In the literature, the Bailey transform has many applications in basic hypergeometric series. In this paper, we derive many new transformation formulas for q-series by means of the Bailey transform. Meanwhile, We also...In the literature, the Bailey transform has many applications in basic hypergeometric series. In this paper, we derive many new transformation formulas for q-series by means of the Bailey transform. Meanwhile, We also obtain some new terminated identities. Furthermore, we establish a companion identity to the Rogers-Ramanujan identity labelled by number (23) on Slater’s list.展开更多
Let R be a ring such that all left semicentral idempotents are central and （S, ≤） a strictly totally ordered monoid satisfying that 0 ≤s for all s ∈S. It is shown that [[R^S≤]], the ring of generalized power ser...Let R be a ring such that all left semicentral idempotents are central and （S, ≤） a strictly totally ordered monoid satisfying that 0 ≤s for all s ∈S. It is shown that [[R^S≤]], the ring of generalized power series with coefficients in R and exponents in S, is right p.q.Baer if and only if R is right p.q.Baer and any S-indexed subset of I（R） has a generalized join in I（R）, where I（R） is the set of all idempotents of R.展开更多
在估计实际品质因子Q值时,因受频段选择、子波叠加、噪声干扰、非本征衰减等因素影响,容易导致Q值估计误差偏大。为此,提出基于不同阶次泰勒级数展开的含非本征衰减频域振幅比平均的Q值估计方法(Am-plitude ratio average in frequency ...在估计实际品质因子Q值时,因受频段选择、子波叠加、噪声干扰、非本征衰减等因素影响,容易导致Q值估计误差偏大。为此,提出基于不同阶次泰勒级数展开的含非本征衰减频域振幅比平均的Q值估计方法(Am-plitude ratio average in frequency domain,FARA法)。该算法首先利用参考频段内振幅比的连乘消除非本征衰减的影响;然后基于振幅因子在参考频点处的1~4阶泰勒级数展开表达式,推导适用于含非本征衰减地震记录的单频点Q值计算公式;其次,采用高、低频双参考频段结合方式削弱参考频段的影响;最后,采用主值频段内所有频点的平均化处理提高算法的稳定性。模型试验表明,采用高、低参考频段结合的模式可以显著提高所提方法的Q值估计精度,相对于对数谱面积双差值(LSADD)法,新方法受时差、时窗及噪声等因素的影响更小。实例应用表明,不同阶次的FARA法Q估计值的一致性较好,且整体大于LSADD法的Q估计值,与模型试验结果吻合,表明由新方法获得的Q值更可靠。展开更多
Let R be a ring and （S, 〈） be a strictly totally ordered monoid satisfying that 0 〈 s for all s C S. It is shown that if A is a weakly rigid homomorphism, then the skew generalized power series ring [[RS,-〈, λ]]...Let R be a ring and （S, 〈） be a strictly totally ordered monoid satisfying that 0 〈 s for all s C S. It is shown that if A is a weakly rigid homomorphism, then the skew generalized power series ring [[RS,-〈, λ]] is right p.q.-Baer if and only if R is right p.q.-Baer and any S-indexed subset of S,（R） has a generalized join in S,（R）. Several known results follow as consequences of our results.展开更多
文摘In the literature, the Bailey transform has many applications in basic hypergeometric series. In this paper, we derive many new transformation formulas for q-series by means of the Bailey transform. Meanwhile, We also obtain some new terminated identities. Furthermore, we establish a companion identity to the Rogers-Ramanujan identity labelled by number (23) on Slater’s list.
基金TRAPOYT(200280)the Cultivation Fund(704004)of the Key Scientific and Technical Innovation Project,Ministry of Education of China
文摘Let R be a ring such that all left semicentral idempotents are central and （S, ≤） a strictly totally ordered monoid satisfying that 0 ≤s for all s ∈S. It is shown that [[R^S≤]], the ring of generalized power series with coefficients in R and exponents in S, is right p.q.Baer if and only if R is right p.q.Baer and any S-indexed subset of I（R） has a generalized join in I（R）, where I（R） is the set of all idempotents of R.
文摘在估计实际品质因子Q值时,因受频段选择、子波叠加、噪声干扰、非本征衰减等因素影响,容易导致Q值估计误差偏大。为此,提出基于不同阶次泰勒级数展开的含非本征衰减频域振幅比平均的Q值估计方法(Am-plitude ratio average in frequency domain,FARA法)。该算法首先利用参考频段内振幅比的连乘消除非本征衰减的影响;然后基于振幅因子在参考频点处的1~4阶泰勒级数展开表达式,推导适用于含非本征衰减地震记录的单频点Q值计算公式;其次,采用高、低频双参考频段结合方式削弱参考频段的影响;最后,采用主值频段内所有频点的平均化处理提高算法的稳定性。模型试验表明,采用高、低参考频段结合的模式可以显著提高所提方法的Q值估计精度,相对于对数谱面积双差值(LSADD)法,新方法受时差、时窗及噪声等因素的影响更小。实例应用表明,不同阶次的FARA法Q估计值的一致性较好,且整体大于LSADD法的Q估计值,与模型试验结果吻合,表明由新方法获得的Q值更可靠。
基金The Youth Foundation(QN2012-14)of Hexi University
文摘Let R be a ring and （S, 〈） be a strictly totally ordered monoid satisfying that 0 〈 s for all s C S. It is shown that if A is a weakly rigid homomorphism, then the skew generalized power series ring [[RS,-〈, λ]] is right p.q.-Baer if and only if R is right p.q.-Baer and any S-indexed subset of S,（R） has a generalized join in S,（R）. Several known results follow as consequences of our results.
