Let H be a commutative, noetherian, semisimple and cosemisimple Hopf algebra with a bijective antipode over a field k. Then the semisimplicity of YD(H) is considered, where YD (H) means the disjoint union of the c...Let H be a commutative, noetherian, semisimple and cosemisimple Hopf algebra with a bijective antipode over a field k. Then the semisimplicity of YD(H) is considered, where YD (H) means the disjoint union of the category of generalized Yetter-Drinfeld modules nYD^H( α, β) for any α, β E Aut Hopf(H). First, the fact that YD(H) is closed under Mor is proved. Secondly, based on the properties of finitely generated projective modules and semisimplicity of H, YD(H) satisfies the exact condition. Thus each object in YD(H) can be decomposed into simple ones since H is noetherian and cosemisimple. Finally, it is proved that YD (H) is a sernisimple category.展开更多
A module Mis called generalized extending if for any submodule N of M, there is a direct summand K of M such that N≤K and KIN is singular. Any extending module and any singular module are generalized extending. Any h...A module Mis called generalized extending if for any submodule N of M, there is a direct summand K of M such that N≤K and KIN is singular. Any extending module and any singular module are generalized extending. Any homomorphic image of a generalized extending module is generalized extending. Any direct sum of a singular (uniform) module and a semi-simple module is generalized extending. A ring R is a right Co-H-ring if and only if all right R modules are generalized extending modules.展开更多
Let R be a commutative ring and (S, ≤) a strictly totally ordered monoid which satisfies the condition that 0 ≤ s for every s ∈ S. In this paper we show that if RM is a PS-module, then the module [[MS≤]] of genera...Let R be a commutative ring and (S, ≤) a strictly totally ordered monoid which satisfies the condition that 0 ≤ s for every s ∈ S. In this paper we show that if RM is a PS-module, then the module [[MS≤]] of generalized power series over M is a PS [[RS,≤]]-module.展开更多
This paper investigates the bit-interleaved coded generalized spatial modulation(BICGSM) with iterative decoding(BICGSM-ID) for multiple-input multiple-output(MIMO) visible light communications(VLC). In the BICGSM-ID ...This paper investigates the bit-interleaved coded generalized spatial modulation(BICGSM) with iterative decoding(BICGSM-ID) for multiple-input multiple-output(MIMO) visible light communications(VLC). In the BICGSM-ID scheme, the information bits conveyed by the signal-domain(SiD) symbols and the spatial-domain(SpD) light emitting diode(LED)-index patterns are coded by a protograph low-density parity-check(P-LDPC) code. Specifically, we propose a signal-domain symbol expanding and re-allocating(SSER) method for constructing a type of novel generalized spatial modulation(GSM) constellations, referred to as SSERGSM constellations, so as to boost the performance of the BICGSM-ID MIMO-VLC systems.Moreover, by applying a modified PEXIT(MPEXIT) algorithm, we further design a family of rate-compatible P-LDPC codes, referred to as enhanced accumulate-repeat-accumulate(EARA) codes,which possess both excellent decoding thresholds and linear-minimum-distance-growth property. Both analysis and simulation results illustrate that the proposed SSERGSM constellations and P-LDPC codes can remarkably improve the convergence and decoding performance of MIMO-VLC systems. Therefore, the proposed P-LDPC-coded SSERGSM-mapped BICGSMID configuration is envisioned as a promising transmission solution to satisfy the high-throughput requirement of MIMO-VLC applications.展开更多
Let HLB be the category of generalized Long modules, that is, H-modules and B-comodules over Hopf algebras B and H. We describe a new Turaev braided group category over generalized Long module HLB (S(π)) where th...Let HLB be the category of generalized Long modules, that is, H-modules and B-comodules over Hopf algebras B and H. We describe a new Turaev braided group category over generalized Long module HLB (S(π)) where the opposite group S(π) of the semidirect product of the opposite group πopof a group π by π. As an application, we show that this is a Turaev braided group-category HLBfor a quasitriangular Turaev group-coalgebra H and a coquasitriangular Turaev group-algebra B.展开更多
