This is a survey of results and open problems concerning the structure of periodic group with prescribed orders of their elements. In particular, an outline of a proof of the following recent result is given: every pe...This is a survey of results and open problems concerning the structure of periodic group with prescribed orders of their elements. In particular, an outline of a proof of the following recent result is given: every periodic group whose set of element orders coincides with {1,2,3,4,8} is locally finite.展开更多
The phase group synchronization between any signals is further revealed,which is based on proposing the new concepts of the greatest common factor frequency,the least common multiple period,quantized phase shift resol...The phase group synchronization between any signals is further revealed,which is based on proposing the new concepts of the greatest common factor frequency,the least common multiple period,quantized phase shift resolution,equivalent phase comparison frequency and so on.Then the problem of phase comparison and processing between different frequency signals is solved and shown in detail.Using the basic principle and the variation law of group phase difference,the frequency stability better than 10-14/s can be easily obtained in the time&frequency measurement and control domain,and experimental results also show the phase relations between atomic energy level transition signal and the locked crystal oscillator signal in an active hydrogen atomic clock are strict phase group synchronization,and locked precision with 10-13/s can be reached based on phase group synchronization.The phase group synchronization can provide technical support to frequency linking among radio frequency,microwave and light frequency.展开更多
基金supported by Russian Foundation of Basic Research (Grant Nos. 06-01-39001, 08-01-00322)the State Maintenance Program for the Leading Scientific Schools of the Russian Federation (Grant No. NSh–344.2008.1)+2 种基金Siberian Branch of RAS (complex integration project 2008.01.02)National Natural Science Foun-dation of China (Grant No. 10871032)the Specialized Research Fund for the Doctoral Program of Higher Education of China (Grant No. 20060285002)
文摘This is a survey of results and open problems concerning the structure of periodic group with prescribed orders of their elements. In particular, an outline of a proof of the following recent result is given: every periodic group whose set of element orders coincides with {1,2,3,4,8} is locally finite.
基金supported by the Joint Fund for Fostering Talents of National Natural Science Foundation of China and Henan Province(Grant No.U1304618)the Open Fund of Key Laboratory of Precision Navigation and Timing Technology of Chinese Academy of Sciences(Grant No.2012PNTT01)+4 种基金the Postdoctoral Grant of China(Grant Nos.2011M501446,2012T50798)the Basic and Advanced Technology Research Foundation of Henan Province(Grant No.122300410169)The Key Science and Technology Foundation of Zhengzhou City(Grant Nos.131PPTGG411-6,131PCXTD594)the Doctor Fund of Zhengzhou University of Light Industry(Grant No.2011BSJJ031)the Fundamental Research Funds for the Central Universities(Grant No.K5051204003)
文摘The phase group synchronization between any signals is further revealed,which is based on proposing the new concepts of the greatest common factor frequency,the least common multiple period,quantized phase shift resolution,equivalent phase comparison frequency and so on.Then the problem of phase comparison and processing between different frequency signals is solved and shown in detail.Using the basic principle and the variation law of group phase difference,the frequency stability better than 10-14/s can be easily obtained in the time&frequency measurement and control domain,and experimental results also show the phase relations between atomic energy level transition signal and the locked crystal oscillator signal in an active hydrogen atomic clock are strict phase group synchronization,and locked precision with 10-13/s can be reached based on phase group synchronization.The phase group synchronization can provide technical support to frequency linking among radio frequency,microwave and light frequency.
