In this paper, we introduce the signed weak gliding hump property in a dual pair with the structure of a system of sections and show that if a dual pair [E, F] has the signed weak gliding hump property, then the β-du...In this paper, we introduce the signed weak gliding hump property in a dual pair with the structure of a system of sections and show that if a dual pair [E, F] has the signed weak gliding hump property, then the β-dual space of E is a weak sequentially complete space if and only if for every n ∈N,(F[n] ,σ(F[n] ,E[n] )) is sequentially complete. Furthermore, we also prove that if [E,F] has the signed weak gliding hump property, then (E,τ(E,E<β> )) is an AK- space.展开更多
In This paper, the concept of weakly dual ring is introduced, which is a proper generalization of the dual ring. If R is a right weakly dual ring, then (1) Z(RR) = J(R); (2) If R is also a zero-division power ring, th...In This paper, the concept of weakly dual ring is introduced, which is a proper generalization of the dual ring. If R is a right weakly dual ring, then (1) Z(RR) = J(R); (2) If R is also a zero-division power ring, then R is a right AP-injective ring. In addition, some properties of weakly dual rings are given.展开更多
In this paper, we have studied the topology of some classical functional spaces. Among these spaces, there are standard spaces, spaces that can be metrizable and others that cannot be metrizable. But they are all topo...In this paper, we have studied the topology of some classical functional spaces. Among these spaces, there are standard spaces, spaces that can be metrizable and others that cannot be metrizable. But they are all topological vector spaces and it is in this context that we have chosen to present this work. We are interested in the topology of its spaces and in the topologies of their dual spaces. The first part, we presented the fundamental topological properties of topological vector spaces. The second part, we studied Frechet spaces and particularly the space S(R<sup>n</sup>) of functions of class C<sup>∞ </sup>on R<sup>n</sup> which are as well as all their rapidly decreasing partial derivatives. We have also studied its dual S'(Rn</sup>) the space of tempered distributions. The last part aims to define a topological structure on an increasing union of Frechet spaces called inductive limit of Frechet spaces. We study in particular the space D(Ω) of functions of class C<sup>∞</sup> with compact supports on Ω as well as its dual D' (Ω) the space distributions over the open set Ω.展开更多
Some strong convergence theorems of explicit composite iteration scheme for nonexpansive semi-groups in the framework of Banach spaces are established. Results presented in the paper not only extend and improve the co...Some strong convergence theorems of explicit composite iteration scheme for nonexpansive semi-groups in the framework of Banach spaces are established. Results presented in the paper not only extend and improve the corresponding results of ShiojiTakahashi, Suzuki, Xu and Aleyner-Reich, but also give a partially affirmative answer to the open questions raised by Suzuki and Xu.展开更多
We theoretically investigate the application of the fringe-locking method（FLM） in the dual-species quantum test of the weak equivalence principle（WEP）.With the FLM,the measurement is performed invariably at the mi...We theoretically investigate the application of the fringe-locking method（FLM） in the dual-species quantum test of the weak equivalence principle（WEP）.With the FLM,the measurement is performed invariably at the midfringe,and the extraction of the phase shift for atom interferometers is linearized.For the simultaneous interferometers,this linearization enables a good common-mode rejection of vibration noise,which is usually the main limit for high precision WEP tests of the dual-species kind.We note that this method also allows for an unbiased determination of the gravity accelerations difference,which meanwhile is ready to be implemented.展开更多
谐振式光纤陀螺(R-FOG)是利基于光学Sagnac效应实现高精度的转动检测惯性传感器件。在R-FOG系统中,陀螺信号的处理占有非常重要的地位。根据R-FOG系统中,光纤环形谐振腔的谱线宽度高达几十MHz以及RFOG输出信号具有弱信号、大噪声特点。...谐振式光纤陀螺(R-FOG)是利基于光学Sagnac效应实现高精度的转动检测惯性传感器件。在R-FOG系统中,陀螺信号的处理占有非常重要的地位。根据R-FOG系统中,光纤环形谐振腔的谱线宽度高达几十MHz以及RFOG输出信号具有弱信号、大噪声特点。设计了一种用于提取被噪声淹没的微弱信号的双相位锁相放大器,优点在于不需要进行相位调整。在对双相位锁相放大器各部分电路进行具体设计和分析的基础上,完成了对整体电路的性能测试。测试结果表明,研制的锁相放大器在载波频率为900 k Hz时,将整个电路应用于R-FOG系统中,解调出的信号效果良好,可以实现锁频要求。展开更多
基金Supported by Research Fund of Kumoh National Institute of Technology,Korea
文摘In this paper, we introduce the signed weak gliding hump property in a dual pair with the structure of a system of sections and show that if a dual pair [E, F] has the signed weak gliding hump property, then the β-dual space of E is a weak sequentially complete space if and only if for every n ∈N,(F[n] ,σ(F[n] ,E[n] )) is sequentially complete. Furthermore, we also prove that if [E,F] has the signed weak gliding hump property, then (E,τ(E,E<β> )) is an AK- space.