A hybrid control strategy has been designed and developed for the electro-hydraulic posi-tion servo control system with generalized Pulse code modulation (GPCM), which is suitable for the area where the work conditi...A hybrid control strategy has been designed and developed for the electro-hydraulic posi-tion servo control system with generalized Pulse code modulation (GPCM), which is suitable for the area where the work condition is poor and a large flow rate is required. It is difficult to control the GPCM system because the system is discrete. With consideration of the stability and speediness of the GPCM position servo control system, a control strategy is developed through the theoretical and ex-perimental analyses. The control strategy integrates the merits of Bang-Bang control, PID control and fuzzy control. With this hybrid control strategy, the electro hydraulic control system has good per-formances, and the servo control is carried out with GPCM through on-off valves.展开更多
Gray mapping is a well-known way to improve the performance of regular constellation modulation,but it is challenging to be applied directly for irregular alternative.To address this issue,in this paper,a unified bit-...Gray mapping is a well-known way to improve the performance of regular constellation modulation,but it is challenging to be applied directly for irregular alternative.To address this issue,in this paper,a unified bit-to-symbol mapping method is designed for generalized constellation modulation(i.e.,regular and irregular shaping).The objective of the proposed approach is to minimize the average bit error probability by reducing the hamming distance(HD)of symbols with larger values of pairwise error probability.Simulation results show that the conventional constellation modulation(i.e.,phase shift keying and quadrature amplitude modulation(QAM)with the proposed mapping rule yield the same performance as that of classical gray mapping.Moreover,the recently developed golden angle modulation(GAM)with the proposed mapping method is capable of providing around1 d B gain over the conventional mapping counterpart and offers comparable performance to QAM with Gray mapping.展开更多
Let g be a classical complex simple Lie algebra and q be a parabolic subalgebra.Let M be a generalized Verma module induced from a one dimensional representation of q.Such M is called a scalar generalized Verma module...Let g be a classical complex simple Lie algebra and q be a parabolic subalgebra.Let M be a generalized Verma module induced from a one dimensional representation of q.Such M is called a scalar generalized Verma module.In this paper,we will determine the reducibility of scalar generalized Verma modules associated to maximal parabolic subalgebras by computing explicitly the Gelfand-Kirillov dimension of the corresponding highest weight modules.展开更多
In this paper we obtain a Douglas type factor decomposition theorem about certain important bounded module maps. Thus, we come to the discussion of the topological continuity of bounded generalized inverse module maps...In this paper we obtain a Douglas type factor decomposition theorem about certain important bounded module maps. Thus, we come to the discussion of the topological continuity of bounded generalized inverse module maps. Let X be a topological space, x →Tx : X→L(E) be a continuous map, and each R(Tx) be a closed submodule in E, for every fixed x C X. Then the map x→ Tx^+: X→L(E) is continuous if and only if ||Tx^+|| is locally bounded, where Tx^+ is the bounded generalized inverse module map of Tx. Furthermore, this is equivalent to the following statement: For each x0 in X, there exists a neighborhood ∪0 at x0 and a positive number λ such that (0, λ^2)lohtatn in ∩x∈∪0C/σ(Tx^+Tx), where a(T) denotes the spectrum of operator T.展开更多
Pre-coding aided quadrature spatial modulation(PQSM) is a promising multiple input multiple output(MIMO) transmission technology. The multiuser(MU) detection in PQSM system is investigated in this paper. Based on the ...Pre-coding aided quadrature spatial modulation(PQSM) is a promising multiple input multiple output(MIMO) transmission technology. The multiuser(MU) detection in PQSM system is investigated in this paper. Based on the known channel state information, pre-coding matrix is designed to pre-process the in-phase and quadrature signals of quadrature spatial modulation(QSM) to reduce the inter-channel interference. In order to lower the complexity at the receiver brought by the orthogonality of the PQSM system, an orthogonal matching pursuit(OMP) detection algorithm and a reconstructed model are proposed. The analysis and simulation results show that the proposed algorithm can obtain a similar bit error rate(BER) performance as the maximum likelihood(ML) detection algorithm with more than 80% reduction of complexity.展开更多
