We study critical behaviors of the reduced fidelity susceptibility for two neighboring sites in the onedimensional transverse field Ising model. It is found that the divergent behaviors of the susceptibility take the ...We study critical behaviors of the reduced fidelity susceptibility for two neighboring sites in the onedimensional transverse field Ising model. It is found that the divergent behaviors of the susceptibility take the form of square of logarithm, in contrast with the global ground-state fidelity susceptibility which is power divergence. In order to perform a scaling analysis, we take the square root of the susceptibility and determine the scaling exponent analytically and the result is further confirmed by numerical calculations.展开更多
Based on the absolute and relative gravity observations in North China from 2009 to 2014,spatial dynamic variations of the regional gravity field are obtained. We employed the Euler deconvolution method and the theore...Based on the absolute and relative gravity observations in North China from 2009 to 2014,spatial dynamic variations of the regional gravity field are obtained. We employed the Euler deconvolution method and the theoretical model to get the best estimates of parameters. Gravity field change caused by the depth and distribution in North China is calculated by back analysis. The results show the structural index that equals 1 is suitable for inversion of the gravity variation data. The inversion results indicate that the depths of anomaly field sources are spread over the Hetao fault. The research method of this paper can be used in the quantitative study on the field source and may shed new light on the interpretations of gravity change, and also provide quantitative basis for earthquake prediction index criterions based on the gravity change.展开更多
In 2002, Faugere presented the famous F5 algorithm for computing GrSbner basis where two cri- teria, syzygy criterion and rewritten criterion, were proposed to avoid redundant computations. He proved the correctness o...In 2002, Faugere presented the famous F5 algorithm for computing GrSbner basis where two cri- teria, syzygy criterion and rewritten criterion, were proposed to avoid redundant computations. He proved the correctness of the syzygy criterion, but the proof for the correctness of the rewritten criterion was left. Since then, F5 has been studied extensively. Some proofs for the correctness of F5 were proposed, but these proofs are valid only under some extra assumptions. In this paper, we give a proof for the correctness of F5B, an equivalent version of F5 in Buchberger＇s style. The proof is valid for both homogeneous and non-homogeneous polynomial systems. Since this proof does not depend on the computing order of the S-pairs, any strategy of selecting S-pairs could be used in F5B or F5. Furthermore, we propose a natural and non-incremental variant of F5 where two revised criteria can be used to remove almost all redundant S-pairs.展开更多
基金Supported by National Natural Science Foundation of China under Grant Nos. 10874151 and 10935010National Fundamental Research Program of China under Grant No. 2006CB921205+1 种基金Program for New Century Excellent Talents in University (NCET)Science Foundation of Chinese University
文摘We study critical behaviors of the reduced fidelity susceptibility for two neighboring sites in the onedimensional transverse field Ising model. It is found that the divergent behaviors of the susceptibility take the form of square of logarithm, in contrast with the global ground-state fidelity susceptibility which is power divergence. In order to perform a scaling analysis, we take the square root of the susceptibility and determine the scaling exponent analytically and the result is further confirmed by numerical calculations.
基金funded by the Natural Science Foundation of China(61627824,41274083)the Youth Foundation of Earthquake Prediction(2017010227)
文摘Based on the absolute and relative gravity observations in North China from 2009 to 2014,spatial dynamic variations of the regional gravity field are obtained. We employed the Euler deconvolution method and the theoretical model to get the best estimates of parameters. Gravity field change caused by the depth and distribution in North China is calculated by back analysis. The results show the structural index that equals 1 is suitable for inversion of the gravity variation data. The inversion results indicate that the depths of anomaly field sources are spread over the Hetao fault. The research method of this paper can be used in the quantitative study on the field source and may shed new light on the interpretations of gravity change, and also provide quantitative basis for earthquake prediction index criterions based on the gravity change.
基金supported by National Key Basic Research Project of China (Grant No.2011CB302400)National Natural Science Foundation of China (Grant Nos. 10971217 and 61121062)
文摘In 2002, Faugere presented the famous F5 algorithm for computing GrSbner basis where two cri- teria, syzygy criterion and rewritten criterion, were proposed to avoid redundant computations. He proved the correctness of the syzygy criterion, but the proof for the correctness of the rewritten criterion was left. Since then, F5 has been studied extensively. Some proofs for the correctness of F5 were proposed, but these proofs are valid only under some extra assumptions. In this paper, we give a proof for the correctness of F5B, an equivalent version of F5 in Buchberger＇s style. The proof is valid for both homogeneous and non-homogeneous polynomial systems. Since this proof does not depend on the computing order of the S-pairs, any strategy of selecting S-pairs could be used in F5B or F5. Furthermore, we propose a natural and non-incremental variant of F5 where two revised criteria can be used to remove almost all redundant S-pairs.
