 ms。并且随着放电电压的增加,预击穿时间减小,双路模块的预击穿平均时间从放电电压为1300 V时的2.686 ms降到1800 V时的1.036 ms。     

混合模式直线型变压器驱动源模块

在对Marx发生器和直线型变压器驱动源(LTD)电路拓扑结构及等效参数进行分析对比的基础上,结合两种电路拓扑结构的技术特点,提出了基于Marx基本回路的混合模式LTD模块构想。在混合模式LTD模块中,每个基本回路是一个多级的Marx发生器回路,回路中只有前一级或几级开关需要外部触发,而后级开关工作在自击穿模式。计算分析表明：混合模式LTD模块设计可以有效降低LTD系统对多路同步触发的要求;独立回路式结构可提高整个混合模式LTD模块的可维护性;回路间耦合触发的方式可提高整个混合模式LTD的工作可靠性。最后,还探讨了回路内阻、磁芯损耗及Marx发生器回路中后级自击穿开关抖动对混合模式LTD模块参数设计的影响。     

铜铟镓硒薄膜光伏组件中电池与封装材料界面的光学特性对组件性能的影响

根据测试数据,分析模拟了铜铟镓硒(CIGS)薄膜光伏组件中电池的活性区域、非活性区域与封装材料之间界面的光学特性对组件的短路电流产生的影响。根据组件结构建立了光学模型,从光学模拟结果分析组件内的反射与吸收。发现电池前电极透明导电氧化物薄膜(TCO)与封装材料界面的反射不可忽视,提出通过在透明导电氧化物薄膜与封装材料之间添加减反射层,并以MgO作为膜层材料以降低活性区域的界面反射;模拟了在非活性区域一次反射光角度与二次反射的关系,由此分析了非活性区域反射面倾角、镜面反射与漫反射比例对光利用的影响。模拟结果显示,活性区域的减反层结构可降低透明导电氧化物薄膜表面的反射率1%以上,而通过在非活性面积区域制备光反射结构,理论上能够利用非活性区域光照超过50%。     

Point Cloud Geometry Compression Based on Multi-Layer Residual Structure

Point cloud data are extensively used in various applications, such as autonomous driving and augmented reality since it can provide both detailed and realistic depictions of 3D scenes or objects. Meanwhile, 3D point clouds generally occupy a large amount of storage space that is a big burden for efficient communication. However, it is difficult to efficiently compress such sparse, disordered, non-uniform and high dimensional data. Therefore, this work proposes a novel deep-learning framework for point cloud geometric compression based on an autoencoder architecture. Specifically, a multi-layer residual module is designed on a sparse convolution-based autoencoders that progressively down-samples the input point clouds and reconstructs the point clouds in a hierarchically way. It effectively constrains the accuracy of the sampling process at the encoder side, which significantly preserves the feature information with a decrease in the data volume. Compared with the state-of-the-art geometry-based point cloud compression (G-PCC) schemes, our approach obtains more than 70–90% BD-Rate gain on an object point cloud dataset and achieves a better point cloud reconstruction quality. Additionally, compared to the state-of-the-art PCGCv2, we achieve an average gain of about 10% in BD-Rate.     

高功率氙灯脉冲放电过程中石英管壁热损伤机理

基于高功率激光装置对脉冲氙灯工程运行可靠性的要求,利用现有的能源模块开展了氙灯放电考核实验。实验结果表明：虽然氙灯运行在安全的能量负载水平,当能源模块单个放电回路的峰值功率超过300 MW时,氙灯石英玻璃管壁存在热损伤风险。肉眼观察到管壁损伤后在反射器对侧的灯管内壁出现乳白色沉积层。经扫描电镜和X射线光电子能谱测试分析,证实热损伤形成的乳白色沉积物为二氧化硅。为探究管壁热损伤机制,采用高速摄影观测了氙灯放电等离子体沟道发展过程。图像显示放大器内金属反射器的几何形状对放电沟道的分布产生了显著影响,尤其是在侧灯箱,灯内电弧沟道会靠近反射器一侧集中分布,因此,导致等离子体对灯管的偏烧。当放电峰值功率超过石英热负载极限时,管壁表面二氧化硅材料会被烧蚀至蒸发、气化,并随后沉积在灯管较冷部位。研究结果表明放电回路的放电峰值功率过高、放大器内金属反射器均会对氙灯造成热损伤。     

可补Hilbert C*-模及其有界模映射

给出了可补Hilbert C^*-模一系列等价刻画，获得了一类有界模映射的分解定理。     

A vanishing theorem for modular symbols on locally symmetric spaces

A modular symbol is the fundamental class of a totally geodesic submanifold embedded in a locally Riemannian symmetric space , which is defined by a subsymmetric space . In this paper, we consider the modular symbol defined by a semisimple symmetric pair (G,G'), and prove a vanishing theorem with respect to the -component in the Matsushima-Murakami formula based on the discretely decomposable theorem of the restriction . In particular, we determine explicitly the middle Hodge components of certain totally real modular symbols on the locally Hermitian symmetric spaces of type IV. Received: December 8, 1996