This paper is motivated by S. Park [10] in which the injective cover of left R[x]- module M[x? ] of inverse polynomials over a left R-module M was discussed. The 1 author considers the ?-covers of modules and shows th...This paper is motivated by S. Park [10] in which the injective cover of left R[x]- module M[x? ] of inverse polynomials over a left R-module M was discussed. The 1 author considers the ?-covers of modules and shows that if η : P ?→ M is an ?- cover of M, then [ηS, ] : [PS, ] ?→ [MS, ] is an [?S, ]-cover of left [[RS, ]]-module ≤ ≤ ≤ ≤ ≤ [MS, ], where ? is a class of left R-modules and [MS, ] is the left [[RS, ]]-module of ≤ ≤ ≤ generalized inverse polynomials over a left R-module M. Also some properties of the injective cover of left [[RS, ]]-module [MS, ] are discussed. ≤展开更多
In this paper,a powerful model-driven deep learning framework is exploited to overcome the challenge of multi-domain signal detection in spacedomain index modulation(SDIM)based multiple input multiple output(MIMO)syst...In this paper,a powerful model-driven deep learning framework is exploited to overcome the challenge of multi-domain signal detection in spacedomain index modulation(SDIM)based multiple input multiple output(MIMO)systems.Specifically,we use orthogonal approximate message passing(OAMP)technique to develop OAMPNet,which is a novel signal recovery mechanism in the field of compressed sensing that effectively uses the sparse property from the training SDIM samples.For OAMPNet,the prior probability of the transmit signal has a significant impact on the obtainable performance.For this reason,in our design,we first derive the prior probability of transmitting signals on each antenna for SDIMMIMO systems,which is different from the conventional massive MIMO systems.Then,for massive MIMO scenarios,we propose two novel algorithms to avoid pre-storing all active antenna combinations,thus considerably improving the memory efficiency and reducing the related overhead.Our simulation results show that the proposed framework outperforms the conventional optimization-driven based detection algorithms and has strong robustness under different antenna scales.展开更多
In this paper, we study the closeness of strongly (∞)-hopfian properties under some constructions such as the ring of Morita context, direct products, triangular matrix, fraction ring etc. Also, we prove that if M[...In this paper, we study the closeness of strongly (∞)-hopfian properties under some constructions such as the ring of Morita context, direct products, triangular matrix, fraction ring etc. Also, we prove that if M[X] is strongly hopfian (resp. strongly co-hopfian) in R[X]-Mod, then M is strongly hopfian (resp. strongly co-hopfian) in R-Mod.展开更多
Let (S,≤) be a strictly totally ordered monoid which is also artinian, and R a right noetherian ring. Assume that M is a finitely generated right R-module and N is a left Rmodule. Denote by [[MS,≤]] and [NS,≤] the ...Let (S,≤) be a strictly totally ordered monoid which is also artinian, and R a right noetherian ring. Assume that M is a finitely generated right R-module and N is a left Rmodule. Denote by [[MS,≤]] and [NS,≤] the module of generalized power series over M, and the generalized Macaulay-Northcott module over N, respectively. Then we show that there exists an isomorphism of Abelian groups:Tori[[ RS,≤]]([[MS,≤]],[NS,≤])≌ s∈S ToriR (M,N).展开更多
For a ring R and a strictly totally ordered monoid(S,≤),letω:S→End(R)be a monoid homomorphism and M an(S,ω)-weakly rigid right R-module(i.e.,for any elements m∈M,b∈R and s∈S,mRb=0 if and only if mω(s)(Rb)=0),w...For a ring R and a strictly totally ordered monoid(S,≤),letω:S→End(R)be a monoid homomorphism and M an(S,ω)-weakly rigid right R-module(i.e.,for any elements m∈M,b∈R and s∈S,mRb=0 if and only if mω(s)(Rb)=0),where End(R)is the ring of ring endomorphisms of R.It is shown that the skew generalized power series module M[[S]]_(R[[S,ω]])is a principally quasi-Baer module if and only if the annihilator of every submodule generated by an S-indexed subset of M is generated by an idempotent as a right ideal of R.As a consequence we deduce that for an(S,ω)-weakly rigid ring R,the skew generalized power series ring R[[S,ω]]is right principally quasi-Baer if and only if R is right principally quasi-Baer and any S-indexed subset of right semicentral idempotents in R has a generalized S-indexed join in R.The range of previous results in this area is expanded by these results.展开更多
