We define the direct limit of the asymptotic direct system of C^(*)-algebras and give some properties of it.Finally,we prove that a C^(*)-algebra is a locally AF-algebra,if and only if it is the direct limit of an asy...We define the direct limit of the asymptotic direct system of C^(*)-algebras and give some properties of it.Finally,we prove that a C^(*)-algebra is a locally AF-algebra,if and only if it is the direct limit of an asymptotic direct system of finite-dimensional C^(*)-algebras.展开更多
Semenov-Tian-Shansky has given the solution of the modified classical Yang-Baxter equation, which was called the modified r-matrix. Relevant studies have been extensive in recent times. In this paper, we introduce the...Semenov-Tian-Shansky has given the solution of the modified classical Yang-Baxter equation, which was called the modified r-matrix. Relevant studies have been extensive in recent times. In this paper, we introduce the concept and representations of modified RotaBaxter Hom-Lie algebras. We develop a cohomology of modified Rota-Baxter Hom-Lie algebras with coefficients in a suitable representation. As applications, we study formal deformations and abelian extensions of modified Rota-Baxter Hom-Lie algebras in terms of second cohomology groups.展开更多
In DSP-based SerDes application,it is essential for AFE to implement a pre-ADC equalization to provide a better sig-nal for ADC and DSP.To meet the various equalization requirements of different channel and transmitte...In DSP-based SerDes application,it is essential for AFE to implement a pre-ADC equalization to provide a better sig-nal for ADC and DSP.To meet the various equalization requirements of different channel and transmitter configurations,this paper presents a 112 Gbps DSP-Based PAM4 SerDes receiver with a wide band equalization tuning AFE.The AFE is realized by implementing source degeneration transconductance,feedforward high-pass branch and inductive feedback peaking TIA.The AFE offers a flexible equalization gain tuning of up to 17.5 dB at Nyquist frequency without affecting the DC gain.With the pro-posed AFE,the receiver demonstrates eye opening after digital FIR equalization and achieves 6×10^(-9) BER with a 29.6 dB inser-tion loss channel.展开更多
In this paper,we show that an ideal generated by matching Rota-Baxter equations is a bideal of a Hopf algebra on decorated rooted forests.We then get a bialgebraic structure on the space of decorated rooted forests mo...In this paper,we show that an ideal generated by matching Rota-Baxter equations is a bideal of a Hopf algebra on decorated rooted forests.We then get a bialgebraic structure on the space of decorated rooted forests modulo this biideal.As an application,a connected graded bialgebra and so a graded Hopf algebra on matching Rota-Baxter algebras are constructed,which simplifies the Hopf algebraic structure proposed by[Pacific J.Math.,2022,317(2):441-475].展开更多
基金Supported by Natural Science Foundation of Jiangsu Province,China (No.BK20171421)。
文摘We define the direct limit of the asymptotic direct system of C^(*)-algebras and give some properties of it.Finally,we prove that a C^(*)-algebra is a locally AF-algebra,if and only if it is the direct limit of an asymptotic direct system of finite-dimensional C^(*)-algebras.
基金Supported by the Universities Key Laboratory of System Modeling and Data Mining in Guizhou Province(Grant No.2023013)the National Natural Science Foundation of China(Grant No.12161013)the Science and Technology Program of Guizhou Province(Grant No.ZK[2023]025)。
文摘Semenov-Tian-Shansky has given the solution of the modified classical Yang-Baxter equation, which was called the modified r-matrix. Relevant studies have been extensive in recent times. In this paper, we introduce the concept and representations of modified RotaBaxter Hom-Lie algebras. We develop a cohomology of modified Rota-Baxter Hom-Lie algebras with coefficients in a suitable representation. As applications, we study formal deformations and abelian extensions of modified Rota-Baxter Hom-Lie algebras in terms of second cohomology groups.
基金supported by National Key R&D Program of China No.2022YFB2803401.
文摘In DSP-based SerDes application,it is essential for AFE to implement a pre-ADC equalization to provide a better sig-nal for ADC and DSP.To meet the various equalization requirements of different channel and transmitter configurations,this paper presents a 112 Gbps DSP-Based PAM4 SerDes receiver with a wide band equalization tuning AFE.The AFE is realized by implementing source degeneration transconductance,feedforward high-pass branch and inductive feedback peaking TIA.The AFE offers a flexible equalization gain tuning of up to 17.5 dB at Nyquist frequency without affecting the DC gain.With the pro-posed AFE,the receiver demonstrates eye opening after digital FIR equalization and achieves 6×10^(-9) BER with a 29.6 dB inser-tion loss channel.
基金Supported by NSFC(No.12101316)Belt and Road Innovative Talents Exchange Foreign Experts project(No.DL2023014002L)。
文摘In this paper,we show that an ideal generated by matching Rota-Baxter equations is a bideal of a Hopf algebra on decorated rooted forests.We then get a bialgebraic structure on the space of decorated rooted forests modulo this biideal.As an application,a connected graded bialgebra and so a graded Hopf algebra on matching Rota-Baxter algebras are constructed,which simplifies the Hopf algebraic structure proposed by[Pacific J.Math.,2022,317(2):441-475].
