勾股定理的高维推广

在欧氏空间的框架下,使用向量模的定义导出了二维平面的勾股定理,类似地导出了三维空间推广的勾股定理.最后,给出了一般性的勾股定理的高维推广形式.     

三维悬线式力矩器的等效刚度模型

三维悬线式力矩器是高密度光学头系统中的核心组件,其等效平动刚度和转动刚度直接决定着光学头克服和补偿系统误差的能力。该文根据三维悬线式力矩器的悬浮支撑模型,依据外力作用下悬线的变形协调关系,利用卡氏最小功原理建立了三维悬线式力矩器在各个有效运动方向上的等效刚度模型。进而由等效刚度可计算出三维悬线式力矩器的固有频率。最后利用Doppler激光测振仪对实验样品进行固有频率测试,实验结果与理论结果相比,最大误差不超过8.5%。该等效刚度模型对力矩器可动部的设计具有重要的理论指导作用。     

区域上Hardy空间的对偶定理

利用原子分解的方法，该划了外正则区域Ω包含R^n（n≥3)上局部Hardy空间h^pr(Ω）（0＜p≤1)的对偶空间。     

Effect of the free surface on the earthquake energy: A case study of reverse faulting

Based on the representation theorem of seismic energy radiation, in this study, we have quantitatively investigated the effect of free surface on the radiation energy distribution due to a coupling interaction between free surface and near surface finite fault for the reverse earthquake faulting. Corresponding to the finite faulting, a 2-D pseudostatic-reverse-fault-dislocation solution has been used in the calculation of the work done by the seismic response against free surface. The results indicate that, due to a strong coupling interaction between the free surface and near surface fault, the total radiated seismic energy ER is much larger than that radiated only from the fault itself （EF）, especially for the shallow reverse faulting. In convention, EF is commonly used in the estimation of earthquake energy radiation. However, when the fault depth H, the distance between the free surface and top of fault location, increases, the effect of the coupling interaction between the fault and free surface decreases gradually. Therefore, the total radiated energy ER approaches to the EF when the depth H is about 2 times the fault length L The current study could provide us a partial explanation of the apparent stress discrepancy observed at the far field and near field in the recent large earthquake. Moreover, the current study also has a significant implication of how to quantitatively describe the near fault strong ground motion and associated seismic hazard from the earthquake source energy point of view.     

Rough law generation and its separation-recognition

By using function S-rough sets (function singular rough sets), this paper gives rough law generation and the theorem of rough law generation. Based on these results above, the paper proposes rough law separation, the theorem of rough law separation, the compound generation theorem of rough law bands, and the principle of rough law bands. In the end, an application of rough law separation in recognizing the risk law of profit is presented.     

宽带微波取样器

本文简单介绍了微波取样器的工作原理,同时介绍了一种宽带微波取样器的设计。在文章的最后给出了所研制取样器的实测数据。     

一类广义的含脉冲的n个物种竞争模型的正周期解的存在性(英文)

运用一个锥中的不动点定理,讨论得到了一类广义的含脉冲的n个物种竞争模型的正周期解存在的充分条件.     

Taub定理的完整证明

采用Hawking和Ellis证明Birkhoff定理的方法,完整地证明了Taub定理,即Einstein方程的平面对称真空解必然为Taub时空.     

无穷格子系统的新型周期行波解

研究了无穷格子系统q（n）＋f＇（g（n））=V^t（g（n＋1）-g（n））-V^t（g（n）-g（n-1）），n∈Z周期行波解的存在性．其中：q（n）=q（n，t）是第n个质点在t时刻的坐标；f表示质点的位势函数；V表示相邻2个质点间的相互作用函数．应用山路定理和环绕定理，获得了该系统新型周期行波解的存在性定理．     

一类具有激波层现象的二次Dirichlet问题

为了在较弱的条件下研究一类具有内激波层现象的二次Dirichlet问题.用合成展开法构造出该问题的一阶渐近表达式,并利用不动点定理证明了解的存在性及其当ε→0时的渐近性质。在一定程度上,它比起传统的微分不等式方法放宽了对所提问题的条件限制。