In recent years,the conventional degrees of freedom in frequency and time have been fully used.It is difficult to further improve the performance of communication systems with such degrees of freedom.Orbital angular m...In recent years,the conventional degrees of freedom in frequency and time have been fully used.It is difficult to further improve the performance of communication systems with such degrees of freedom.Orbital angular momentum(OAM),which provides a new degree of freedom for millimeter-wave(mmWave)wireless communication systems,has been recognized as a key enabling technique for future mobile communication networks.By combining OAM beams that have theoretically infinite and mutually orthogonal states with the generalized spatial modulation(GSM)strategy,a new OAM-GSM mmWave wireless communication system is designed in this paper.A bit error rate(BER)model of the OAM-GSM system is established based on channel flip precoding.The channel capacity,energy efficiency,and BER of the proposed OAM-GSM mmWave wireless communication system are simulated.Numerical results show that,compared with traditional GSM systems,the OAM-GSM system has more complex transmission and reception mechanisms but the channel capacity and maximum achievable energy efficiency are increased by 80%and 54%,respectively,and the BER drops by 91.5%.展开更多
A novel monolithic digitalized random carrier frequency modulation spread-spectrum clock generator (RCF-SSCG) is proposed.In this design,the output frequency of the proposed RCF-SSCG changes with the intensity of th...A novel monolithic digitalized random carrier frequency modulation spread-spectrum clock generator (RCF-SSCG) is proposed.In this design,the output frequency of the proposed RCF-SSCG changes with the intensity of the capacitive charge and discharge current.Its analytical model is induced and the effect of the modulation parameters on the spread spectrum is numerically simulated and discussed.Compared with other works,this design has the advantages of small size,low power consumption and good robustness.The circuit has been fabricated in a 0.5μm CMOS process and applied to a class D amplifier in which the proposed RCF-SSCG occupies an area of 0.112 mm^2 and consumes 9 mW.The experimental results confirm the theoretical analyses.展开更多
We propose and demonstrate a simplified and tunable frequency interval optical frequency comb(OFC) generator based on a dual-drive Mach-Zehnder modulator(DD-MZM) using a single continuous-wave(CW) laser and low-power ...We propose and demonstrate a simplified and tunable frequency interval optical frequency comb(OFC) generator based on a dual-drive Mach-Zehnder modulator(DD-MZM) using a single continuous-wave(CW) laser and low-power radio frequency(RF) driven signal. A mathematical model for the scheme is established. The 21-and 29-mode OFCs with frequency interval ranging from 6 GHz to 40 GHz are obtained under DD-MZM driven by a low-power RF signal within a maximum bandwidth of 1.12 THz. The generated OFCs exhibit spectral flatnesses of less than 0.5 d B and 0.8 d B within bandwidths of 160 GHz and 400 GHz, respectively.展开更多
基金The National Natural Science Foundation of China(No.11371088)the Fundamental Research Funds for the Central Universities(No.3207013906)the Natural Science Foundation of Jiangsu Province(No.BK2012736)
文摘Let H be a commutative, noetherian, semisimple and cosemisimple Hopf algebra with a bijective antipode over a field k. Then the semisimplicity of YD(H) is considered, where YD (H) means the disjoint union of the category of generalized Yetter-Drinfeld modules nYD^H( α, β) for any α, β E Aut Hopf(H). First, the fact that YD(H) is closed under Mor is proved. Secondly, based on the properties of finitely generated projective modules and semisimplicity of H, YD(H) satisfies the exact condition. Thus each object in YD(H) can be decomposed into simple ones since H is noetherian and cosemisimple. Finally, it is proved that YD (H) is a sernisimple category.
基金Project (No. 102028) supported by the Natural Science Foundation of Zhejiang Province, China
文摘A module Mis called generalized extending if for any submodule N of M, there is a direct summand K of M such that N≤K and KIN is singular. Any extending module and any singular module are generalized extending. Any homomorphic image of a generalized extending module is generalized extending. Any direct sum of a singular (uniform) module and a semi-simple module is generalized extending. A ring R is a right Co-H-ring if and only if all right R modules are generalized extending modules.
基金The NNSF (10171082) of China and the Teaching and Research Award Program for Outstanding Young Teachers in Higher Education Institutions of MOE, P.R.C.
文摘Let R be a commutative ring and (S, ≤) a strictly totally ordered monoid which satisfies the condition that 0 ≤ s for every s ∈ S. In this paper we show that if RM is a PS-module, then the module [[MS≤]] of generalized power series over M is a PS [[RS,≤]]-module.
