Let R be an infinite ring with a maximal finite subring. We prove that R has a largest finite ideal and a largest finite nilpotent ideal N By a B ring, we mean an infinite ring with 1 containing a maximal finite subr...Let R be an infinite ring with a maximal finite subring. We prove that R has a largest finite ideal and a largest finite nilpotent ideal N By a B ring, we mean an infinite ring with 1 containing a maximal finite subring which is a subfield containing 1. It is shown that R/NUVW, where U is a finite ring, V is a finite direct sum of matrix rings over B rings, and W is a ring containing no nonzero finite subrings.展开更多
在文 [7]中 ,史福贵借助于 L - fuzzy关系引入了 L - fuzzy集间的 L - fuzzy映射的概念并借助于其水平截集给出了它的一些等价刻画但没有给出一个 L - fuzzy集的像与逆像的表示。本文的目的就是给出一个 L - fuzzy集的像与逆像的各种等...在文 [7]中 ,史福贵借助于 L - fuzzy关系引入了 L - fuzzy集间的 L - fuzzy映射的概念并借助于其水平截集给出了它的一些等价刻画但没有给出一个 L - fuzzy集的像与逆像的表示。本文的目的就是给出一个 L - fuzzy集的像与逆像的各种等价表示并给出了它们在 L - fuzzy代数中的几个简单应用。展开更多
We demonstrate a stable narrow linewidth single-frequency erbium-doped fiber laser(EDFL)operating at 1.6μm.A Fabry–Perot fiber Bragg grating and two cascaded subrings are incorporated in the main ring cavity to achi...We demonstrate a stable narrow linewidth single-frequency erbium-doped fiber laser(EDFL)operating at 1.6μm.A Fabry–Perot fiber Bragg grating and two cascaded subrings are incorporated in the main ring cavity to achieve singlefrequency operation.The experimentally measured optical signal-to-noise ratio is greater than 73 dB.Furthermore,the linewidth of the EDFL is measured to be about 480 Hz by the self-built short-delayed self-heterodyne interferometry device.The laser shows superior stability,with no mode-hopping during the 60-min observation period.The proposed EDFL provides a new experimental idea for realizing a single-frequency fiber laser in the L-band.展开更多
文摘Let R be an infinite ring with a maximal finite subring. We prove that R has a largest finite ideal and a largest finite nilpotent ideal N By a B ring, we mean an infinite ring with 1 containing a maximal finite subring which is a subfield containing 1. It is shown that R/NUVW, where U is a finite ring, V is a finite direct sum of matrix rings over B rings, and W is a ring containing no nonzero finite subrings.
文摘在文 [7]中 ,史福贵借助于 L - fuzzy关系引入了 L - fuzzy集间的 L - fuzzy映射的概念并借助于其水平截集给出了它的一些等价刻画但没有给出一个 L - fuzzy集的像与逆像的表示。本文的目的就是给出一个 L - fuzzy集的像与逆像的各种等价表示并给出了它们在 L - fuzzy代数中的几个简单应用。
基金supported by the Shaanxi Key Science and Technology Innovation Team Project(No.2023-CX-TD-06)。
文摘We demonstrate a stable narrow linewidth single-frequency erbium-doped fiber laser(EDFL)operating at 1.6μm.A Fabry–Perot fiber Bragg grating and two cascaded subrings are incorporated in the main ring cavity to achieve singlefrequency operation.The experimentally measured optical signal-to-noise ratio is greater than 73 dB.Furthermore,the linewidth of the EDFL is measured to be about 480 Hz by the self-built short-delayed self-heterodyne interferometry device.The laser shows superior stability,with no mode-hopping during the 60-min observation period.The proposed EDFL provides a new experimental idea for realizing a single-frequency fiber laser in the L-band.