代数$\Omega$-范畴的等价范畴

本文基于$\Omega$-范畴研究了(连续) $\mathcal{I}$-余万备$\Omega$-范畴的一些性质. 我们给出了双完备$\Omega$-范畴和逼近双模的概念并讨论了它们的性质, 证明了任何$\mathcal{I}$-余万备$\Omega$-范畴都是双完备$\Omega$-范畴. 得到了代数$\Omega$-范畴范畴等价于双完备$\Omega$-范畴.     

On categories associated to a Quasi-Hopf algebra

A quasi-Hopf algebra H can be seen as a commutative algebra A in the center 𝒵(H-Mod) of H-Mod. We show that the category of A-modules in 𝒵(H-Mod) is equivalent (as a monoidal category) to H-Mod. This can be regarded as a generalization of the structure theorem of Hopf bimodules of a Hopf algebra to the quasi-Hopf setting.     

Bounded complexes of cotorsion sheaves

We provide a necessary and su?cient condition which ensure that every flat quasi-coherent sheaf has finite cotorsion dimension. Also, we will show that every locally noetherian scheme with a dualizing complex has this requirement.     

Galois G-covering of quotients of linear categories

In this paper, we introduce the notion of G-liftable ideals, which extends the liftable ideas defined by Assem and Le Meur. We characterize the G-liftable ideals and construct the Galois G-coverings of quotients of categories associated to the G-liftable ideals. In particular, we study the behavior of G-liftable admissible ideals under Galois G-coverings. Furthermore, we show that the ideals generated by finite dimensional projective modules over a locally bounded linear categories are admissible G-liftable ideals. As an application, we provide a reduction technique for dealing with the existence of Serre functors in the stable categories of Gorenstein projective objects.     

Surface Acoustic Wave Characterization of Equivalent Young's Moduli for Patterned Films北大核心CSCD

Based on the equivalent elasticity theory for layered materials, the micro-mechanics equivalent models for single and dual damascene structures were established. The equivalent elastic constant of the patterned structure was introduced, to establish the propagation model for the surface acoustic waves propagating in the layered structure of the patterned film/ substrate, and the theoretical dispersion curves of the surface acoustic waves were calculated with Green’s function and the matrix method. The finite element method was used to calculate 24 numerical examples of damascene structures with different volume ratios, and the results were compared with those of the strain energy method. The results show that, the average relative errors of the equivalent Young’s moduli of the 300 nm-thick dual damascene film and the 100 nm-thick single damascene film are 2.06% and 2.27%, respectively. The research verifies the correctness of the equivalent patterned structure model and the feasibility of the surface acoustic wave method to characterize the mechanical properties of patterned films, and provides a reference for the development of suitable chemico-mechanical polishing technologies for patterned films under low pressure. © 2023 Editorial Office of Applied Mathematics and Mechanics. All rights reserved.     

正交正放类网架结构固有频率及屈曲分析的样条Galerkin法

本文根据考虑剪切变形的具有３个广义位移的平板弯曲理论，把正交正放类平板网架假设为由三层不同性质材料组成的各向正交异性夹层板。文中以双５次Ｂ样条函数中的一组基底作为试函数，用加权残值法中的离散型Ｇａｌｅｒｋｉｎ法，导出了这类网架的频率方程和屈曲方程。数值算例表明，这种方法是方便而精确的。     

DISCUSSION ON TWO PROBLEMS OF THEORETICAL MECHANICS IN COLLEGE MECHANICS COMPETITION1)

针对两道力学竞赛试题,从欧拉动力学方程出发分别给出了更加简化的固连系选取方法,分别命名为"Serret-Andoyer近似固连系"和"虚固连系",在此基础上对第1届全国青年力学竞赛理论力学试题第9题,拓展讨论了大球同步旋转时,小球的稳 定性条件,结果表明后者的稳定临界转速要求更低,这将更有利于提高旋转结构的稳定性;对第12届全国周培源大学生力学 竞赛第3题,剖析了任一纬度的运动规律,发现当体系初始角动量为零时会出现一种简洁又优美的运动模式。     

石英晶体多路微天平等效电路和相关实验研究

从AT切的石英晶体等效电路出发，利用电路理论推导单片石英晶体上耦合电极的相互影响，相互耦合作用用复电阻描述，然后通过实验观察复电阻的频率特性，分析其具体的形式，同时通过实验初步观察了MQCM(multi-channel quartz crystal microbalance)对石英片谐振频率的影响，以及不同电极尺寸对耦合的影响。     

用均匀化理论分析蜂窝结构的等效弹性参数

在线弹性范围内,根据均匀化理论,并结合有限元方法推导出适用于二维周期性结构的均匀化的有限元格式（Homo FEM）,计算出不同相对密度下的规则蜂窝结构的等效弹性模量Ee和泊松比νe.同时,利用蜂窝结构的代表胞元模型,用常规的有限元方法（FEM）模拟计算出相应的等效弹性参数.最后将两种数值计算结果与己有的理论公式进行了比较和分析讨论.结果表明:在考察的相对密度全场范围内（0～0.4）,HOmO FEM得到的蜂窝结构的 Ee和νe 与 FEM使用平面实体单元模拟计算得到的结果一致吻合,反映出 Homo FEM数值方法的客观准确性和可行性.而 Gibson公式和 W-K得到的等效弹性模量值 Ee只是在较小相对密度的情况下（小于0.15）与数值计算结果吻合.当结构的相对密度较大时,必须考虑胞棱附近区域由应力集中导致的复杂的应力和应变分布的影响.     

Strong explosion near a parallelepipedic structure

The purpose of this paper is to report the blast loading characteristics resulting from the detonation of a stoichiometric propane–oxygen mixture, and to validate the approach which relies on simulating TNT explosions at large scale by small-scale experiments of gaseous explosions. Several dimensionless correlations are obtained from experimental data. These relationships allow determination of the parameters of a blast wave interacting with a structure as a function of the positions of the explosive charge and the structure. Simulations carried out with the Autodyn code show good correlation with experimental results. The Hopkinson law is suggested to predict the blast wave’s parameters at large scale on the basis of small-scale experiments and simulations. This paper was based on work that was presented at the 20th International Colloquium on the Dynamics of Explosions and Reactive Systems, Montreal, Canada, July 31–August 5, 2005.