基金supported in part by the NSF of China under Grant 62322106,62071131the Guangdong Basic and Applied Basic Research Foundation under Grant 2022B1515020086+2 种基金the International Collaborative Research Program of Guangdong Science and Technology Department under Grant 2022A0505050070in part by the Open Research Fund of the State Key Laboratory of Integrated Services Networks under Grant ISN22-23the National Research Foundation,Singapore University of Technology Design under its Future Communications Research&Development Programme“Advanced Error Control Coding for 6G URLLC and mMTC”Grant No.FCP-NTU-RG-2022-020.
文摘This paper investigates the bit-interleaved coded generalized spatial modulation(BICGSM) with iterative decoding(BICGSM-ID) for multiple-input multiple-output(MIMO) visible light communications(VLC). In the BICGSM-ID scheme, the information bits conveyed by the signal-domain(SiD) symbols and the spatial-domain(SpD) light emitting diode(LED)-index patterns are coded by a protograph low-density parity-check(P-LDPC) code. Specifically, we propose a signal-domain symbol expanding and re-allocating(SSER) method for constructing a type of novel generalized spatial modulation(GSM) constellations, referred to as SSERGSM constellations, so as to boost the performance of the BICGSM-ID MIMO-VLC systems.Moreover, by applying a modified PEXIT(MPEXIT) algorithm, we further design a family of rate-compatible P-LDPC codes, referred to as enhanced accumulate-repeat-accumulate(EARA) codes,which possess both excellent decoding thresholds and linear-minimum-distance-growth property. Both analysis and simulation results illustrate that the proposed SSERGSM constellations and P-LDPC codes can remarkably improve the convergence and decoding performance of MIMO-VLC systems. Therefore, the proposed P-LDPC-coded SSERGSM-mapped BICGSMID configuration is envisioned as a promising transmission solution to satisfy the high-throughput requirement of MIMO-VLC applications.
基金The NSF (11101128) of Chinathe NSF (102300410049) of Henan Provincethe NSF (BK2012736) of Jiangsu Province
文摘Let HLB be the category of generalized Long modules, that is, H-modules and B-comodules over Hopf algebras B and H. We describe a new Turaev braided group category over generalized Long module HLB (S(π)) where the opposite group S(π) of the semidirect product of the opposite group πopof a group π by π. As an application, we show that this is a Turaev braided group-category HLBfor a quasitriangular Turaev group-coalgebra H and a coquasitriangular Turaev group-algebra B.
文摘A hybrid control strategy has been designed and developed for the electro-hydraulic posi-tion servo control system with generalized Pulse code modulation (GPCM), which is suitable for the area where the work condition is poor and a large flow rate is required. It is difficult to control the GPCM system because the system is discrete. With consideration of the stability and speediness of the GPCM position servo control system, a control strategy is developed through the theoretical and ex-perimental analyses. The control strategy integrates the merits of Bang-Bang control, PID control and fuzzy control. With this hybrid control strategy, the electro hydraulic control system has good per-formances, and the servo control is carried out with GPCM through on-off valves.
基金supported in part by the National Key Research and Development Program of China under Grant 2021YFB2900502in part by the National Science Foundation of China under Grant 62001179in part by the Fundamental Research Funds for the Central Universities under Grant 2020kfy XJJS111。
文摘Gray mapping is a well-known way to improve the performance of regular constellation modulation,but it is challenging to be applied directly for irregular alternative.To address this issue,in this paper,a unified bit-to-symbol mapping method is designed for generalized constellation modulation(i.e.,regular and irregular shaping).The objective of the proposed approach is to minimize the average bit error probability by reducing the hamming distance(HD)of symbols with larger values of pairwise error probability.Simulation results show that the conventional constellation modulation(i.e.,phase shift keying and quadrature amplitude modulation(QAM)with the proposed mapping rule yield the same performance as that of classical gray mapping.Moreover,the recently developed golden angle modulation(GAM)with the proposed mapping method is capable of providing around1 d B gain over the conventional mapping counterpart and offers comparable performance to QAM with Gray mapping.
基金Supported by the National Science Foundation of China(Grant No.12171344)the National Key R&D Program of China(Grant Nos.2018YFA0701700 and 2018YFA0701701)。
文摘Let g be a classical complex simple Lie algebra and q be a parabolic subalgebra.Let M be a generalized Verma module induced from a one dimensional representation of q.Such M is called a scalar generalized Verma module.In this paper,we will determine the reducibility of scalar generalized Verma modules associated to maximal parabolic subalgebras by computing explicitly the Gelfand-Kirillov dimension of the corresponding highest weight modules.