基金Foundationitem:The NNSP(19971073) of China and the NSF of Yangzhou University
文摘In This paper, the concept of weakly dual ring is introduced, which is a proper generalization of the dual ring. If R is a right weakly dual ring, then (1) Z(RR) = J(R); (2) If R is also a zero-division power ring, then R is a right AP-injective ring. In addition, some properties of weakly dual rings are given.
文摘In this paper, we have studied the topology of some classical functional spaces. Among these spaces, there are standard spaces, spaces that can be metrizable and others that cannot be metrizable. But they are all topological vector spaces and it is in this context that we have chosen to present this work. We are interested in the topology of its spaces and in the topologies of their dual spaces. The first part, we presented the fundamental topological properties of topological vector spaces. The second part, we studied Frechet spaces and particularly the space S(R<sup>n</sup>) of functions of class C<sup>∞ </sup>on R<sup>n</sup> which are as well as all their rapidly decreasing partial derivatives. We have also studied its dual S'(Rn</sup>) the space of tempered distributions. The last part aims to define a topological structure on an increasing union of Frechet spaces called inductive limit of Frechet spaces. We study in particular the space D(Ω) of functions of class C<sup>∞</sup> with compact supports on Ω as well as its dual D' (Ω) the space distributions over the open set Ω.
基金Project supported by the Natural Science Foundation of Sichuan Province of China(No.2005A132)
文摘Some strong convergence theorems of explicit composite iteration scheme for nonexpansive semi-groups in the framework of Banach spaces are established. Results presented in the paper not only extend and improve the corresponding results of ShiojiTakahashi, Suzuki, Xu and Aleyner-Reich, but also give a partially affirmative answer to the open questions raised by Suzuki and Xu.
基金Project supported by the National Natural Science Foundation of China(Grant Nos.41127002,11574099,and 11474115)the National Basic Research Program of China(Grant No.2010CB832806)
文摘We theoretically investigate the application of the fringe-locking method（FLM） in the dual-species quantum test of the weak equivalence principle（WEP）.With the FLM,the measurement is performed invariably at the midfringe,and the extraction of the phase shift for atom interferometers is linearized.For the simultaneous interferometers,this linearization enables a good common-mode rejection of vibration noise,which is usually the main limit for high precision WEP tests of the dual-species kind.We note that this method also allows for an unbiased determination of the gravity accelerations difference,which meanwhile is ready to be implemented.
文摘谐振式光纤陀螺(R-FOG)是利基于光学Sagnac效应实现高精度的转动检测惯性传感器件。在R-FOG系统中,陀螺信号的处理占有非常重要的地位。根据R-FOG系统中,光纤环形谐振腔的谱线宽度高达几十MHz以及RFOG输出信号具有弱信号、大噪声特点。设计了一种用于提取被噪声淹没的微弱信号的双相位锁相放大器,优点在于不需要进行相位调整。在对双相位锁相放大器各部分电路进行具体设计和分析的基础上,完成了对整体电路的性能测试。测试结果表明,研制的锁相放大器在载波频率为900 k Hz时,将整个电路应用于R-FOG系统中,解调出的信号效果良好,可以实现锁频要求。