基金Project supported by NSF of China"Maximal regularity for vector-valued boundary problems"(10571099)NSF of China(10571003)
文摘In this paper we obtain a Douglas type factor decomposition theorem about certain important bounded module maps. Thus, we come to the discussion of the topological continuity of bounded generalized inverse module maps. Let X be a topological space, x →Tx : X→L(E) be a continuous map, and each R(Tx) be a closed submodule in E, for every fixed x C X. Then the map x→ Tx^+: X→L(E) is continuous if and only if ||Tx^+|| is locally bounded, where Tx^+ is the bounded generalized inverse module map of Tx. Furthermore, this is equivalent to the following statement: For each x0 in X, there exists a neighborhood ∪0 at x0 and a positive number λ such that (0, λ^2)lohtatn in ∩x∈∪0C/σ(Tx^+Tx), where a(T) denotes the spectrum of operator T.
基金partially supported by the National Natural Science Foundation of China (Grant No. 61701063)Scientific and Technological Research Program of Chongqing Municipal Education Commission (No. KJ1600435)
文摘Pre-coding aided quadrature spatial modulation(PQSM) is a promising multiple input multiple output(MIMO) transmission technology. The multiuser(MU) detection in PQSM system is investigated in this paper. Based on the known channel state information, pre-coding matrix is designed to pre-process the in-phase and quadrature signals of quadrature spatial modulation(QSM) to reduce the inter-channel interference. In order to lower the complexity at the receiver brought by the orthogonality of the PQSM system, an orthogonal matching pursuit(OMP) detection algorithm and a reconstructed model are proposed. The analysis and simulation results show that the proposed algorithm can obtain a similar bit error rate(BER) performance as the maximum likelihood(ML) detection algorithm with more than 80% reduction of complexity.
基金the National Natural Science Foundation of China (No.10171082) the Teaching and Research Award Program for Outstanding Young Teachers in Higher Education Institutions of the Ministry of Education of China and NWNU-KJCXGC212.
文摘This paper is motivated by S. Park [10] in which the injective cover of left R[x]- module M[x? ] of inverse polynomials over a left R-module M was discussed. The 1 author considers the ?-covers of modules and shows that if η : P ?→ M is an ?- cover of M, then [ηS, ] : [PS, ] ?→ [MS, ] is an [?S, ]-cover of left [[RS, ]]-module ≤ ≤ ≤ ≤ ≤ [MS, ], where ? is a class of left R-modules and [MS, ] is the left [[RS, ]]-module of ≤ ≤ ≤ generalized inverse polynomials over a left R-module M. Also some properties of the injective cover of left [[RS, ]]-module [MS, ] are discussed. ≤
基金supported by the National Natural Science Foundation of China under Grant U19B2014the Sichuan Science and Technology Program under Grant 2023NSFSC0457the Fundamental Research Funds for the Central Universities under Grant 2242022k60006.
文摘In this paper,a powerful model-driven deep learning framework is exploited to overcome the challenge of multi-domain signal detection in spacedomain index modulation(SDIM)based multiple input multiple output(MIMO)systems.Specifically,we use orthogonal approximate message passing(OAMP)technique to develop OAMPNet,which is a novel signal recovery mechanism in the field of compressed sensing that effectively uses the sparse property from the training SDIM samples.For OAMPNet,the prior probability of the transmit signal has a significant impact on the obtainable performance.For this reason,in our design,we first derive the prior probability of transmitting signals on each antenna for SDIMMIMO systems,which is different from the conventional massive MIMO systems.Then,for massive MIMO scenarios,we propose two novel algorithms to avoid pre-storing all active antenna combinations,thus considerably improving the memory efficiency and reducing the related overhead.Our simulation results show that the proposed framework outperforms the conventional optimization-driven based detection algorithms and has strong robustness under different antenna scales.
基金Supported by National Natural Science Foundation of China (Grant No. 10961021)
文摘In this paper, we study the closeness of strongly (∞)-hopfian properties under some constructions such as the ring of Morita context, direct products, triangular matrix, fraction ring etc. Also, we prove that if M[X] is strongly hopfian (resp. strongly co-hopfian) in R[X]-Mod, then M is strongly hopfian (resp. strongly co-hopfian) in R-Mod.
基金the National Natural Science Foundation of China (No.10961021)the Teaching and Research Award Program for Outsanding Young Teachers in Higher Education Institutions of Ministry of Education(No.NCET-02-080)
文摘Let (S,≤) be a strictly totally ordered monoid which is also artinian, and R a right noetherian ring. Assume that M is a finitely generated right R-module and N is a left Rmodule. Denote by [[MS,≤]] and [NS,≤] the module of generalized power series over M, and the generalized Macaulay-Northcott module over N, respectively. Then we show that there exists an isomorphism of Abelian groups:Tori[[ RS,≤]]([[MS,≤]],[NS,≤])≌ s∈S ToriR (M,N).
文摘For a ring R and a strictly totally ordered monoid(S,≤),letω:S→End(R)be a monoid homomorphism and M an(S,ω)-weakly rigid right R-module(i.e.,for any elements m∈M,b∈R and s∈S,mRb=0 if and only if mω(s)(Rb)=0),where End(R)is the ring of ring endomorphisms of R.It is shown that the skew generalized power series module M[[S]]_(R[[S,ω]])is a principally quasi-Baer module if and only if the annihilator of every submodule generated by an S-indexed subset of M is generated by an idempotent as a right ideal of R.As a consequence we deduce that for an(S,ω)-weakly rigid ring R,the skew generalized power series ring R[[S,ω]]is right principally quasi-Baer if and only if R is right principally quasi-Baer and any S-indexed subset of right semicentral idempotents in R has a generalized S-indexed join in R.The range of previous results in this area is expanded by these results.
基金Project supported by the National Natural Science Foundation of China(No.U2001210)。
文摘In recent years,the conventional degrees of freedom in frequency and time have been fully used.It is difficult to further improve the performance of communication systems with such degrees of freedom.Orbital angular momentum(OAM),which provides a new degree of freedom for millimeter-wave(mmWave)wireless communication systems,has been recognized as a key enabling technique for future mobile communication networks.By combining OAM beams that have theoretically infinite and mutually orthogonal states with the generalized spatial modulation(GSM)strategy,a new OAM-GSM mmWave wireless communication system is designed in this paper.A bit error rate(BER)model of the OAM-GSM system is established based on channel flip precoding.The channel capacity,energy efficiency,and BER of the proposed OAM-GSM mmWave wireless communication system are simulated.Numerical results show that,compared with traditional GSM systems,the OAM-GSM system has more complex transmission and reception mechanisms but the channel capacity and maximum achievable energy efficiency are increased by 80%and 54%,respectively,and the BER drops by 91.5%.
基金Project supported by the National Natural Science Foundation of China(No.60436030).
文摘A novel monolithic digitalized random carrier frequency modulation spread-spectrum clock generator (RCF-SSCG) is proposed.In this design,the output frequency of the proposed RCF-SSCG changes with the intensity of the capacitive charge and discharge current.Its analytical model is induced and the effect of the modulation parameters on the spread spectrum is numerically simulated and discussed.Compared with other works,this design has the advantages of small size,low power consumption and good robustness.The circuit has been fabricated in a 0.5μm CMOS process and applied to a class D amplifier in which the proposed RCF-SSCG occupies an area of 0.112 mm^2 and consumes 9 mW.The experimental results confirm the theoretical analyses.
基金supported by the National Natural Science Foundation of China(No.61571251)the Public Technical Application Research Project of Zhejiang(No.2015C34004)+2 种基金the Discipline Open Fund Project of Zhejiang(No.xkxl1534)the National Education Research of Information Technology(No.146232081)the K.C.Wong Magna Fund in Ningbo University
文摘We propose and demonstrate a simplified and tunable frequency interval optical frequency comb(OFC) generator based on a dual-drive Mach-Zehnder modulator(DD-MZM) using a single continuous-wave(CW) laser and low-power radio frequency(RF) driven signal. A mathematical model for the scheme is established. The 21-and 29-mode OFCs with frequency interval ranging from 6 GHz to 40 GHz are obtained under DD-MZM driven by a low-power RF signal within a maximum bandwidth of 1.12 THz. The generated OFCs exhibit spectral flatnesses of less than 0.5 d B and 0.8 d B within bandwidths of 160 GHz and 400 GHz, respectively.